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William Herschel and the “Front-View” Telescopes

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The Scientific Legacy of William Herschel

Part of the book series: Historical & Cultural Astronomy ((HCA))

Abstract

William Herschel is rightly regarded as one of the greatest telescope makers in history. His instruments vastly exceeded in aperture and light-gathering power all those that came before his time, and established the reflecting telescope as a formidable instrument of astronomical research. To understand his research successes – and the limits of his success – we must understand the performance of his telescopes.

The present chapter attempts a comprehensive evaluation of the optical performance of Herschel’s telescopes. This is possible because of the vast documentation he left behind relating to his building and usage of telescopes, and also because a substantial number of his surviving mirrors have been tested using modern methods. After an introduction the chapter proceeds with a review of how the reflecting telescope developed before Herschel, and a consideration of engineering and materials problems in building reflectors. It then turns to optical matters, considering the types of imaging errors (aberrations) found particularly in Newtonian telescopes, the design form favored by Herschel. Further on the chapter considers how the theory of those errors (aberration theory) developed before Herschel and into the nineteenth century. Study of the forms of aberration and the history of aberration theory is necessary for understanding what optical errors Herschel saw in his telescopes, and what he could know – or not know – about them.

Following this we consider Herschel’s methods of fabrication and optical testing, in particular concentrating on the small elliptical flat mirrors (“secondaries” or “diagonals”) that are a critical part of any Newtonian telescope, even today. These petite mirrors form a relatively neglected area of study compared to Herschel’s more physically imposing primary mirrors, which have often been tested optically. It is ironic, therefore, that these small mirrors, precisely because they are used at a 45° tilt, called “oblique incidence” – versus the primaries used at “normal incidence” – have the potential to affect the final telescopic image just as gravely as the primaries, unless they are rigorously flat. Yet before the late nineteenth century there was no accurate method of assessing the surface profile of flat mirrors. The question, therfore, arises: How could Herschel make optically usable diagonal mirrors for Newtonian telescopes? The analysis and solution of this question forms one of the most important results of the present chapter. The upshot is that because Herschel (and other eighteenth-century telescope makers) could not make accurate flat mirrors – or any usable diagonal mirrors of large dimension – Herschel turned to the so-called “front-view,” or “Herschelian,” telescope for his largest instruments.

With all this as background, the next sections present a detailed discussion of the performance of eighteenth and early nineteenth-century Newtonian telescopes, and a similar consideration of “front-views.” Attention is also devoted throughout the chapter to explaining how Lord Rosse’s giant Newtonian telescopes of the mid-nineteenth century consituted a dramatic improvement on what came before and paved the way for the final triumph of the reflecting telescope over the refracting in astronomical research at the beginning of the twentieth century.

The final section of the chapter discusses the protracted cover-up and controversy surrounding the failure of Herschel’s most famous telescope, his so-called 40-ft front-view – by far the most massive telescope constructed before the mid-nineteenth century – containing a 48-in. diameter mirror. The cover-up of this monumentally expensive failure ultimately ricocheted onto William Herschel’s son, John, who became embroiled in an acrimonious exchange of letters in the 1840s with Thomas Romney Robinson, director of the Armagh Observatory and ardent admirer of Lord Rosse’s grand achievements. Robinson emerged from the exchange victorious, but John, the dutiful son, although scathed, appeared the nobler figure. The tragic clash between these great men closes out the chapter.

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Notes

  1. 1.

    RAS MS Herschel W.2/3.6, sweep 600 (memorandum). Cf. also Bennett, J.A., “‘On the power of penetrating into space’: the telescopes of William Herschel,” JHA, vii (1976), 75–108, p. 85.

  2. 2.

    Herschel, W., “Catalogue of one thousand new nebulae and clusters of stars,” PT, lxxvi (1786), 457–499, p. 499 [TSP, i, 260–303, p. 294].

  3. 3.

    Herschel, W., “An account of the discovery of two satellites revolving round the Georgian planet,” PT, lxxvii (1787), 125–129, p. 125 [TSP, i, 312–314, p. 312]; and idem, “Description of a forty-feet reflecting telescope,” PT, lxxxv (1795), 347–409, p. 382 [TSP, i, 485–527, p. 509].

  4. 4.

    For extravagant claims, cf. e.g.: Pearson, W., An introduction to practical astronomy, ii, (London, 1829), p. 76, where it is said that powers as high as 6652× were used; also, Brewster, D., A treatise on optics, (London, 1831), p. 356, where the high power is given as 6450×. The best modern accounts of the 40-ft are: Hoskin, M., “Herschel’s 40 ft. reflector: funding and functions,” JHA, xxxiv (2003), 1–32; and idem, Discoverers of the universe, William and Caroline Herschel, (Princeton, 2011), pp. 114–128 and 171–178.

  5. 5.

    By restricting use of the instrument to a few trusted persons, and devising public rationales to explain his own lack of use. Cf. e.g.: Pearson, W., “Telescope,” in A. Rees (ed.), The cyclopædia; or, universal dictionary of arts, sciences, and literature,” xxxv, (London, 1819), 61, column two of the article: “…this is probably the reason why few persons have been in a situation to form an estimate of the merits of this transcendent instrument”; Hoskin, M., [op. cit. ref. 4, (2011)], p. 176: “…almost nobody was ever allowed actually to look through the telescope….”; and Dreyer, J.L.E., TSP, i, pp. liii–liv: “…Herschel is supposed not to have allowed anyone else (except Prof. Vince) to use this telescope,” and “…all the same it is likely enough that the instrument did not generally perform well.” Herschel’s expressed reasons for not using the instrument are enumerated at, e.g.: Herschel, W., “A series of observations of the satellites of the Georgian planet, etc.,” PT, cv (1815), 293–362, pp. 295–296 [TSP, ii, pp. 543–544]. More will be said about his reasons later in the present work.

  6. 6.

    Texereau, J., How to make a telescope, 2nd English ed., (Willmann-Bell, 1984), pp. 107–108 and 116.

  7. 7.

    Reeves, E., Galileo’s glassworks, the telescope and the mirror, (Harvard, 2008); Ariotti, P.E., “Bonaventura Cavalieri, Marin Mersenne, and the reflecting telescope,” Isis, lxvi (1975), 302–321; Zucchi, N., Optica philosophia, i, (Lugduni, 1652), p. 126 [quoted in Pezenas, E., Cours complet d’optique, traduit de l’anglois de Robert Smith, etc., ii, (Avignon & Paris, 1767), pp. 420–421]; and Danjon, A. & A. Couder, Lunettes et télescopes, (Paris, 1935; reprint, Paris 1979), pp. 604–609.

  8. 8.

    Cavalieri, B., Lo specchio ustorio, (Bologna, 1632), pp. 29ff. (conjugate properties of conics); 103ff. (confocal paraboloidal mirrors); and p. 126 (catoptric and catadioptric afocal telescopes); and Mersenne, M., Harmonie universelle contenant la théorie et la pratique de la musique, (Paris, 1636), pp. 61–62; and idem, L’optique et la catoptrique, (Paris, 1651), pp. 102–103 and 127. Mersenne was aware of Cavalieri’s earlier work.

  9. 9.

    Willach, R., “The development of the reflecting telescope in the 18th century from John Hadley to James Short,” Storia della scienza e della tecnica, atti della “Fondazione Giorgio Ronchi,” lxii (2007), 255–288.

  10. 10.

    Simpson, A.D.C, “James Gregory and the reflecting telescope,” JHA, xxiii (1992), 77–92, p. 88; idem, “The beginnings of commercial manufacture of the reflecting telescope in London,” JHA, xl (2009), 421–466; and Court, T.H. & M. von Rohr, “A history of the development of the telescope from about 1675 to 1830 based on documents in the Court collection,” TOS, xxx (1929), 207–260, p. 218.

  11. 11.

    Newton, I., Opticks, book i, (London, 1704), pp. 75–80; Simpson, A.D.C., [op. cit. ref. 10, (2009)], pp. 423–427; Court, T.H. & M. von Rohr, (op. cit. ref. 10), pp. 218–219; and Hall, A.R. & A.D.C. Simpson, “An account of the Royal Society’s Newton telescope,” NRRS, l (1996), 1–11.

  12. 12.

    Simpson, A.D.C., [op. cit. ref. 10, (2009)], pp. 427–451; Court, T.H. & M. von Rohr, (op. cit. ref. 10), pp. 219–227; and Passemant, C.-S., Construction d’un télescope de réflexion, (Paris, 1738). This last item is Passemant’s complete treatise on the making of reflecting telescopes, a book that he describes on its title page as “useful to artisans who would like to essay this novel art…[utile aux Artistes qui voudront s’appliquer à cet Art nouveau].”

  13. 13.

    Willach, R., (op. cit. ref. 9), pp. 265–273; Mudge, J., “Directions for making the best composition for the metals of reflecting telescopes; together with a description of the process for grinding, polishing, and giving the great speculum the true parabolic curve,” PT, lxvii (1777), 296–349; Edwards, J., “Directions for making the best composition for the metals of reflecting telescopes, etc.,” The nautical almanac and astronomical ephemeris, for the year 1787, (London, 1783), appendix, pp. 3–22; idem, “An account of several compositions of metals and semi-metals, on which trials were made to find out the most proper mixture for the specula of reflecting telescopes,” ibid., pp. 23–48; Oxmantown, Lord, “An account of experiments on the reflecting telescope,” PT, cxxx (1840), 503–527, pp. 503–506; and Herschel, J.F.W., The telescope, (Edinburgh, 1861), pp. 123–130.

  14. 14.

    For modern methods of supporting large mirrors, cf. Lemaitre, G.R., Astronomical optics and elasticity theory, (Berlin, 2009), pp. 16–21 and 413–415; Wilson, R.N., Reflecting telescope optics, ii, 2nd ed., (Springer, 2001), pp. 242–273; and Kärcher, H.J., “Die Kunst, Linsen und Spiegel zu halten,” Sterne und Weltraum, (3/2012), 52–63. For a historical perspective, cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 91–97. On the density of speculum, cf. Texereau, J., (op. cit. ref. 6), p. 25; on the origin of whiffle-trees, cf. Oxmantown, Lord, (op. cit. ref. 13), p. 524 and Rosse, Earl of, “On the construction of specula of six-feet aperture, etc.,” PT, cli (1861), 681–745, pp. 689–691 and plate xxiv, fig. 10; and on the origin of astatic levers, cf. Lassell, W., “Description of an observatory erected at Starfield, near Liverpool,” MmRAS, xii (1842), 265–272, p. 269. And for the earliest surviving whiffle-tree, cf. Fig. 4.33 below.

  15. 15.

    For cracking, cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 126–130; for dew and ice accumulating on a mirror, cf. e.g., Herschel, W., “Astronomical observations relating to the sidereal part of the heavens, and its connection with the nebulous part; arranged for the purpose of a critical examination,” PT, civ (1814), 248–284, p. 275, footnote * [TSP, ii, p. 536]; for water vapour causing damage, cf. e.g., RAS MS Herschel W.2/2.5, Review No. 5, f. 57v [TSP, ii, p. 600]: “1799, Dec. 28, 40 feet telescope…my mirror has been injured by condensed vapours”; also, RAS MS Herschel W.5/9.1 (instructions for the Russian 20 ft telescope), p. 10: “Then if we should lift up the [mirror] cover after an observation at night, some drops of dew or crumbling of hoar frost might fall on the open mirror, and such accidents would soon destroy it.” Herschel always took care to emphasize the need to keep mirrors dry. Cf. also, Schrader, J.G.F., “Beschreibung des Mechanismus eines unweit Kiel errichteten sechs und zwanzigfüßigen Teleskops,” Schleswig-Holsteinische Provinzialberichte, viii (1794), 1–19, p. 13: “If the composition of the speculum metal is not of the best type, [mirrors] very soon lose some of their polish and shine by frequent fogging, or in common parlance, they tarnish. [Ist die Komposition des Spiegelmetalles nicht von der besten Art, so verlieren [die Spiegel] durch das häufige Beschlagen sehr bald von ihrer Politur and Glanze, oder in der gemeinen Sprache zu reden, sie laufen an.]”

  16. 16.

    South, J., “Sir W. Herschel’s Forty Feet Reflector,” Times of London¸ 6-Oct-1838 (letter to the editor), p. 5.

  17. 17.

    For reflectivity of speculum and silver, cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 87–88; for modern aluminum coatings, cf. Bass, M. et al., Handbook of optics, iv, 3rd edition, (New York, 2010), 7.106–109. William Herschel occasionally constructed other forms of telescopes, such as the Gregorian reflector, since this design gives upright images and can be used in the daytime to look about the countryside. The configuration of this two-mirror system (as well as its cousin, the Cassegrain reflector) can easily be found by consulting books and the internet. Since the present chapter concerns Herschel’s astronomical work and centers on the telescopes he constructed as research tools to further that work, I do not wish to lengthen an already long chapter by discussing extraneous forms of instruments which at most formed occasional sidelights to Herschel’s predominate work.

  18. 18.

    For the CTE and conductivity (also called “diffusivity”) of speculum and various glasses, cf. Texereau, J., (op. cit. ref. 6), p. 25; and in general Lemaitre, G.R., (op. cit. ref. 14), pp. 416–423. During hand working Herschel typically attached a wooden polishing handle on the backs of his mirrors: “Polishing without a handle is properly speaking to polish in an artificial temperature, and must be liable to all the inconveniencies of it; it is therefore advisable to use a handle on account of preserving a more equal temperature in the mirror,” RAS MS Herschel W.5/14.1, section 4.2, f. 13r. Such a handle is sometimes called a “spivvy” among modern opticians; cf. Gregory, J., “A quest for the perfect refractor,” Sky and telescope, lxiii (1987), 662–667, p. 665. With glass optics, spivvies are not necessary; cf. Texereau, J., (op. cit. ref. 6), pp. 35–53. To avoid difficulties arising from temperature changes in speculum during fabrication, Lord Rosse introduced the practice of partially submerging his mirrors in a tank of water to act as a heat stabilizer: “…in working large specula, the [fabrication] uncertainty was so great, that it gave rise to difficulties which I found it impossible to combat, and therefore I resorted to the simple expedient of making the speculum revolve in water, kept at a uniform temperature of 55° [F]: all change also in the figure of the speculum, from variation of temperature during the process, was thus at the same time prevented.” Cf. Oxmantown, Lord, (op. cit. ref. 13), p. 520.

  19. 19.

    For pores and crystallizations, cf. Willach, R., (op. cit. ref. 9). Also cf. RAS MS Herschel W.5/14.1, section 31.7, f. 136r: “Burs are extremely troublesome, it is therefore necessary to prevent them, or if they happen to be contracted to get rid of them as soon as possible. Holes in the face of a mirror are very apt to contract burs about them, which become very troublesome in polishing”; and f. 137r: “Very coarse crystallizations are bad faults in the face of a mirror, and show themselves often in polishing. I surmise that when they are not to be seen they still may render a mirror less distinct. Some are so bad that it is best to throw the mirror aside.” For an instructive account of casting and fabricating a speculum metal mirror blank, cf. Bailey, E.F., “I tried to follow Herschel,” The sky, iii (Sept. 1939), 6–7.

  20. 20.

    Lemaitre, G.R., (op. cit. ref. 14), pp. 418–419.

  21. 21.

    As we noted previously, on the order of a few dozen nanometers. In optical testing it is easy to see how heat from the hand can distort an optical surface: cf. also the comments of Grubb, H., “Telescopic objectives and mirrors: their preparation and testing,” Nature, xxxiv (1886), 85–92, p. 90, col. 1. Grubb’s article is filled with highly useful information about optical fabrication and testing. The finest optical figuring was done (and even today sometimes still is) using the tips of the optician’s fingers or thumbs charged with polishing compound: “…Mr. [Alvan G.] Clark took up an old castaway disk [of glass] and gave it less than a dozen sharp rubs with the smooth, soft thick of his thumb. ‘There,’ said he, ‘if this had been a perfect lens, that would have changed its shape enough to ruin it.’ I wanted to accuse the man of playing upon me, but his earnestness forbade.” In Hawkins, W.B., “The Clarks,” Popular Astronomy, xxxiv (1926), 379–382, p. 382.

  22. 22.

    RAS MS Herschel W.5/14.1, section 1.4, f. 6r: “A…very desirable quality is that a reflecting metal should not be very liable to tarnish when exposed to air. I cannot however put this quality in competition with the reflection of light; but will readily allow that the perishable nature of mirrors ought to be an additional inducement for us to bring the art of making and repolishing them to perfection.” Herschel wished to make polishing a predictable process, which he called “giving figure,” consisting of manipulating the motions of his polishing machines and pitch laps by definite rules, making the frequent repolishing less onerous. For an overview, cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 140–151.

  23. 23.

    RAS MS Herschel W.1/1.1, p. 22: quoted in Lubbock, C.A., The Herschel chronicle, (Cambridge, 1933), p. 103. At the end of his life Herschel pronounced to James South about mirrors: “I have done much for them – they have done much for me – they are, however, in their infancy, as you will live to see,” in South, J., (op. cit. ref. 16).

  24. 24.

    For discussions of geometrical aberrations and image spot diagrams, cf. Smith, W., Modern optical engineering, 3rd ed., (SPIE-McGraw Hill, 2000), pp. 61–89; and Smith, G.H., Practical computer-aided lens design, (Willmann-Bell, Richmond, 1998), pp. 55–97. For introductory texts, cf. Rutten, H.G.J. & M.A.M van Venrooij, Telescope optics, a comprehensive manual for amateur astronomers, (Willmann-Bell, 1999), pp. 21–44; and Smith, G.H., R. Ceragioli, and R. Berry, Telescopes, eyepieces, and astrographs, (Willmann-Bell, 2012), pp. 64–74.

  25. 25.

    On point-spread functions, cf. Smith, W., (op. cit. ref. 24), pp. 361–362 and 385–391. For physical optics aberrations in general, cf. Suiter, H.R., Star testing astronomical telescopes, 2nd edition, (Willmann-Bell, Richmond, 2008).

  26. 26.

    For Airy’s original paper, cf. Airy, G.B., “On the Diffraction of an Object-Glass with Circular Aperture,” TCPS, v (1835), 284–291. On the distribution of light in a perfect Airy pattern, cf. Smith, W., (op. cit. ref. 24), p. 160.

  27. 27.

    Because the modern wave theory of light, on which the formation of the Airy pattern rests, was not yet established. Cf. below, section “Herschel’s manufacture and testing of telescope mirrors.” Cf. also Herschel, J.F.W., Treatises on physical astronomy, light and sound, contributed to the Encyclopaedia Metropolitana, (ca. 1827), p. 491. That Herschel’s best instruments showed stars as small disks with little or no asymmetry evoked wonder in the 1780s. Therefore, it was long remembered in the Herschel family how in 1786 William Herschel attended a dinner party and was seated next to Henry Cavendish (1731–1810), the famous chemist and physicist, a man who spoke but little: “Some time passed without his uttering a word, then he suddenly turned to his neighbour and said: ‘I am told you see the stars round, Dr. Herschel.’ ‘Round as a button,’ was the reply. A long silence ensued till, towards the end of the dinner, Cavendish again opened his lips to say in a doubtful voice: ‘Round as a button?’ ‘Exactly, round as a button,’ repeated Herschel, and so the conversation ended.” Quoted in Lubbock, C.A., (op. cit. ref. 23), p. 102.

  28. 28.

    Toomer, G.J., Diocles on burning mirrors, (Berlin, 1976), pp. 15–16. Diocles (third-second century BCE), demonstrated that a concave mirror must be paraboloidal to concentrate the light of the sun to a perfect focus.

  29. 29.

    Della Porta, G.B., De refractione, (Neapolis, 1593), pp. 35–64 (Book 2); Kepler, J., Dioptrice, (Augusta Vindelicorum, 1611), pp. 21–22 (Propositio LIX). Cf. also Riekher, R., Fernrohre und ihre Meister, 2nd ed., (Berlin, 1990), p. 31; and Smith, A.M., From sight to light, the passage from ancient to modern optics, (Chicago, 2015), pp. 322ff.

  30. 30.

    Descartes, R., La dioptrique, discourses 8–9, and La géométrie, livre 2, in Adam, C. & P. Tannery, Oeuvres de Descartes, Discours de la méthode & essais, vi (Paris, 1902), pp. 165–211 and 428–441. Already Kepler had suggested the use of a hyperboloid (op. cit. ref. 29).

  31. 31.

    Apollonius of Perga (third-second century BCE), in his treatise on conic sections had demonstrated the conjugate properties of the foci in ellipses and hyperbolas, although without direct reference to mirrors. Cf. Heath, T.L., Apollonius of Perga, treatise on conic sections, (Cambridge, 1961), pp. 112–118.

  32. 32.

    Ariotti, P.E., (op. cit. ref. 7), and cf. ref. 8 above. Cf. also, Baranne, A. and R. Launay, “Cassegrain: un célèbre inconnu de l’astronomie instrumentale,” Journal of optics, xxviii (1997), 158–172.

  33. 33.

    Newton, I., (op. cit. ref. 11), book i, pp. 59–74.

  34. 34.

    The best overall account of these developments is given by Boegehold, H., “Zur Vor- und Frühgeschichte der achromatischen Fernrohrobjektive,” Forschungen zur Geschichte der Optik, iii (1943), 81–114. Cf. also, Rudd, M.E. et al., “New light on an old question: who invented the achromatic telescope?,” Journal of the Antique Telescope Society, xix (2000), 3–12; and Riekher, R., (op. cit. ref. 29), pp. 102–118.

  35. 35.

    For a succinct history with much documentation on the recognition of astigmatism, cf. von Rohr, M. (ed.), Geometrical investigation of the formation of images in optical instruments, (London, 1920), pp. 201–209. This is the English translation of von Rohr’s German treatise, Die Bilderzeugung in optischen Instrumenten vom Standpunkte der geometrischen Optik, (Berlin, 1904), pp. 199–205.

  36. 36.

    Young, T., “On the mechanism of the eye,” PT, xci (1801), 23–88, p. 30 and Fig. 28.

  37. 37.

    Airy, G.B., “On a peculiar defect in the eye, and a mode of correcting it,” TCPS, ii (1827), 267–271; idem, “On a change in the state of an eye affected with a mal-formation,” TCPS, viii (1849), 361–362; idem, “Substance of the lecture delivered by the Astronomer Royal on the large reflecting telescopes of the Earl of Rosse and Mr. Lassell, at the last November Meeting,” MNRAS, ix (1849), 110–122, p. 119; Green, J., “On the detection and measurement of astigmatism,” The American journal of the medical sciences, liii (1866), 117–127; von Rohr, M., “Der Astigmatismus in sprachlicher und sachlicher Hinsicht,” Die Naturwissenschaften, xx (1932), 848–850; and Levene, J.R., “Sir George Biddell Airy, F.R.S. (1801–1892) and the discovery and correction of astigmatism,” NRRS, xxi (1966), 180–199.

  38. 38.

    Airy, G.B., “On the spherical aberration of the eye-pieces of telescopes,” TCPS, iii (1830), 1–63, p. 2 and Fig. 6; and Coddington, H., A system of optics, i, (Cambridge, 1829), pp. 20–35 (esp. 26–28) and 66–72.

  39. 39.

    For bibliography, cf. von Rohr, M., (op. cit. ref. 35).

  40. 40.

    Potter, R., An elementary treatise on optics, ii (London, 1851), p. 113.

  41. 41.

    Cf. Boegehold, H., “Die Leistungen von Clairaut und d’Alembert für die Theorie des Fernrohrobjektivs und die französischen Wettbewerbsversuch gegen England in den letzten Jahrzehnten des 18. Jahrhunderts,” Zeitschrift für Instrumentenkunde, lv (1935), 97–111, p. 98 and 102; and also Church, J.A., “Clairaut’s Forgotten Legacy,” Sky and telescope, lxvi (1983), 259–261.

  42. 42.

    Herschel, J.F.W., “On the aberrations of compound lenses and object-glasses,” PT, cxi (1821), 222–267, pp. 226–227. This is true as long as the objective lens is made properly square (“collimated”) to the axis of the telescope tube. If it is not square, and if the lens has not been corrected for coma in design (most nineteenth century telescope objectives were not so corrected), then the aberration would be glaringly apparent in the middle of the field of view. Hence most refractor makers and users must have been familiar with coma empirically. Still, because it could be eradicated on axis by aligning the objective lens and simultaneously made vanishingly small off-axis over the limited visual field, coma elicited no great interest or theoretical study until the mid-to-late nineteenth century. See further below in the present chapter for more details.

  43. 43.

    Lister, J.J., “On some properties in achromatic object-glasses applicable to the improvement of the microscope,” PT, cxx (1830), 187–200, p. 193.

  44. 44.

    Hamilton, W.R., “On some results of the view of a characteristic function in optics,” Report of the third meeting of the British Association for the Advancement of Science, (London, 1834), 360–370; and Rayleigh, Lord, “Hamilton’s principle and the five aberrations of von Seidel,” The London, Edinburgh, and Dublin philosophical magazine and journal of science, xv (1908), 677–687.

  45. 45.

    Kingslake, R., A history of the photographic lens, (Academic Press, 1989), pp. 1–8; Wilson, R.N., Reflecting telescope optics, i, 2nd ed., (Springer, 2007), p. 63; and Petzval, J., “Fortsetzung des Berichtes über optische Untersuchungen,” Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der kaiserlichen Akademie der Wissenschaften, xxiv (Wein, 1857), 92–105, pp. 95ff.

  46. 46.

    von Seidel, L., “Zur Theorie der Fernrohr-Objective,” AN, xxxv (1853), 301–316; idem, “Zur Dioptrik,” AN, xxxvii (1854), 105–120; and idem, “Zur Dioptrik,” AN, xliii (1856), 289–304, 305–320, and 321–332. Seidel worked closely with Carl August von Steinheil and his son Hugo Adolph on camera optics (among other things), and developed refined methods of trigonometrical “ray tracing” for them: cf. Franz, H. & E. Reutinger, Steinheil, Münchner Optik mit Tradition, (ca. 2001, Stuttgart), pp. 66–67 & 94–95; and Seidel, L., “Trigonometrische Formeln für den allgemeinsten Fall der Brechung des Lichtes an centrirten sphärischen Flächen,” Sitzungsberichte der königl. bayer. Akademie der Wissenschaften zu München, ii (1866), 263–283.

  47. 47.

    Potter, R., (op. cit. ref. 40), pp. iv–vi; 28–42; and 108–116. Cf. also the important comments of H.D. Taylor in Taylor, H.D., A system of applied optics, (London, 1906), pp. 3–4.

  48. 48.

    Potter, R., (op. cit. ref. 40), pp. 18–23 and 28–33. On p. 22 Potter found that for a spherical mirror in a 7-ft Herschel Newtonian: “the diameter of the least circle of aberration [on-axis] subtends…an angle of 5/8 of one second of a degree; and this would not prevent the telescope separating the images of many difficult double stars, which are considered most effectual test-objects for telescopes [Potter’s emphasis].” Also cf. Potter, R. An elementary treatise on optics, i (London, 1851), 129–130, where speaking about front-view telescopes, he says: “The image being formed by pencils reflected obliquely by the mirror, is never distinct.” But Potter notes the value of the front-view for viewing faint objects.

  49. 49.

    Potter, R., (op. cit. ref. 40), p. 113.

  50. 50.

    On the general development of astrophotography at the time, cf. Gill, D., “Observations of the Great Comet, 1882. II.,” Annals of the Royal Observatory, Cape of Good Hope, ii.1 (1885); idem, “The applications of photography in astronomy,” Obs, x (1887), 267–272 and 283–294; Anon., “Direct photography of the heavens,” The astronomical register, xxiv (1886), 245–248; Barnard, E.E., “On some celestial photographs made with a large portrait lens at the Lick Observatory,” MNRAS, l (1890), 310–314; and idem “The development of photography in astronomy i–ii,” Science, viii (1898), 341–353 and 386–395. For the Carte du Ciel project, cf. Chinnici, I., La carte du ciel, (Paris & Palermo, 1999), pp. 3–10; Grubb, H., “The construction of telescope object-glasses for the international photographic survey of the heavens,” The scientific transactions of the Royal Dublin Society, iv (1891), 475–480; and Taylor, H.D., “Telescope objectives for photographic purposes,” MNRAS, liii (1893), 359–368.

  51. 51.

    Vogel, H.C., “Über Spiegelteleskope mit relativ kurzer Brennweite,” Sitzungsberichte der königlich preussischen Akademie der Wissenschaften, (Jahrgang 1906), 332–350; and the English translation in Vogel, H.C., “On reflecting telescopes of relatively short focus,” ApJ, xxiii (1906), 370–389.

  52. 52.

    Schaeberle, J.M., “On the photographic efficiency of a 13-inch reflector of 20-inches focus,” AJ, xxiii (1903), 109–113.

  53. 53.

    For contemporary discussions of off-axis aberrations in reflectors (i.e. coma), cf. Poor, C.L., “The aberration of parabolic mirrors,” AJ, xviii (1897), 98–99; Schaeberle, J.M., “On the fundamental optical imperfection of the parabolic reflecting telescope,” AN, cxliv (1897), 377–380; idem, “On a fundamental optical defect in the images formed by a parabolic reflector,” AJ, xviii (1897) 35–38; Crockett, C.W., “The parabolic mirror,” ApJ, vii (1898), 362–366; Plummer, H.C., “On the star-image formed by a parabolic mirror,” AJ, xix (1898), 21–23; Poor, C.L., “The aberration of parabolic mirrors,” ApJ, vii (1898), 114–123; Schaeberle, J.M., “General theory of the aberration in the focal plane of a parabolic reflector,” AJ, xix (1898), 17–21; idem, “On the definition and intensity of a star’s image in the field of view of a parabolic reflecting telescope,” PA, vi (1898), 33–38; idem, “On the aberration of parabolic mirrors,” PA, vi (1898), 38–40; Wadsworth, F.L.O., “On the ‘worthlessness’ of methods of geometrical optics in dealing with the problems relating to the definition and the delineating and resolving power of telescopes,” PA, v (1898), 528–536; Reese, S.C., “Field of the reflecting telescope,” ApJ, xii (1900), 219–227; Plummer, H.C., “On the images formed by a parabolic mirror,” MNRAS, lxii (1902), 352–369 and lxiii, 16–26. For references to “Schaeberlian aberration,” cf. e.g., Anon., “New form of achromatic telescope – Airy’s Gregorian,” English mechanic and world of science, mdccclxv (1900), 428–429, p. 429, column i, infra; and Musson, W.B., “New forms of telescopes and other optical instruments,” Obs, xxiii (1900), 350–352, p. 352.

  54. 54.

    Schwarzschild, K., “Untersuchungen zur geometrischen Optik I-III,” Astronomische Mitteilungen der königlichen Sternwarte zu Göttingen, ix (1905), i, 3–31; ii, 3–28; and iii, 3–54. For complete modern treatments of image aberrations in reflecting telescopes, cf. Schroeder, D.J., Astronomical optics, 2nd ed., (London & San Diego, 2000); and Wilson, R.N., (op. cit. ref. 45). For an expert overview of Schwarzschild’s work, cf. also: Wilson, R.N., “Karl Schwarzschild and Telescope Optics,” Reviews in Modern Astronomy, vii (1994), 1–29.

  55. 55.

    Chrétien, H., “Le télescope de Newton et le télescope aplanétique,” Revue d’optique, i (1922), 13–22 and 49–64.

  56. 56.

    RAS MS Herschel W.5/12.1-4. Two thousand one hundred sixty-one experiments are enumerated in the four volumes.

  57. 57.

    Results is found in two redactions, RAS MS Herschel W.5/13.1 and W.5/14.1. The second redaction was reviewed by John Herschel who pronounced it the “most perfect copy.” John also executed a large series of drawings of his father’s grinding and polishing machines to accompany the second redaction. This is preserved as RAS MS Herschel W.5/14.2.

  58. 58.

    Hoskin, M., [op. cit. ref. 4, (2011)], pp. 158–207.

  59. 59.

    Herschel, J.F.W., Results of astronomical observations made during the years 1834, 5, 6, 7, 8, at the Cape of Good Hope; being the completion of a telescopic survey of the whole surface of the visible heavens, commenced in 1825, etc., (London, 1847).

  60. 60.

    Herschel, J.F.W., (op. cit. ref. 13), pp. 126–151.

  61. 61.

    For modern methods, cf. Texereau, J., (op. cit. ref. 6), pp. 17–59. Newton introduced the use of pure pitch to form the polishing lap, which has been essential to the production of precision optics even up to today: Newton, I., (op. cit. ref. 11), pp. 76–77; and most recently, Williamson, R., Field guide to optical fabrication, (SPIE Press, 2011), p. 39. Other opticians used paper, cloth, and pitch-impregnated silk laps: Smith, R., A compleat system of opticks, (Cambridge, 1738), book 3, pp. 296–297 and 307–309. But James Short, and John Mudge recommended pure pitch, which is what Herschel nearly always used, as shown in RAS MS Herschel W.5/12.1-4 and W.5/14.1, sections vi–vii. Cf. also, Short, J., “A method of working the object glasses of refracting telescopes truly spherical,” PT, lix (1769), 507–511, pp. 509–510; and Mudge, J., (op. cit. ref. 13), pp. 317–327 and 344–345. Mudge severely criticized other types of polishing laps as described by Smith.

  62. 62.

    RAS MS Herschel W.5/14.1, section viii.

  63. 63.

    On Herschel’s machines in general, cf. Herschel, W., “On polishing specula by a machine,” in TSP, i, pp. cviii-cix; and Herschel, J.F.W., (op. cit. ref. 13), 142–151. For the intricate details, cf. RAS MS Herschel W.5/14.1, section iv. For polishing elliptical diagonals, cf. RAS MS Herschel W.5/14.1, sections iv, f. 25r and xxxiv, article 1. RAS MS Herschel W.5/14.2, Figs. 4.22, 4.23 and 4.28 illustrate the bracket used to hold an elliptical diagonal, as well as an entire small polishing machine for a diagonal, with a diagonal mirror atop a pitch lap. An earlier hand-lapping procedure of Herschel’s for finishing diagonals is discussed in Edwards, J., (op. cit. ref. 13), p. 43. This corresponds to Herschel’s letter to him, dated 2-May-1782, in RAS MS Herschel W.1/1.1, p. 53.

  64. 64.

    RAS MS Herschel W.5/12.3, Exp. 366 (25-ft mirror): “Upon the flag of Windsor castle it shows all the threads of the canvas.”

  65. 65.

    Mudge, J., (op. cit. ref. 13), pp. 335–338 and Fig. 3; RAS MS Herschel W.5/14.1, section xxxii, articles 2–3; and Herschel, J.F.W., (op. cit. ref. 13), pp. 154–156.

  66. 66.

    Herschel, J.F.W., (op. cit. ref. 13), pp. 173–178. For modern discussions of the Foucault knife-edge test, cf. Texereau, J., (op. cit. ref. 6), pp. 65–87; and Lecleire, K. & J.-M., A manual for amateur telescope makers, (Willmann-Bell, 2003), pp. 109–119.

  67. 67.

    RAS MS Herschel W.5/14.1, section xxxii, article 2, f. 146r: “Astronomical observations alone are the criterion of the perfection of a mirror.”

  68. 68.

    Goodwin, E.P. & J.C. Wyant, Field Guide to Interferometric Optical Testing, (SPIE Press, 2006).

  69. 69.

    On the difficulty of making optical flats, cf. e.g., Grubb, H., (op. cit. ref. 21), pp. 90–91; Kitchiner, W., Economy of the eyes – part ii: of telescopes, (London, 1825), pp. 104–105, 114, and 235–236; and Potter, R., “On various improvements in the casting, working, etc. of specula for reflecting telescopes, with sundry hints for amateur opticians,” The Edinburgh journal of science, iv, (1831), 13–27, p. 20: “It is acknowledged to be the most difficult part of the art of the working optician to produce a lens or speculum with a good plane surface; and those amateurs who undertake the Newtonian telescope for astronomical purposes, − if they find their instrument when finished will not show difficult astronomical objects well, may satisfy themselves that it is a hundred to one the greatest fault lies in the small oval speculum not being truly plane; and this may be told from the figure of the planets, etc. appearing oblong in place of round….” Even Newton discovered the difficulty: “I should tell you also, that the little plain piece of metall, next the eye-glass, is not truly figured…I hope, that by correcting its figure, (in which I find more difficulty than one would expect)…,” in Newton, I., “Mr. Newton’s letter to the publisher of March 26, 1672, etc.,” PT, vii (1672), p. 4032. On diagonal flat tolerances, cf. Texereau, J., (op. cit. ref. 6), pp. 107–108; and Suiter, H.R., (op. cit. ref. 25), pp. 365–366.

  70. 70.

    Suiter, H.R., (op. cit. ref. 25), pp. 282–283. Even Herschel was aware of this. In RAS MS Herschel W.5/14.1, section xxxiv, article 1, f. 158v, he says: “A plain mirror must be perfect in figure from the grinding, which is not so necessary with object mirrors; a few tenths of an inch more or less focal length is of no consequence, but the least deviation from a plain will be concave or convex.”

  71. 71.

    This cancellation was understood in the eighteenth and nineteenth centuries: Mudge, J., (op. cit. ref. 13), pp. 340–341; Kitchiner, W., (op. cit. ref. 69), pp. 92–94; and Pearson, W., (op. cit. ref. 5), p. 9 of article, column 1 (quoting George Dollond): “Mr. Short, the celebrated maker of reflecting telescopes, used to proceed by first making his large metal as nearly correct or parabolical as he could, and then, from a number of small metals, to select, by trial, that which corrected the large one in the best manner.”

  72. 72.

    Texereau, J., (op. cit. ref. 6), p. 108: “Errors [in flatness of Newtonian secondaries] of fully a wave are common. We had occasion once even to see a convexity of nine fringes [4½ waves] in a beautiful 12-inch telescope!” Lecleire, K. & J.-M., (op. cit. ref. 66), p. 125: “A complete plan for making a Newtonian secondary diagonal mirror is detailed below. However, this step is not essential in the construction of the…telescope. Although purchasing a finished mirror may seem to go against the spirit of this project, beginners are advised to buy their secondary mirror [authors’ emphasis].”

  73. 73.

    For an early account of interference testing of glass flat mirrors, cf. Brashear, J.A., “Critical Methods of Detecting Errors in Plane Surfaces,” Scientific American supplement, xix, no. 484, (11-April-1885), 7724–7726. For Fraunhofer’s possible use of testplates (Probegläser), cf. Riekher, R., (op. cit. ref. 29), pp. 154–155. For modern methods, cf. Selby, H.H., “Flats,” in ATM, ii, pp. 535–554 (with many pictures of interference fringes); Texereau, J., (op. cit. ref. 6), pp. 111–115; and Lecleire, K. & J.-M., (op. cit. ref. 66), pp. 131–133.

  74. 74.

    For an overview of Newtonian corpuscular theory and the subsequent wave theory of light, cf. Darrigol, O., A history of optics from Greek antiquity to the nineteenth century, (Oxford, 2012), pp. 98–108 and 166ff. Newton’s own discussion of his theory of “fits” is in Newton, I., (op. cit. ref. 11), book ii, parts iii–iv, pp. 78–112. For Herschel’s papers, cf. Herschel, W., “Experiments for investigating the cause of colored concentric rings, discovered by Sir Isaac Newton, between two object-glasses laid upon one another,” PT, xcvii (1807), 180–233 [TSP, ii, pp. 368–398]; idem, “Continuation of experiments for investigating the cause of colored concentric rings, and other appearances of a similar nature,” PT, xcix (1809), 259–302 [TSP, ii, pp. 414–440]; and idem, “Supplement to the first and second part of the paper of experiments, for investigating the cause of colored concentric rings between object glasses, and other appearances of a similar nature,” PT, c (1810), 149–177 [TSP, ii, pp. 441–458]. Cf. also Dreyer’s comments on the controversy surrounding publication of Herschel’s papers: TSP, i, pp. lvi-lviii; and Hoskin’s comments: Hoskin, M., [op. cit. ref. 4, (2011)], p. 154.

  75. 75.

    Cf. Mills, A.A. and R. Hall, “The production of a plane surface as illustrated by specula from some early Newtonian telescopes,” NRRS, xxxvii (1983), 147–166, p. 153. This highly important paper will be discussed below.

  76. 76.

    RAS MS Herschel W.5/14.1, section xxxiv, article ii. RAS MS Herschel W.5/12.1, Experiment 426, pp. 135–136 (dated 20-Aug-1790), gives a more detailed account and illustrates some brass testing hardware.

  77. 77.

    Herschel mentions both these methods, e.g., at RAS MS Herschel W.5/12.1, experiment 295, #2, p. 75 (May-June 1787): “These [brass] tools were turned flat by a straight gage and afterwards ground with emery, two and two alternately till all the three fitted each other completely.” For a modern discussion, cf. Lecleire, K. & J.-M., (op. cit. ref. 66), pp. 129–131. As to Herschel’s two-card method, illustrated in Fig. 4.17, it is possible to show geomtrically that (if we assume a reasonable value for the angular accuity of the eye, namely 2 arcmin), by using this two-card method Herschel could reliably arrive at curvatures on his diagonals which are comparable to those found below in Figs. 4.22, 4.23, 4.24, and 4.25. Flatter than this the method could not guarantee.

  78. 78.

    That Lord Rosse devised this method of testing is claimed by Brashear, J.A., (op. cit. ref. 73), p. 7724. Rosse did publish details of the method in 1840 in Oxmantown, Lord, (op. cit. ref. 13), p. 524, but spoke of the method as “the usual way,” as if it were nothing new. It was discussed earlier in 1829 without attribution by Pearson, W., (op. cit. ref. 4), pp. 69–70. A modern discussion of the method can be found in Suiter, H.R., (op. cit. ref. 25), pp. 287–288.

  79. 79.

    For a modern discussion of the method, cf. Texereau, J., (op. cit. ref. 6), pp. 115–118. For Common’s discussion cf. Common, A.A., “Note on Testing Polished Flat Surfaces,” MNRAS, xlviii (1888), 105–106.

  80. 80.

    Herschel’s production methods are specified at RAS MS Herschel W.5/14.1, section xxxiv, article 1–4.

  81. 81.

    Cf. RAS MS Herschel W.1/1, pp. 53–54 for Herschel’s description of his Newtonian secondaries.

  82. 82.

    Williamson, R., (op. cit. ref. 61), p. 39; Karrow, H.H., Fabrication methods for precision optics, (Wiley-Interscience, 1993), pp. 206–209.

  83. 83.

    RAS MS Herschel W.5/14.1, section xxxiv, article 1, f. 158r: “The diameter of a polisher for a plain mirror of an elliptical form must not exceed much the transverse of the ellipsis…A polisher of 1,05 L is of a sufficient size…A plain mirror having L = 5,6 came out of a fine figure with a polisher 6 inches or 1,07 L in diameter…A polisher of 2 inch diameter for an elliptical plain mirror 1,6 inch the transverse axis or 1,25 L is large but with proper management will do extremely well.” Here L is the “transverse” or major axis of the ellipse. William Herschel did sometimes employ elliptical polishers; perhaps that is what is depicted in Fig. 4.20.

  84. 84.

    For milling and blocking methods, cf. Texereau, J., (op. cit. ref. 6), pp. 118–122; Lecleire, K. & J.-M., (op. cit. ref. 66), pp. 127–129; and Williamson, R., (op. cit. ref. 61), pp. 17–18. For “surrounds” with elliptical orifices, cf. Potter, R., (op. cit. ref. 69), pp. 20–21; and Hindle, J., “How to make a diagonal for a Newtonian,” in ATM, i, pp. 164–165.

  85. 85.

    For continuous polishing machines, cf. Williamson, R., (op. cit. ref. 61), p. 45; Karrow, H.H., (op. cit. ref. 82), pp. 451–463.

  86. 86.

    Mills, A.A. and R. Hall, (op. cit. ref. 75). Recently, the author using a polishing machine at the University of Arizona experimented on a small glass elliptical flat mirror of commercial grade. Polishing this on top of a circular flat pitch lap proportioned to match or slightly exceed in diameter the major axis of the elliptical flat mirror, in a matter of 5–6 h of machine time and using a stroke pattern like that which Herschel would have used, the author was able to convert the originally straight interference fringes (see below in text) provided by the commercial diagonal, to elliptical fringes. That is, the author found it easy and natural to convert a flat surface on the elliptical mirror to a toroid, similar to the surfaces shown below in Figs. 4.22, 4.23, 4.24, and 4.25 of this paper from Herschel and Short.

  87. 87.

    Texereau, J., (op. cit. ref. 6), pp. 111–115; Lecleire, K. & J.-M., (op. cit. ref. 66), pp. 73–76 and 131–133; Williamson, R., (op. cit. ref. 61), pp. 86–90; and Selby, H.H, (op. cit. ref. 73), pp. 535–555. For a thorough treatment, cf. Karrow, H.H., (op. cit. ref. 82), chapter 6.1.

  88. 88.

    Mills, A.A. and R. Hall, (op. cit. ref. 75), p. 152.

  89. 89.

    The catalog numbers of Herschel diagonals (e.g. A-13, etc.), refer to designations established by W.H. Steavenson in his 1924 paper: “Catalogue of instruments made and (or) used by Sir William Herschel, as preserved at Slough and examined there in 1924, May and June,” TOS, xxvi (1924), 221–238, p. 232. Diagonal A-13 is said to have a minor-axis of 1.15 in., which corresponds to the dimension of diagonals for Herschel’s 7-ft Newtonians: RAS MS Herschel W.5/14.1, section i, article 1, f. 4v.

  90. 90.

    Karrow, H.H., (op. cit. ref. 82), p. 674, equation 6.38.

  91. 91.

    A simple calculation for the minimum minor-axis size of any given Newtonian telescope is presented by Texereau, J., (op. cit. ref. 6), pp. 109–111. Using Texereau’s equation 18, the minimum minor-axis size for a diagonal mirror that just fully intercepts the axial ray bundle arriving from the primary mirror is Dl/f, or in other words l/(focal ratio). In RAS MS Herschel W.5/14.1, section i, article 1, f. 4v, Herschel states that the minor-axis (“conjugate diameter”) size used in his 10-ft telescopes is 1.5 in. or 38.1 mm. This equals the minor-axis dimension of diagonal A-7. Hence, we may assume that A-7 was intended for a 10-ft Newtonian. On f. 4r, Herschel says that the clear optical diameter of his 10-ft mirrors was 8.8 in. (although he made 1 of 9.82 in.). Assuming the latter, and a distance from the focus to the minor-axis equal to 1/2 the mirror diameter plus 4 in. (this equals Texereau’s variable l), then the minor-axis dimension of the axial ray bundle for a 10-ft Herschel Newtonian, employing a 9.82-in. diameter mirror, would be [(9.82/2) + 4]/(120/9.82) = 0.73 in. This is about 1/2 of the actual minor-axis dimension of A-7’s speculum surface. Accordingly, the ray bundle would entirely miss the turned-down edge of this diagonal, and the image of an on-axis star or planet would not be degraded. In fact, as we will show later, it would seem perfect and so too therefore would the diagonal: off-axis stars could not be magnified enough to show the effects of the turned edge in Herschel’s narrow field-of-view singlet eyepieces. Such stars would fall outside the field of his high-power eyepieces.

  92. 92.

    Davies, C.D.P., “Herschel’s 18¾-inch speculum (‘the 20 ft.’),” MNRAS, lxxxiv (1923), 23–26 (Davies knife-edge tested one of the mirrors John Herschel used at the Cape); Steavenson, W.H., (op. cit. ref. 89), pp. 224–231 (Steavenson examined 13 Herschel mirrors, testing many of them via knife-edge; and one via a star-test); idem, “The Herschel instruments at Slough,” Obs, xlvii (1924), 262–267 and 303–308 (for further discussion by Steavenson); idem, “A peep into Herschel’s workshop,” TOS, xxvi (1924), 210–220 (still more discussion); idem, “Herschel’s first 40-ft speculum,” Obs.¸ l (1927), 114–118 (Steavenson’s report on finding the thinner of Herschel’s two 40-ft mirrors); Ainslie, M.A., “Note on the performance of two specula by Sir William Herschel,” JBAA, xlii (1931), 65–68 (Ainslie reports on testing two 7-ft mirrors via knife-edge and star-test); Hysom, E.J., “Tests of the shape of mirrors by Herschel,” JHA, xxvii (1996), 349–352 (Hysom knife-edge tested three mirrors by Herschel, using a Dall null-lens: a 10-ft mirror, a 7-ft, and a 7-in. diameter mirror for a Gregorian telescope); and Leue, H-J., “Johann Gottlieb Schrader und der Lilienthaler Fernrohrbau,” in Dick, W. and J. Hamel (eds), Astronomie von Olbers bis Schwarzschild, Acta historica astronomiae, xiv, (Harri Deutsch, 2002) 37–50, pp. 44–46. Leue gives Ronchi tests of the 10-ft Goettingen mirror by Herschel from 1786, and the 7-ft and 10-ft mirrors now in the Mathematisch-Physicalischer Salon, Dresden.

  93. 93.

    On Steavenson, cf. Dewhirst, D.W., “William Herbert Steavenson,” Quarterly journal of the Royal Astronomical Society, xviii (1977), 147–154.

  94. 94.

    Acceptable means diffraction-limited. For the meaning of the conic constant, cf. Schroeder, D.J., (op. cit. ref. 54), pp. 41–42.

  95. 95.

    RAS MS Herschel W.5/14.1, section xxxii, article 2, ff. 145v-146r. On folio 146r Herschel recognizes that some difference in zonal foci is acceptable, but recommends striving for zero difference: “A 20 feet mirror [i.e. 12-inch f/20] with a difference of 0,05 inches more the inside than the two outside foci will show extremely well; but we ought to make them exactly alike.”

  96. 96.

    Cf. ref. 61. Herschel reported results from using many other types of polishers besides pitch, but found them all defective. He found that cloth polishers produced what he called a “scabrous” polish, which appears to mean what opticians now call a “lemon peel” finish – a well-known result from polishing with cloth. RAS MS Herschel W.5/14.1, section vi, article 12, f. 50r-50v; and section xxxi, article 12, f. 140r.

  97. 97.

    Steavenson, W.H., (op. cit. ref. 89), pp. 230–231.

  98. 98.

    On Ainslie, cf. Mobberley, M.P., “Captain M. A. Ainslie, (1869–1951): his observations and telescopes,” JBAA, cxx, 1, (2010).

  99. 99.

    Ainslie, M.A., (op. cit. ref. 92), pp. 65–66. Cf. also TSP, i, p. li, footnote †: “A 10-foot Newtonian of 9-inch diameter, giving excellent images, is now in the possession of H[erschel]’s great-grandson, Mr. J.A. Hardcastle.”

  100. 100.

    Cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 81–82. This must be kept in mind when we read in his father’s letters, for example, the proud claim to control all forms of conic aspheres: “The mirrors of my telescopes are perfectly parabolical, and have no aberration from sphericity.... Any figure of the conic sections can be given to them, intirely [sic] by mechanical contrivances, and chance has no share in the operation.... The method of making and giving figure to mirrors has been established by a long series of experiments, and is recorded in several volumes, reduced to a systematic order.” By “mechanical contrivances” William Herschel means his polishing machines. Cf. RAS MS Herschel W.1/1.1, p. 293, letter to Capt. Krusenstern, dated 12-Oct-1814.

  101. 101.

    Ainslie, M.A., (op. cit. ref. 92), p. 65.

  102. 102.

    Ainslie, M.A., (op. cit. ref. 92), pp. 65–66. For “astigmatism” Ainslie really means “coma and astigmatism.”

  103. 103.

    Ainslie, M.A., (op. cit. ref. 92), p. 66. For theoreticians, cf. R. Potter (ref. 40) cited above. Also, Coddington, H., A system of optics ii, (Cambridge, 1830), pp. 34–35, who politely says that in Herschel’s 40-ft “the circle of least confusion in the image must have been 0.015 of an inch [381 microns], giving rise to a degree of indistinctness which would hardly be tolerated in a refracting telescope.” The theoretical Airy disk for Herschel’s 40-ft at f/10 was only 13.4 μm in diameter, or nearly 30× smaller in linear extent. For observers beside Ainslie, cf. e.g. Lord Rosse in Oxmantown, Lord, (op. cit. ref. 13), p. 524 (speaking of his 36-in. reflector): “I use it as a Newtonian, as I find that…the saving of light by the Herschellian [sic] construction is not at all an equivalent for the sacrifice of defining power”; and Gill, D., “Telescope,” Encyclopædia Britannica, 9th ed., (London, 1894), 135–154, p. 145: “In consequence of the tilting of the mirror aberration is created, and this increases rapidly with increased tilting. The construction is thus limited to telescopes in which the proportion of aperture to focal length is not too great.” Even John Herschel admitted the problem in 1861: “Among [the front-view’s] disadvantages, it must be considered that the aberration of the mirror is much increased by the oblique incidence of the…rays,” and suggested that “from the facility with which glass prisms of sufficient purity and silver mirrors on glass can now be obtained, it seems probable that the Newtonian will supersede all other forms.” Cf. Herschel, J.F.W., (op. cit. ref. 13), pp. 81–82.

  104. 104.

    Ainslie, M.A., (op. cit. ref. 92), pp. 66–67.

  105. 105.

    For the criterion of “Strehl ratio” as a metric of image sharpness, cf. Smith, W., (op. cit. ref. 24), p. 356–360; and Suiter, R. (op. cit. ref. 25), pp. 7–10 and 399–400.

  106. 106.

    RAS MS Herschel W.1/1.1, p. 53.

  107. 107.

    RAS MS Herschel W.5/12.1, Experiment 426, pp. 135–136.

  108. 108.

    Herschel, W., “On the remarkable appearances at the polar regions of the planet Mars, the inclination of its axis, the position of its poles, and its spheroidal figure; with a few hints relating to its real diameter and atmosphere,” PT, lxxiv, (1784), 233–273, p. 270 [TSP, i, p. 155]. Cf. also Potter in ref. 69 above.

  109. 109.

    Cf. also Potter, R., (op. cit. ref. 69), p. 20.

  110. 110.

    For Schroeter’s equipment, cf. Gerdes, D., Die Lilienthaler Sternwarte 1781 bis 1818, (Lilienthal, 1991), pp. 226–234 and passim. For Herschel’s 12-in.“small” 20-ft, cf. Bennett, J.A., (op. cit. ref. 1), pp. 79–83; and for the Glasgow 14-ft Newtonian, cf. Warner, B., “The William Herschel 14-foot telescope,” Monthly notes of the Astronomical Society of South Africa, xlvi (1987), 158–163.

  111. 111.

    Mills, A.A. & R. Hall, (op. cit. ref. 75), p. 157.

  112. 112.

    Cf. Turner, G.L’E., “James Short, F.R.S., and his contribution to the construction of reflecting telescopes,” NRRS, xxiv (1969), 91–108, plate 10, which presents a broadsheet from Short giving directions for the use of his Gregorians. About two-third of the way to the bottom of the sheet, we read: “There is a black Stroke on the Back of the great Mettal, and Care must be taken, that this Stroke always points upwards from the Hole.” Cf. also Mudge, J., (op. cit. ref. 13), pp. 339–340.

  113. 113.

    For rotational adjustment of primaries, cf. e.g. Herschel, W., “On the discovery of four additional satellites of the Georgium sidus,” PT, lxxxviii (1798), 47–79, p. 68 [TSP, ii, p. 14] and RAS MS Herschel W.1/1, p. 54. For the term “lateral faults,” cf. RAS MS Herschel W.5/14.1, section xxx, article 2, f. 131v: “When a mirror has lateral faults, they may be detected by limitting [sic] diaphragms of proper shapes… A limiting aperture of one quadrant open, the other three being excluded, is the best way to find whether a mirror has lateral faults, for if it has any the foci of the four quadrants separately taken will differ… The corner of a card, or a fine cross drawn upon it being viewed by a mirror that has lateral faults will discover them; when the perpendicular is in focus, the horizontal will be out; and vice versa.” This last test – examining the focus differences of two sharp edges or lines at right angles – is an imaging test for astigmatism. It is reasonable to conclude, therefore, that Herschel understood the concept of a toroidal mirror surface, but did not possess the terminology to name it or its imaging consequences.

  114. 114.

    Edwards, J., “An account of the cause and cure of the tremors particularly affecting reflecting telescopes more than refracting ones,” The nautical almanac and astronomical ephemeris for the year 1787, (London, 1783), pp. 51–54; and Maskelyne, N., “Remarks on the tremors peculiarly affecting reflecting telescopes more than refracting ones,” ibid., pp. 57–60.

  115. 115.

    On “cases,” cf. RAS MS Herschel W.5/14.1, section iv, article 13. For Schroeter’s description, cf. Schröter, J.H., “Darstellung des Herschelschen siebenfüβigen Teleskops mit praktischen Bemerkungen,” Beiträge zu den neuesten astronomischen Entdeckungen, (Berlin, 1788), 154–209, pp. 175–177; reproduced in Gerdes, D., (op. cit. ref. 110), pp. 71–74.

  116. 116.

    RAS MS Herschel W.1/3.1-6; and Spaight, J.T., “‘For the good of astronomy’: the manufacture, sale, and distant use of William Herschel’s telescopes,” JHA, xxxv (2004), 45–69, p. 60.

  117. 117.

    RAS MS Herschel W.5/14.1, section xxxix, article 1, f. 170r: “In the box that holds the mirror should be no pasteboard, or other thing to prevent a considerable shake which it ought to have.”

  118. 118.

    Texereau, J., (op. cit. ref. 6). pp. 123–128: “It is essential that the mounting impose no restraint whatever on the mirror disk [author’s emphasis]”; otherwise there may ensue: “severe image deterioration, caused by the resulting serious mechanical strain,” which in extreme cases may lead to “the hazard of fracture.”

  119. 119.

    On the use of three peripheral contact points, cf. Texereau, J., (op. cit. ref. 6), pp. 123–126; and Riekher, R., (op. cit. ref. 29), pp. 156–157.

  120. 120.

    Herschel, J.F.W., (op. cit. ref. 59), p. xi–xii.

  121. 121.

    Herschel, J.F.W., (op. cit. ref. 59), p. x. Edwards had already counselled likewise for much smaller mirrors in 1783: Edwards, J., (op. cit. ref. 114), pp. 53–54.

  122. 122.

    Quoted by B. Warner from the unpublished ms. notes of John Herschel to his volume of Cape results, in Warner, B., “Sir John Herschel’s description of his 20-ft reflector,” Vistas in astronomy, xxii (1979), 75–107, p. 96.

  123. 123.

    RAS MS Herschel W.5/14.2, Figure 55, discussed in RAS MS Herschel W.5/14.1, section iv, article 15, f. 38r. For an illustration of the front of the cell (with protecting cover in place) and a detailed description, cf. Herschel, W., [op. cit. ref. 3 (1795)], pp. 403–407 and Figs. 46 and 47 [TSP, i, p. 524–526].

  124. 124.

    This mirror is said by Herschel to be about 3.5-in. thick and to have weighed 2118 lb as cast. The thinner mirror also survives and is housed at the London Science Museum. For a good description of it, cf. Steavenson, W.H., “Herschel’s first 40-foot speculum,” Obs, l (1927), 114–118. According to Steavenson it is 1.9 in. thick at the periphery, was intended to be meniscus, but has a central depression of about 0.9 in. Herschel recognized that the blank was too thin ever to keep a stable figure and so he cast the second, thicker one.

  125. 125.

    Cf. also the comments of J.L.E. Dreyer about the 40-ft in the introduction to the 1912 edition of William Herschel’s scientific papers, in TSP, i, p. liv: “[A]ll the same it is likely enough that the instrument did not generally perform well. The speculum was supported in an iron ring, resting there at its lowest point and confined there by an iron cross over its back. It would seem that a speculum weighing a ton and supported in this simple manner must have been subject to considerable flexure and cannot as a rule have done justice to the skill of its maker.”

  126. 126.

    For Grubb, Romney, Rosse, and South, cf. Glass, I.S., Victorian Telescope Makers, (Bristol, 1997), especially pp. 17–22. For the origin of the whiffle-tree, cf. ref. 14 above, and also Robinson, T.R. & T. Grubb, “Description of the Great Melbourne Telescope,” PT, clix (1869), 127–161, p. 145.

  127. 127.

    Hoskin, M., [op. cit. ref. 4, (2011)], p. 172. Cf. also, South, J., (op. cit. ref. 16): “[L]et me quote the words as they escaped from Sir W. Herschel’s lips to me, nearly 20 years ago: – ‘I shall never more do anything to this instrument myself; it must be remade – the metals are spoiled, and to make new ones will be in fact remaking the instrument; and should John, after my death, attempt it, you will, I trust, do your utmost to dissuade him.’” South’s letter to the Times came in response to a call from an anonymous “Lover of Science” to obtain a government subvention or to establish a private subscription to re-erect the 40-ft (now that Sir John Herschel had returned home from the Cape of Good Hope). South counter-suggested a new mirror, for which he sent a check of £20 to the Times. John Herschel then put a stop to proceedings, writing 4 days later: “With reference to such a project, and before it goes further, I may be allowed to say that I have often and maturely considered the question of re-erecting, improving, or entirely remodelling that instrument, and have very deliberately come to the conclusion (on grounds perfectly satisfactory to myself) to take no step of the kind”: Herschel, J.F.W., “Herschel’s Telescope,” The Times of London, 10-Oct-1838 (letter to the editor), p. 5.

  128. 128.

    Ref. 118.

  129. 129.

    Examples of very close doubles include ζ Cnc, η CrB, δ Cyg, ω Leo, ξ Sco. Cf. TSP, ii, pp. 662–667.

  130. 130.

    E.g., RAS MS Herschel W.1/3.6; W.5/6; W.5/8, f. 8v-10r; & W.5/14.1, section xxxix, article 2, ff. 170v-171r. In addition, the Whipple Museum of the History of Science at the University of Cambridge (UK) has a set of instructions relating to a 7-feet telescope. Other sets also exist.

  131. 131.

    Texereau, J., (op. cit. ref. 6), pp. 297–300; Lecleire, K. & J.-M., (op. cit. ref. 66), pp. 261–263; and Suiter, H.R., (op. cit. ref. 25), pp. 111–129.

  132. 132.

    Maskelyne, N., (op. cit. ref. 114), p. 59.

  133. 133.

    For the 4.5-in. in general, cf. RAS MS Herschel W.1/13.1, S.12-S.15, a set of letters from Schroeter to Herschel. The last of these letters, dated 14-Jan-1784 announces the arrival of the mirror-set. For the 6.5-in. in general, cf. RAS MS Herschel W.1/1.1, p. 136, a letter from Herschel to Schroeter, dated 20-July-1785; and RAS MS Herschel W.1/13.1, S.16-S.27, a large set of letters from Schroeter to Herschel. A memorandum from Herschel preserved with letter S.24, says: “Sent to Mr. Schroeter in a Box…Drawing of the stand & parallelogram with an accurate description & measures of its size.” For the Darstellung, cf. ref. 115, where Schroeter reproduced Herschel’s drawing as Fig. 1. For an overview of Schroeter’s life and writings, cf. Voigt, H.-H., “Johann Hieronymus Schroeter – Lilienthal – Astronomische Gesellschaft,” Sterne und Weltraum, xxxix (2000), 1040–1047. For detailed accounts, cf. Gerdes, D., (op. cit. ref. 110); and Schumacher, H.A., “Die Lilienthaler Sternwarte,” Abhandlungen herausgegeben vom naturwissenschaftlichen Vereine zu Bremen, xi, (1890), 39–170.

  134. 134.

    Schroeter, J.H., Selenotopographische Fragmente zur genauern Kenntniss der Mondfläche, etc., (Göttingen, 1791). For the quotations of Schroeter, cf. RAS MS Herschel W.1/13.1, S.17(3), bottom: “Mein 4. füssiger Reflector hat den einzigen Fehler, daß er die Sterne der 1. und 2ten Grösse in zu vielem, wie eine kleine Fackel daranhängenden falschen Lichte, undeutlich erscheinen läßt…da das Instrument sonst so herrlich scharf und gut ist….” For “undeutlich” Schroeter has written “erndeutlich” probably in anticipation of the following word “erscheinen.”

  135. 135.

    For Schroeter’s comments and request, cf. RAS MS Herschel W.1/13.1, S.28, f. 4v-5r: “Die Doppelsterne der 2 ten Classe sehe ich sehr deutlich und äusserst scharf…; allein es hat noch den Umstand, daß es bey hellen Sternen z[um] E[xempel] α Lyrae Castor Rigel den Hauptstern nicht rund zeiget und zu viele falsche Stralen wirft, welches wol unstreitig ein Fehler des Concentrirens ist…Sollte in England vom Concentriren der Neut. Telescope eine Abhandlung oder Werkgen vorhanden seyn; so würden Ew. Wohlgeb. mich äusserst verpflichten, wenn Sie mir solches, es koste was es wolle, zu übersenden geneigten.” For Herschel’s reply, cf. RAS MS Herschel W.1/1.1, p. 157.

  136. 136.

    For the Astronomisches Jahrbuch, cf. Schwemin, F., Der Berliner Astronom: Leben und Werk von Johann Elert Bode 1747–1826, in Dick, W.R. and J. Hammel (eds), Acta historica astronomiae, xxx (2006), pp. 21–24 and 27–28. This yearbook (begun by Bode in 1774 and continued by him until 1826) combined an ephemeris, a section of essays by various authors, and news notes. It was a predecessor of the more widely known (and still current) Astronomische Nachrichten. The French astronomer, Joseph-Jerôme de Lalande (1732–1807), later said of Bode’s yearbook and its commencement: “C’est depuis ce temps-là que les astronomes sont obligés d’apprendre l’allemand; car on ne peut se passer de ce recueil [It is from that time that astronomers have been obliged to learn German; for one cannot do without this collection].” Cf. De Lalande, J.-J., Bibliographie astronomique, (Paris, 1803), p. 539. Already as an appendix to his letter of December 1786, Schroeter had sent Herschel an 8-point description of an early attempt at precise opto-mechanical alignment: RAS MS Herschel W.1/13.1, S.28, f. 7–8.

  137. 137.

    Schroeter, J.H., “Bermerkung über das Concentriren der telescopischen Spiegel,” in AJJ 1795, (Berlin 1792), 138–142, p. 138 [Gerdes, D., (op. cit. ref. 110), 106–109, p. 106]: “Es wäre zu wünschen, daß uns Herr D. Herschel mit der verbesserten parabolischen Figur, welche er den großen Spiegeln seiner Telescope giebt, und dabei auch mit der Art, wie er seine Telescope concentriret, genauer bekannt machte.”

  138. 138.

    Schroeter, J.H., (op. cit. ref. 137), p. 139 [Gerdes, D., (op. cit. ref. 110), p. 106]: “Wahrscheinlich gewann Herr Herschel dadurch wohl eben nicht mehr, sondern eher weniger, aber besseres Licht und mehr Deutlichkeit.”

  139. 139.

    RAS MS Herschel W.1/1.1, p. 198, a letter from Herschel to Schroeter dated 4-Jan-1794: “The eye glass, in the front-view must be 2 inches more than the semidiameter of the Speculum from the center of the tube, and inclined so as to be directed to the center of the Speculum; which latter, of course must be inclined in such a manner as to throw a full pencil of rays into the eye glass [emphasis added].”

  140. 140.

    Schroeter, J.H., (op. cit. ref. 137), p. 142 [Gerdes, D., (op. cit. ref. 110), p. 109]: “…als er mich vor einiger Zeit einlud, ihn zu besuchen und mit ihm zu beobachten, verlangte er, daß ich den Objectivspiegel mitbringen möchte, um ihn zu verbessern, weil er jetzt den Spiegeln eine merklich bessere Figure zu geben wisse.” Privately Schroeter told the physicist and philosopher Georg Christoph Lichtenberg in Göttingen: “In addition, I have markedly improved the 7-feet reflector by giving the large mirror an inclination of 1° 50′ to the axis of the telescope [Auch habe ich den 7f. Refl. dadurch merklich verbessert, daß ich dem grossen Spiegel eine inclination von 1° 50′ gegen die Axe des Telescops gegeben habe].” Cf. Joost, U. & A. Schöne (eds), Georg Christoph Lichtenberg Briefwechsel, Band III (1785–1792), p. 973.

  141. 141.

    For information on Schrader, cf. Leue, H.-J., (op. cit. ref. 92). Schroeter wrote about Schrader’s activity in a letter to William Herschel, dated 16-Sept-1792, RAS MS Herschel W.1/13.1, S.37, f. 1v-2r: “Desto interessanter ist es aber für mich, daß H. Schrader, Prof. der Physik und Chemie in Kiel, ein junger, thätiger und geschickter Mann, der sich zu gleichen Zweck mit könig[lichem] Urlaube von Ostern bis gegen Weihnachten bey mir aufhält, wirklich zwey ganz vortreffliche 7, einen 12 und einen 13füssigen Spiegel unter meiner Mitwirkung zu Stande gebracht hat, die sammtlich eine so genaue vortreffliche Figur haben, daß sie unter völliger Oeffnung von 6 ½, 9 and 9 ½ eng. Zollen und sehr starken Vergrösserungen ein sehr lichtvolles und deutliches Bild geben. Für mich habe ich einen 7 und den 13füssigen gewählt. [All the more interesting is it for me that Mr. Schrader, prof. of physics and chemistry in Kiel, a young, active, and skilled man, who is staying with me on a royal sabbatical for the same purpose from Easter until about Christmas, has really completed two quite excellent 7-, a 12-, and a 13-feet mirror with my collaboration, which collectively have such a precise, excellent figure, that at their full apertures of 6½, 9, and 9½ English inches and under very strong magnifications, present a very bright and clear image. For myself I have selected one 7-feet and the 13-feet.]”

  142. 142.

    For the telescopes, cf. the extracts from Schroeter’s and Schrader’s writings reprinted in Gerdes, D., (op. cit. ref. 110), p. 114–123, 126–131, and 137–204; and letters which passed between Schrader and Georg Christoph Lichtenberg in Joost, U. & A. Schöne, (op. cit. ref. 140), Band III (1785–1792), pp. 1138–1139 and 1174; and Band IV (1793–1799), pp. 61–62 and 69. For Edwards’ account of his speculum mixture containing arsenic, cf. ref. 13. Edwards revived the practice of adding arsenic, on the recommendation of Newton. Herschel avoided arsenic, wisely it seems since Edwards died from the fumes in 1784: Croarken, M., “Mary Edwards: computing for a living in 18th-century England,” IEEE Annals of the History of Computing, xxv (2003), Oct-Dec, 9–15, p. 11. Cf. also, Schrader, J.G.F., (op. cit. ref. 15), p. 13; and especially, Schroeter, J.H., Aphroditographische Fragmente zur genauern Kenntniss des Planeten Venus; sammt beygefügter Beschreibung des Lilienthalischen 27 füßigen Telescops, etc. [Aphroditographical fragments toward a more precise understanding of the planet Venus, together with an appended description of the Lilienthal 27-feet telescope, etc.], (Helmstedt, 1796), 201–250, p. 203: “Beyde [Spiegel] sind von gewöhnlicher Edwardischer, besonders aber das neuere größere von vorzüglich schöner, überaus dichter weisgläzender Composition, deren Metall mit ungefähr 5 Pfund Arsenik abgedampft ist. [Both mirrors (especially the newer larger one) are of typical Edwards composition: extremely beautiful, exceedingly compact, and white-gleaming. The metal has been volatilized with about 5 pounds of arsenic.]” This statement by Schroeter has been misunderstood in recent times to mean that the mirrors were “vapor-deposited” with arsenic when completed. But the technical term for vapor deposition in German is “aufdampfen” and not “abdampfen.” Schroeter most probably refers to the well-known volatilisation of arsenic when added to a copper-tin melt during formation of speculum. Cf. Willach, R., (op. cit. ref. 9), p. 266: “The use of arsenic also had a very old tradition. Already in early times it was well known that a small amount of arsenic mixed with the molten copper gave the alloy a white shine, making it look like silver. That technique was sometimes used to produce fake silver coins. However, the method was very dangerous because the vapor is extremely toxic and since arsenic does not melt, at a temperature of 615°C it vaporizes.” C.-S. Passemant in his treatise on making reflecting telescopes from 1738 confirms this: “…as for the arsenic, its weight is to be accounted as nothing, since the greatest part of it goes off as vapors… […pour l’arsenic, son poids n’est à compter pour rien, la plus grande partie s’en allant en fumée…].” Cf. Passemant, C.-S., (op. cit. ref. 12), p. 25.

  143. 143.

    von Zach, F.X., “Auszug aus einem astronomischen Tagebuche, geführt auf einer Reise nach Celle, Bremen und Lilienthal im September 1800,” MC, iii (1801), 476–491, p. 489–491 [Gerdes, D., (op. cit. ref. 110), p. 38]; Bessel, F.W., “Auszug aus einem Schreiben des Herrn Bessel,” in F.X. von Zach (ed), MC, xv (1807), 373–376, pp. 375–376; and de Lalande, J., Histoire abrégée de l’astronomie, depuis 1781 jusqu’à 1802, (Paris, 1803), pp. 837–838.

  144. 144.

    Bessel, F.W., (op. cit. ref. 143): “Der Opticus Gefken freute sich sehr, zu hören, daß er noch in Ihrem gütigen Andenken fortlebt. Die Vortrefflichkeit seiner Spiegel scheint jetzt den höchsten Punct erreicht zu haben, wovon der neue 15füßige Reflector des Hrn. Justizraths Schröter einen sehr redenden Beweis gibt. Sie kennen die vorzügliche Güte des hiesigen 13füßigen Telescops, und dennoch ist es gewiß, daß sich seine Wirkung gar nicht gegen die des 15füßigen vergleichen läßt. Die außserordentliche Deutlichkeit dieses schönen Reflectors, verbunden mit seiner großen Lichtstärke, machen ihn äußerst schätzbar, und man kann ihn als eine wahre Zierde des hiesigen Instrumenten-Vorraths ansehen.” For an assessment of Bessel’s life, cf. Herschel, J.F.W., A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, (London, 1847).

  145. 145.

    Bessel to Gauss, cited in Anon., Briefwechsel zwischen Gauss und Bessel, (Leipzig, 1880), pp. 232–233: “Ich zögere nicht, Ihren eben empfangenen Brief zu beantworten, da Sie eine Nachricht wegen des grossen Teleskops in Lilienthal von mir erwarten. Auch ich muss gestehen, dieses Instrument wenig zu kennen, da es für die Beobachtungen, die mich in Lilienthal vorzüglich beschäftigten, wenig Nutzen gewähren konnte. Indessen glaube ich nicht, dass seine Wirkung so sehr ausgezeichnet ist, als von der Grösse des Instruments erwartet werden sollte. Lichstärke besitzt es allerdings in einem hohen Maasse; allein grosse Deutlichkeit schien es mir nie zu haben. – Vorzügliche Instrumente der dortigen Sammlung waren zu meiner Zeit der 15füssige Reflector und der 10füssige Dollond; beide lassen alles, was ich sonst wohl von der Art gesehen habe, weit hinter sich zurück; namentlich ist der Reflector vortrefflich, oder er war es wenigstens. Auch das 7füssige Herschel’sche Teleskop ist ein gutes Instrument; das 13füssige kennen Sie Selbst. Die übrigen schienen mir immer von geringerm Werthe zu sein, obgleich Schröter oft anderer Meinung war; ich bestehe auf der meinigen auch nicht, da Schröter in dem Gebrauche der grossen Teleskope weit mehr Uebung und Erfahrung besitzt als ich. Indessen glaube ich, dass doch wohl Fälle vorkommen können, wo man das Licht, selbst auf Kosten der Deutlichkeit, gern von einer Oberfläche von 3 bis 4 Quadratfuss gesammelt haben möchte; für diese würde also das Teleskop erwünscht sein, so dass es doch wohl vermisst werden könnte, wenn Sie es nicht aufstellen liessen. Ueberhaupt glaube ich, dass Ihre Sternwarte in allen astronomischen Fällen in Deutschland die letzte Instanz werden muss; dieser Ansicht zu Gefallen würde es mich freuen, wenn Sie das Teleskop aufstellen liessen.”

  146. 146.

    Dieter Gerdes has published the original text of the leasing-agreement in (op. cit. ref. 110), pp. 213–217.

  147. 147.

    Extensive documents relating to the transference survive in Göttingen University Library.

  148. 148.

    Cf. e.g., Bessel, F.W., Untersuchungen über die scheinbare und wahre Bahn des im Jahre 1807 erscheinenen grossen Kometen [Researches on the apparent and true path of the great comet that appeared in the year 1807], (Königsberg, 1810), p. 3: “Die Lilienthaler Sternwarte war zum würdigen Empfange des Kometen vorzüglich gut ausgerüstet; denn sie enthielt, ausser den bekannten grossen und schönen Teleskopen, die recht geeignet waren, uns Aufschlüsse über die räthselhafte physische Beschaffenheit dieses Himmelskörpers zu verschaffen, einige kleinere Instrumente, die sich vorzüglich zu den Ortsbestimmungen des Kometen schickten. Die Beobachtungen zerfielen also in zwei Branchen, die wir, mein verehrter Freund der Herr Justizrath Schröter und ich, unter einander theilten. Der getroffenen Abrede zufolge, beschäftigten den Herrn S. ausschliesslich die physischen Beobachtungen, deren merkwürdigen Resultate er öffentlich bekannt zu machen jetzt im Begriff ist. Über diese schweige ich also ganz; säume aber nicht länger, das was die Ortsbestimmungen des Kometen angeht, mitzutheilen. [The Lilienthal Observatory was exceedingly well fitted out for the worthy reception of the comet. For it contained, aside from the well-known great and beautiful telescopes which were quite appropriate to provide information about the enigmatic physical nature of this celestial body, several smaller instruments which were excellently fitted to positional determinations of the comet. Thus, the observations sundered themselves into two branches, which we – my honored friend, the Justice-Counselor Schröter, and I – divided between ourselves. According to the agreement struck, Mr. Schröter busied himself exclusively with physical observations, whose remarkable results he is now on the verge of publishing. Hence, I pass over these in complete silence, but will not put off any longer communicating what pertains to the comet’s positional determinations.]” Schroeter’s companion book discussing the comet as a physical object was published as, Schroeter, J.H., Beobachtungen des grossen Cometen von 1807 in physischer Hinsicht [Observations of the Great Comet of 1807 from a physical standpoint], (Göttingen, 1811).

  149. 149.

    Gerdes, D., (op. cit. ref. 110), p. 18; Bode, J.E., AJJ 1819, (Berlin, 1816), p. 258; and on “Sir” William Herschel’s knighthood, cf. now, Hanham, A., and M. Hoskin, “The Herschel knighthoods: facts and fiction,” JHA, xliv (2013), 149–164.

  150. 150.

    Bessel, F.W., “Untersuchungen über den Planeten Saturn, seinen Ring und seinen 4ten Trabanten,” Königsberger Archiv für Naturwissenschaft und Mathematik, i (1812), 114–172, pp. 122–123: “Das Teleskop, welches ich zu meinen Messungen der Abstände des 4ten Trabanten benutzte, ist ein 15fussiger Gefkenscher Reflector von vorzüglicher Güte; der eine sehr gute Maschinerie besitzt, und sich so schnell und leicht bewegen lässt, dass es nicht sehr schwierig ist, einen Stern einige Zeit im Sehefelde relativ ruhend zu erhalten. Zu dem Reflector gehören zwei Spiegel, deren erster, obgleich er anfangs sehr vollkommen war, im Frühjahr 1806 anfing, seine Figur etwas zu verändern, und die Bilder nicht immer vollkommen deutlich zu zeigen. Herr Justizrath Schroeter, der der Ursache davon nachspürte, entdeckte sie in der nicht hinlänglichen Dicke des Metalls, die eine Biegung verursacht hatte; und gleich trug er dem Optikus Gefken die Verfertigung eines neuen Spiegels auf, der am 9 July 1806 den Platz des alten einnahm, und der als das Meisterstück seines Verfertigers angesehen werden kann. Mit ausserordenticher Lichtstärke vereinigte das 15fussige Teleskop von nun an die vollkommenste Deutlichkeit; schwerlich möchte mehr als einmal seines Gleichen in der Welt existiren.”

  151. 151.

    Some disparaging comments in the published literature about Schroeter’s telescopes (even his Newtonians) are certainly referable to observers who were not familiar with the difficulties that plague large telescopes, especially reflectors. For example, Wilhelm Olbers visited his friend Schroeter in May 1806 and observed through the 15-ft Newtonian. Olbers had long suspected that Schroeter’s anomalously large measurements of the diameters of the minor planets Ceres, Vesta, and Juno were due to problems with his reflecting telescopes (Olbers’ own instruments consisted of small refractors). And sure enough, Olbers found aberration blurs around double stars in the 15-ft which he reported confidentially to Gauss were larger than 4 arcseconds, seeming to confirm his suspicions. His letter to Gauss survives and has been published and cited to the detriment Schroeter. Yet Bessel’s discussion of this telescope makes clear that he and Schroeter were aware of the problem with the mirror and that Gefken was fabricating a replacement. Seemingly Olbers was not aware of this. But when next he returned to Lilienthal in October 1806 for another visit, Olbers discovered a very different mirror, and reported to Gauss: “There is now in Lilienthal a 15-feet telescope that surpasses everything else I have witnessed there….Never before in such a manner could I discern the separation of double stars there. [In Lilienthal giebt es jetzt ein 15 füssiges Teleskop, das noch alle übertrifft, die ich dort gesehen habe….So habe ich dort noch nie die Zwischenräume der Doppelsterne unterscheiden können.]” Cf. Oestmann, G., “Astronomischer Dilettant oder verkanntes Genie? Zum Bild Johann Hieronymus Schroeters in der Wissenschaftsgeschichte,” in Dick, W. and J. Hamel (eds), Astronomie von Olbers bis Schwarzschild, Acta historica astronomiae, xiv, (Harri Deutsch, 2002), 9–24, p. 12; and Schilling, C., Wilhelm Olbers, sein Leben und seine Werke, Band 2.1, (Berlin, 1900), pp. 300 and 312.

  152. 152.

    Schroeter, J.H., (op. cit. ref. 142), p. 224: “Diese Erfindung des Herrn D. Herschel ist meines Wissens noch nirgends umständlich genug beschreiben, und eben das hat vorher bey mir, so wie bey andern, eine etwas irrige Vorstellung veranlasset. Jetzt aber, da ich sie theoretisch und practisch näher kennen gelernt, ist sie mir so schätzbar geworden, dass ich sie bey diesem grossen Reflector seit geraumer Zeit ganz allein angewandt, den Fangspiegel ganz weggeschaffet, und mir vorgenommen habe, diesen nie wieder dabey mit anzuwenden. Eben so schätzbar scheint mir aber auch die jetzige Gelegenheit, das, was mir von dieser nützlichen Einrichtung bekannt ist, um so mehr zum Besten der Wissenschaft hier mitzutheilen, weil sie auch bey kleinern Telescopen mit Vortheil angewandt werden kann.” The front-view arrangement was used very successfully on small instruments, containing 3.9 to 10-in. mirrors, by the early American telescope maker, Amasa Holcomb. For tests of Holcomb’s telescopes, cf. Hamilton, W., “Report on Amasa Holcomb’s reflecting telescopes,” JFI, xiv (1834), 169–172; xv (1835), 11–13; and xviii (1836), 109–110 and 312; & Mason, E.P., Introduction to practical astronomy, (New York, 1841), pp. 5–20.

  153. 153.

    Herschel, W., [op. cit. ref. 3 (1795)].

  154. 154.

    Herschel, W., [op. cit. ref. 3 (1795)], p. 350 [TSP, i, p. 487].

  155. 155.

    Herschel, Mrs. J., Memoir and correspondence of Caroline Herschel, 2nd ed., (London, 1879), p. 309.

  156. 156.

    Already in October 1787, Georg Christoph Lichtenberg wrote to Schroeter wondering if some misfortune had not befallen the instrument, since no one heard any news about it: Joost & Schöne, (op. cit. ref. 140), Band III, p. 453.

  157. 157.

    Sometime around 1797, Caroline Herschel compiled a ca. 22-page manuscript catalog of notable articles and papers published in Bode’s Astronomisches Jahrbuch¸ in which on a separate sheet of paper inserted near the end, she gave a sequential listing of 38 items from Schroeter, including all those concerned with his telescopes. Cf. RAS MS Herschel C.3/6.

  158. 158.

    Schroeter, J.H., AJJ 1787, (Berlin, 1784), 253–254; idem, AJJ 1789, (Berlin, 1786), 153–154; idem, (op. cit. ref. 115); idem, AJJ 1795, (Berlin, 1792), 108–110; idem, (op. cit. ref. 137); “Descriptio telescopii xiii pedum, et observationum eius ope in Saturno et Luna institutarum,” Commentationes societatis regiae scientiarum Gottingensis, xi (1793), 32–37; idem, AJJ 1796, (Berlin, 1793), 158–160 and 226–234; idem, AJJ 1797, (Berlin, 1794), 184–203; idem, (op. cit. ref. 142); and Schrader, J.G.F., (op. cit. ref. 15). Most of these sources are reproduced in Gerdes, D., (op. cit. ref. 110), pp. 46–204.

  159. 159.

    For the circumstances surrounding the building of the 40-ft, the discovery of Saturn’s additional moons, and the excitement and expectations of the time, cf. Hoskin, M., [op. cit. ref. 4, (2011)], pp. 118–127. In Germany, as well as France and England, there was excitement, but here tinged with pride for a native son made good. Georg Christoph Lichtenberg (who was hunchbacked) declared in June 1787, that as soon as he heard that the 40-ft was finished, he would “gird his loins” and make the journey from Göttingen to Slough, because he could not die peacefully, living at that time and not seeing such a thing!: Joost & Schöne, (op. cit. ref. 140), Band III, p. 368. Schroeter repeatedly wrote to Herschel enquiring for news and stating that he would join Lichtenberg in the journey: “We Germans are extremely fervent in our wish for news about it…[Aeußerst sehnlich wünschen wir Deutschen davon Nachricht zu erhalten….”: RAS MS Herschel W.1/13.1, S.28, f. 5v. And he swooned to think of the sights to follow: “What delights and new discoveries will this astonishing tool not vouchsafe to you? Could I but once enjoy the good fortune to be present at your observations! [Welche Wonne und neue Entdeckungen wird Ihnen nicht dieses bewunderungswürdige Werkzeug gewähren? Könnte ich doch nur ein einzigesmal das Glück geniessen, Ihren Beobachungen beyzuwohnen!]”: RAS MS Herschel W.1/13.1, S.32, f. 2r.

  160. 160.

    For George August Best, cf. Jefcoate, G., “Wilhelm Philipp Best,” in Oxford Dictionary of National Biography, www.oxforddnb.com/index/101039065/Wilhelm-Best, (Oxford, 2004–13).

  161. 161.

    Herschel’s annoyance is evident, e.g., in his paper of 1793, entitled: Observations on the planet Venus,” PT, lxxxiii, 201–219 [TSP, i, 441–451], where he attacked Schroeter’s observations of Venus and suggestions of possible high mountains, and insinuated that Schroeter might have appropriated his own invention of the lamp-micrometer. In a folder of loose notes preserved in the RAS archive, Herschel wrote: “This machine is an immediate application of my lamp & disk micrometers & projection on a wall.” Cf. RAS MS Herschel W.7/14.1, f. 38v. In addition, Herschel later wrote to his friend Prof. Patrick Wilson in a letter, dated 21-Feb-1796: “I must in the next place have turned to a tedious treatise on the solar spots written but lately by Mr. Schroeter, which must infallibly have brought on a controversy, as that Gentleman has sufficiently shewn in his last paper on Venus a disposition to take hold of every opportunity to defend his erroneous as well as his good communications.” On the other hand, Herschel told Joseph Planta in 1793 that he counted himself among among Schroeter’s friends “very sincerely”: RAS MS Herschel W.1/1.1, p. 193. And in 1798 he supported Schroeter’s election to the Royal Society as a foreign fellow (Royal Society Archive item GB 117, EC/1798/05).

  162. 162.

    “Herschel’s und Schröter’s Namen werden wie Castor und Pollux am Himmel glänzen, so lange Sterne am Firmamente funkeln….” Cf. von Zach, F.X., “Joh. Hieron. Schröter, als Astronom,” Allgemeine geographische Ephemeriden, iii (1799), 549–550, p. 550 [Gerdes, D. (op. cit. ref. 110), p. 24].

  163. 163.

    Schroeter, J.H., (op. cit. ref. 142), p. 225–226: “Bey [dem Concentriren] ist überhaupt eine doppelte Reflexion der Lichtstrahlen, welche bey dem Gebrauche eines Fangspiegels Statt findet, sehr lästig, und mehrjährige Erfahrung hat mich überzeuget, daß die Theorie zwar für ein beyläufiges, keinesweges aber für ein pünktlich genaues Concentriren hinreiche. Gewöhnlich muss man zuletzt, wenn man einen bey der besten Figur beyder Spiegel oft übrig bleibenden geringen Schimmer und entfernte Spuren eines doppelten Bildes wegbringen, und die vollkommene Schärfe und Deutlichkeit erhalten will, zu mannichfachen, oft sehr viel Zeit und Geduld erfordernden Experimenten seine Zuflucht nehmen, wordurch die noch übrige, theoretisch unentdeckbare geringe Ungenauigkeit in der Lage beyder Spiegel und des Augenglases vollends gehoben wird. Natürlich nimmt aber diese Schwierigkeit zu, je größer ein Reflector und die Lichtmenge ist, welche auf die Axe des Augenglases concentrirt werden muss, wo die geringste Ungenauigkeit in der Lage der Spiegel das Bild undeutlich und den Reflector unbrauchbar macht. Wie gross also diese Schwierigkeit und Beschwerlichkeit vollends bey einem 27füßigen Reflector werden könne, welcher der Feuchtigkeit und Trockniss, Wärme und Kälte und dabey zwischendurch heftigen Winden in völlig freyer Luft ausgesetzt bleiben muss, wird der practische Kenner am richtigsten beurtheilen. Schon bey meinem 13füßigen, dessen Spiegel sich bey dem ersten Versuche auf den Himmel unmerklich verrückt hatten, mußte ich verschiedene Wochen mit Experimenten zubringen, einen geringen Nebenschimmer oder doppeltes Bild wieder weg zu schaffen, welches den Reflector bey starken ihm sonst sehr angemeßen Vergrößerungen unbrauchbar machte. Wie lästig können also nicht dergleichen Fälle vollends bey einem so großen, der freyen Luft ausgesetzten Instrumente werden, wo bey aller Festigkeit und Dauer der Einrichtung eine so unmerkliche Verrükung viel leichter vorkommen kann?”

  164. 164.

    Schroeter, J.H., (op. cit. ref. 142), p. 226–227: “Allem dergleichen Unheile wird aber durch Wegnehmung des Fangspiegels und der damit verbundenen zweyfachen Reflexion, wenigstens größentheils und so sehr vorgebeugt, daß ich…in etlichen Minuten eben so gut zu concentriren vermögend bin, als ich es unter Anwendung des Fangspiegels vielleicht in eben so viel Tagen nicht seyn würde…Der wichtigste Umstand ist aber, daß durch die zweyte Reflexion des Fangspiegels immer einiges und desto mehr Licht zerstreuet wird und verlohren geht, je weniger seine Figur und seine Lage gegen den Objectivspiegel genau ist. Wie schwer es aber sey, dem Fangspiegel nach der Neutonischen Einrichtung eine vollkommen plane Fläche zu geben, und ihn unter Beybehaltung des Parallelismi pünctlich genau auf 45° zu incliniren, ist practisch bekannt genug.”

  165. 165.

    Schrader, J.G.F., (op. cit. ref. 15), pp. 16–17: “Zum Beschlus dieses kleinen Aufsazes will ich noch ein Paar Bemerkungen hinzufügen. Jeder, der mit praktischen Kentnissen in der Konstruktion der reflektirenden Fernröhre versehen ist, wird wol wissen, welche mühsame und Geduld ermüdende Arbeit das gehörige Centriren der Spiegel sei. Man verrichte diese Arbeit nach allen praktischen Regeln noch so genau, so findet man, daß es zulezt noch auf eine Kleinigkeit in der Stellung ankomme, in die der Spiegel versezt werden mus, um bei zunehmenden Vergrösserungen stets hinlängliche Schärfe zu zeigen. Diese Kleinigkeit in Veränderung der Lage zu finden, sucht man oft viele Wochen ja Monate lang vergebens, bis sie ein glükliches Gerathewohl an die Hand giebt. Oftmals ist auch eine nicht völlig vollkommene Figur des Spiegels Ursache, daß die richtigste Stellung nicht gerade die grösste Schärfe gewährt. Man findet unter diesen Umständen stets einen schwachen Schimmer, der die vollkommenste Deutlichkeit, zumal bei Spiegeln von grossem Durchmesser und bei starken Vergrösserungen hindert. Wahrscheinlich verursachen dies diejenigen Lichtstrahlen, die der Spiegel wegen seiner wiewol öfters nur sehr geringen Unvollkommenheit nicht in einem Punkte vereinigen kan. Ungerne nimt man, zumal wenn man überzeugt ist, daß die Figur des Spiegels der Parabel sehr nahe gekommen sei, zu den sogenanten Blendungen seine Zuflucht, die nothwendig dem Spiegel Licht rauben…Hier zeigt es sich oft, daß eine etwas wenig schiefe Stellung des Objektivspiegels alle erwünschte Schärfe gewährt. Es scheint mir, als wenn dadurch die unrichtig zurükgeworfenen Lichtstralen gleichsam abgeschnitten und verhindert würden ins Auge zu kommen. Allein man irrt sich oft eben so sehr, wenn man diesen Umstand einer Unrichtigkeit der Figur allein zuschreiben wollte. Denn man hat auch andere praktische Regeln, durch welche man sich von der guten Figur des Spiegels überzeugen kan; und daher mus, wie sich auch schon aus den Grundsäzen der höheren Optik erläutern lässt, die kleinste unrichtige Stellung beider, des Objektiv- und Okularspiegels, gegen einander schon allein eine Verminderung der Schärfe bewirken. Herschel verdient daher vielen Dank, daß er die mühsame Arbeit des Centrirens durch Weglassung des Okular- oder Fangspiegels und durch eine seitwärts gerichtete Neigung des Objektivspiegels sehr erleichtert hat….” This essay was noticed in England and a synopsis published in translation: Schrader, J.G.F., “Description of the mechanism of a reflecting telescope twenty-fix feet in length, constructed near Kiel in Holstein,” Philosophical Magazine, i (1798), 113–118.

  166. 166.

    William Kitchiner, the Regency telescope connoisseur, stated: “The Proportion fixed by those Experienced Makers of Reflectors Messrs. Tulley, is one Inch of Aperture to one foot of Focal length. They have assured me that they cannot make them shorter, without the Instrument being much less perfect.” Cf. Kitchiner, W., (op. cit. ref. 69), p. 76. For Charles Tulley and his sons, cf. King, H., The history of the telescope, (London, 1955), pp. 192–196. Cf. also, the Rev. William Pearson’s account of Herschel’s 40-ft (written in consultation with Herschel): “It was not to be expected that a speculum of such large dimensions could have a perfect figure imparted to its surface, nor that the curve, whatever it might be, would remain identically the same in changes of temperature; therefore we are not surprised when we are told, that the magnifying powers used with the telescope seldom exceeded 200, the quantity of light collected by so large a surface being the principal aim of the maker [emphasis added],” in Pearson, W., (op. cit. ref. 4), pp. 74–75.

  167. 167.

    Oxmantown, Lord, (op. cit. ref. 13), p. 524.

  168. 168.

    On the large 10-ft Newtonian, cf. Bennett, J.A., (op. cit. ref. 1), pp. 95–97; and Hoskin, M., [op. cit. ref. 4, (2011)], pp. 173–174. In his polishing log, Herschel also referred to it as his large “X feet.” Cf. RAS MS Herschel W.5/12.4, Exps 403–462.

  169. 169.

    Referring to Herschel, W., “Astronomical observations relating to the sidereal part of the heavens, etc.,” PT, civ (1814), 248–284, pp. 276–277 [TSP, ii, pp. 520–541, pp. 536–537]. The words quoted appear in RAS MS Herschel W.5/8, f. 8r.

  170. 170.

    Cf. Herschel, W., “On the power of penetrating into space by telescopes, etc.,” PT, xc (1800), 49–85 [TSP, ii, pp. 31–52].

  171. 171.

    RAS MS Herschel W.1/4.4, f. 1v-2r. Cf. also, Maurer, A., “Lucien Bonaparte and his Herschel telescopes,” Journal of the Antique Telescope Society, xxxiii (2011), 3–5.

  172. 172.

    On South and his telescopes, cf. Hoskin, M., “Astronomers at war: South v. Sheepshanks,” JHA, xx (1989), 175–212; and Herschel, J.F.W. & J. South, “Observations of the apparent distances and positions of 380 double and triple stars, etc.,…Also a description of a five-feet equatorial instrument employed in the observations,” PT, cxiv (1824), 1–412, pp. 11–12. John Herschel used the Cauchoix objective to discover the sixth star of the Trapezium, θ Orionis: cf. Anon., “Report of the Council of the Society to the tenth annual general meeting, held this day,” MNRAS, i (1831), 151–156, p. 153, footnote *.

  173. 173.

    South, J., “The Earl of Rosse’s Leviathan telescope,” The Times of London, 16-Apr-1845 (letter to the editor), 8–9, p. 8. Paraphrased in American journal of science and arts, xlix (1845), 221–227. Partially reprinted as idem, “Auszug aus einem Berichte über Lord Rosse’s großes Telescop, etc., AN, xxiii (1846), col. 113–118.

  174. 174.

    He is known to have visited in 1820 and 1821 and to have looked through the 20-ft. Cf. Hoskin, M., [op. cit. ref. 4 (2011)], pp. 183–185.

  175. 175.

    Robinson, T.R., “On Lord Rosse’s telescope,” Proceedings of the Royal Irish Academy, iii (1847), 114–133, pp. 131–132.

  176. 176.

    Cf. Herschel, J.F.W., “A synopsis of all Sir William Herschel’s micrometrical measurements and estimated positions, etc.,” MmRAS, xxxv (1867), 21–136, pp. 34 (γ Leonis) and 64 (a second companion much further from ζ Orionis); and Dawes, W.R., “Catalogue of micrometrical measurements of double stars,” ibid., 137–449, pp. 327–328 and 347–348.

  177. 177.

    Herschel, W., “Experiments for ascertaining how far telescopes will enable us to determine very small angles, and to distinguish the real from the spurious diameters of celestial and terrestrial objects, etc.,” PT, xcv (1805) 31–64, pp. 31–32 [TSP, ii, 297–316, pp. 297–298]. John Herschel assigned as a limit “…for the generality of eyes, an angle of about 2½ or 3 minutes….” Cf. Herschel, J.F.W., (op. cit. ref. 13), p. 84.

  178. 178.

    Herschel’s advice to Schroeter is contained in his letter of 4-Jan-1794. Cf. ref. 139 (above). For the clearance distance of the 40-ft, cf. Herschel, W., [op. cit. ref. 3 (1795)], p. 383 [TSP, i, p. 510].

  179. 179.

    Cf. Section 7.4, and Wilson, R.N., (op. cit. ref. 45), pp. 89–90.

  180. 180.

    E.g., RAS MS Herschel W.5/12.1, Exp. 357; W.5/12.2, Exp. 145; W.5/12.3, Exp. 355; and W.2/1.13, f. 31r (“25 ft. reflector”). This contrasts with his Newtonians. For example, on 21-July-1801 Herschel wrote of the 7-ft Newtonian that he was constructing for the King of Spain (RAS MS Herschel W.5/12.3, Exp. 590): “…the stars of the first magnitude were brought to points [emphasis added].” Cf. also, W.5/12.3, Exp. 109 (another 7-ft Newtonian): “It gives a fine well determined point for a star of the 1st magnitude.”

  181. 181.

    Herschel, J.F.W., (op. cit. ref. 27), pp. 403–404. John says here “a little distortion.” Later in his career he seems to have changed his mind, calling the “distortion” much increased. Cf. ref. 103.

  182. 182.

    Proctor, R.A., “The Rosse telescope set to new work,” Fraser’s magazine for town and country, lxxx (1869), 754–760, p. 755.

  183. 183.

    South, J., (op. cit. ref. 173), p. 8.

  184. 184.

    http://www.gmto.org/

  185. 185.

    Coddington, H., (op. cit. ref. 103), p. 34, note †.

  186. 186.

    Herschel, J.F.W., (op. cit. ref. 13), p. 81.

  187. 187.

    Cf. ref. 103.

  188. 188.

    For 157× cf. Herschel, W., (op. cit. ref. 2), p. 457 [TSP, i, p. 260]; for 189× cf. RAS MS Herschel W.2/4, f. 1v; and for 183× cf. the text below at footnote 194.

  189. 189.

    Herschel, W., (op. cit. ref. 170), pp. 53 and 66 [TSP, ii, pp. 33 and 41].

  190. 190.

    Herschel, W., (op. cit. ref. 2).

  191. 191.

    RAS MS Herschel W.2/3.6, sweep 600 (memorandum).

  192. 192.

    Brühl, H.M von, “Astronomische Beobachtungen und Nachrichten aus England,” in J.E. Bode (ed), AJJ 1790, (Berlin 1787), p. 175: “Herr Herschel wird bald mit seinem 40schuhigen Fernrohr zu stande kommen….Man sollte vermuthen, daß eine so merkliche Beugung der Stralen ein undeutliches Bild darstellen müsse. Allein Herr Herschel versichert, daß damit der Deutlichkeit kein merklicher Eintrag geschehe und dabey viel Licht erspart werde.” For Brühl, cf. Brosche, P., Der Astronom der Herzogin, Acta historica astronomiae 12, 2nd ed., (Harri Deutsch, 2008), pp. 35–37.

  193. 193.

    Schrader, J.G.F., (op. cit. ref. 15), p. 17: “Herschel verdient daher vielen Dank, daß er die mühsame Arbeit des Centrirens durch Weglassung des Okular- oder Fangspiegels und durch eine seitwärts gerichtete Neigung des Objektivspiegels sehr erleichtert hat; wiewol dieses nur bei grossen Teleskopen anwendbar ist, weil der Schatten von dem Kopfe des Beobachters den kleinen Spiegeln zu viel Licht nehmen würde.”

  194. 194.

    Probably Schroeter refers here to the axis of the cylinder forming the body of the secondary mirror (cf. Fig. 4.20c). This axis should be made parallel and coincident to the optical axis of the Newtonian primary mirror.

  195. 195.

    Schroeter, J.H., (op. cit. ref. 142), pp. 224–227: “Diese Erfindung des Herrn D. Herschel ist meines Wissens noch nirgends umständlich genug beschrieben, und eben das hat vorher bey mir, so wie bey andern, eine etwas irrige Vorstellung veranlasset. Jetzt aber, da ich sie theoretisch und practisch näher kennen gelernt, ist sie mir so schätzbar geworden, daß ich sie bey diesem grossen Reflector seit geraumer Zeit ganz allein angewandt, den Fangspiegel ganz weggeschaffet, und mir vorgenommen habe, diesen nie wieder dabey mit anzuwenden. Eben so schätzbar scheint mir aber auch die jetzige Gelegenheit, das, was mir von dieser nützlichen Einrichtung bekannt ist,…zum Besten der Wissenschaft hier mitzutheilen….

    Vornehmlich wird aber der Nutzen dieser einfachen Einrichtung…durch eine verhältlich grössere Lichtstärke und Schärfe einleuchtend. Wie oben bemerkt ist, werden die sämmtlichen, durch die Oeffnung des Rohrs auf alle Theile des gleich grossen Objectivspiegels fallenden Lichtstrahlen in einen vollkommen runden vollen Lichtbüschel des Augenglases concentrirt, so daß nicht einmahl das Licht verlohren geht, welches sonst nach der Gregorianischen, Neutonischen und Cassegrainischen Einrichtung, bey dem Einfallen durch den mitten befindlichen kleinen Fangspiegel benommen wird. Der wichtige Umstand ist aber, daß durch die zweyte Reflexion des Fangspiegels immer einiges und desto mehr Licht zerstreuet wird und verlohren geht, je weniger seine Figure und seine Lage gegen den Objectivspiegel genau ist. Wie schwer es aber sey, dem Fangspiegel nach der Neutonischen Einrichtung eine vollkommen plane Fläche zu geben, und ihn unter Beybehaltung des Parallelismi pünctlich genau auf 45° zu incliniren ist practisch bekannt genug. Daher ist das licht mit einem Herschelischen Front view, bey dem dieser Nachtheil wegfällt, viel stärker und weiser, und das Bild erscheinet merklich schärfer, als bey Dazwischenkunft eines Fangspiegels, so daß Herr D. Herschel das Licht beynahe doppelt so stark schätzet. Gewiß ist es, daß ich es ebenfalls weit stärker, als mit einem Fangspiegel, und unter 183 maliger Vergrösserung…das Bild ganz ungleich lichtvoller, als unter nur 136 maliger Vergrösserung des 13 füssigen Reflectors finde.” The first paragraph of this quotation was previously cited in endnote 152 above.

  196. 196.

    RAS MS Herschel W.2/1.12, f. 92r.

  197. 197.

    Not “Vol. 2d” as he mistakenly states in his observing journal.

  198. 198.

    Herschel’s observing records show that he often changed telescopes and even mirrors within his telescopes on one and the same night, in hurried activity.

  199. 199.

    For Zach, cf. Brosche, P., (op. cit. ref. 192).

  200. 200.

    Clerke, A.M., A popular history of astronomy in the 19th century, 4th ed., (London, 1902), pp. 71–72 and Brosche, P., (op. cit. ref. 192), pp. 133–140. For the term “celestial police [Himmels-Polizey],” cf. von Zach, F.X., “Über einen zwischen Mars und Jupiter längst vermutheten, nun wahrscheinlich entdeckten neuen Hauptplaneten unseres Sonnen-Systems,” MC, iii (1801), 592–623, p. 603.

  201. 201.

    von Zach, F.X., (op. cit. ref. 143), pp. 487–489 [Gerdes, D., (op. cit. ref. 110), pp. 34–36]: “Einige heitere Stunden in ein Paar Nächten gewährten uns das Vergnügen, in Gesellschaft des O. A. R. v. Ende und Dr. Olbers, die Wirkungen der vortrefflichen Sehewerkzeuge der Lilienthaler Sternwarte zu erfahren. Wir waren so glücklich, mit denselben manche Musterung am Himmel vorzunehmen, und einige der zärtesten himmlischen Gegenstände, feine Doppelsterne, planetarische Nebelflecke, Sternringe u.s.w. so wie auch die damahls sichtbaren Planeten, vorzüglich den Mars, durch alle Abstufungen dieser herrlichen Instrumente in Betrachtung zu nehmen. Es war wahre Wonne für mich, und ein unbeschreibliches Vergnügen, mich mit eignen Augen von der prachtvollen Wirkung dieser Gesichtswerkzeuge überzeugen zu können. Mit Entzücken und Bewunderung verweilten wir bey Betrachtung der merkwürdigsten himmlischen Gegenstände, und von einem Fenrohre eilten wir zu dem anderen, um sie zu vergleichen und zu prüfen. Aber offenherzig muß ich hier gestehen, daß ich jederzeit am liebsten zu dem 13 füßigen Reflector (den 27 füßigen nicht ausgenommen) zurückkehrte, und aufrichtig lege ich hier das öffentliche Geständnis ab, daß meine Augen den Himmel noch nie mit einem bessern, deutlichern und bestimmtern Werkzeuge beschaut haben. Besonders blickten mir die Planeten Jupiter und Mars, mit diesem vortrefflichen Teleskope besehen, mit einer solchen Schärfe und Deutlichkeit, wie man zu sagen pflegt, bis zum Greifen ins Gesicht, und hinterließen einen unauslöschlichen Eindruck dieses herrlichen Anblicks.

    Mit dem 27 füßigen Reflector hatten wir, ohne Fangspiegel, mit bloßer front-view, einen prachtvollen Blick auf die Milchstraße. Wir ließen diesen großen Naturgegenstand Stunden lang die Musterung passiren, ergötzten und weideten uns mit stiller Betrachtung dieser erhabenen Naturscenen, und mit aufmerksamer Anhörung der lehrreichen Bemerkungen unsers gastfreundlichen Führers, der uns ein so großes, genußreiches Vergnügen bereitete....

    Dicht mit Sternen war das Feld des Oculars auf jeden Blick übersäet; eine gedrungene Gruppe eines vorübereilenden Heeres von Welten machte unaufhörlich einer viel gedrungeren Platz. Selbst da, wo die Sterne weniger zahlreich schienen, blinkten bey näherer Betrachtung noch die feinsten matten Lichtpünktchen, wie Sand am Meer, aus dem Hintergrunde hervor….

    Solche Erfahrungen und Empfindungen mußten natürlich den heißesten Wunsch und das sehnlichste Verlangen nach einem so lichtstarken vortrefflichen Reflector in mir erregen, wie oben angeführter 13 füßiger, in Lilienthal verfertigter; gewiß ein in seiner Art vollkommenes, und nicht leicht zu übertreffendes optisches Werkzeug. Nach meiner Zurückkunft bewilligten Sr. Durchlaucht der Herzog von Gotha, auf meine Bitte und Vorschlag, sogleich die Anschaffung eines solchen 13 bis 15 füßigen Reflectors für die wahrhaft fürstliche Seeberger Sternwarte, und der O. A. S. hatte die Güte, den großen Spiegel zu demselben unter seiner Leitung und Aufsicht sogleich in Arbeit nehmen zu lassen.”

  202. 202.

    Steinicke, W., Observing and cataloguing nebulae and star clusters, (Cambridge, 2010), p. 43. On von Hahn’s 20-ft telescope, cf. also Bode, J.E., “Verzeichniß der vorzüglichsten in dem astronomischen Salon des Herrn Erblandmarschal von Hahn zu Remplin befindlichen Instrumente,” AJJ 1797, (1794), 240–244, pp. 242–243.

  203. 203.

    For general discussions of seeing and its effects on telescopes, cf. Texereau (op. cit. ref. 6), pp. 307–326; Suiter, H.R., (op. cit. ref. 25), pp. 139–154; and MacRobert, A.M., “Beating the Seeing,” Sky and Telescope, lxxxix, (April 1995), 40–43.

  204. 204.

    Proctor, R.A., (op. cit. ref. 182), p. 755.

  205. 205.

    Ellery, R.L.J., Observations of the southern nebulae made with the Great Melbourne Telescope from 1869 to 1885, part i., (Melbourne, 1885), p. 4.

  206. 206.

    Schroeter, J.H., (op. cit. ref. 142), p. 228 [Gerdes, D., (op. cit. ref. 110), p. 183]: “So viel schließlich die Kraft dieses Reflectors betrifft, hat es zwar seine völlige Richtigkeit, daß, wie sich auch Herr D. Herschel äußert, eine zu große Oeffnung eines 20- und mehrfüßigen Reflectors der größten möglichen Deutlichkeit weit öfterer und weit mehr nachtheilig werden könne, als eine kleine eines mittelmäßigen Telescops; weil nicht nur eine ungleich größere Menge von Lichtstrahlen sehr genau concentriret werden müssen, sondern auch die Luft- und Dunstsäule, durch welche sie bis zum Telescope und Spiegel dringen, in ihrem Durchmesser beträchtlich größer ist, und eine gleiche Temperatur eines so großen Spiegels und der innern Luft des Rohrs mit der äußern oft weit langsamer zu erhalten ist; als wodurch natürlich bey ungünstiger Witterung, besonders dann, wann die Atmosphäre in Gährung ist, das sogennate Flimmern oder Beben des Bildes sehr vermehret werden muß. Allein kein geübter Beobachter wird auch wohl je Lust haben, einen so großen Reflector bey ungünstiger Luft zu brauchen, um damit mehr Beobachtungen über die Modification der Atmosphäre, als über den Himmel zu machen….Wahrheit ist und bleibt es freylich, daß ein völlig zweckmäßiger Gebrauch eines so grossen telescopischen Körpers bey der besten denkbaren mechanischen Einrichtung dennoch weit langsamer, eingeschränkter und überhaupt größern Unbequemlichkeiten unterworfen sey; allein dagegen wird auch bey recht günstiger Witterung eine weit größere Lichtstärke und Schärfe dem Beobachter desto größere, wenn gleich seltenere Vortheile gewähren. Wenigstens halte ich mich überzeuget, daß die Wirkung dieses Reflectors meiner Erwartung völlige Genüge leiste, daß er nach wiederholter Vergleichung mit einem sonst so herrlichen 13füßigen, mehr als zweymal so viel Lichtstärke habe, und gegen diesen gewiß reichlich eben so viel kraftvoller sey, als es der 13füßige gegen einen 7füßigen ist.”

  207. 207.

    Herschel, W., “On the rotation of the planet Saturn upon its axis,” PT, lxxxiv (1794), 48–66, p. 50, footnote * [TSP, i, 458–469, p. 459, footnote ‡]. Cf. also Herschel, W., (op. cit. ref. 170), p. 80–81 [TSP, ii, 49].

  208. 208.

    RAS MS Herschel W.1/4.4, f. 2r.

  209. 209.

    Cf. Herschel, W., (op. cit. ref. 207), p. 51, footnote [TSP, i, p. 460, footnote *]; and for Gauss, cf. Anon., (op. cit. ref. 145), p. 232. Note that the numbers given here for the absolute angular blur sizes of the aberrations (derived from ray-tracing in ZEMAX™ optical design software) differ substantially from the equivalent numbers found in Wilson, R.N., (op. cit. ref. 45), p. 19. In emails with the author during 2008–2009, Wilson acknowledged his numbers to be in error. They are many times too small.

  210. 210.

    For “encircled energy,” cf. Smith, G.H., (op. cit. ref. 24), p. 160. For stray light and baffling, cf. Rutten and van Venrooij, (op. cit. ref. 24), pp. 227–234.

  211. 211.

    For an illustration of an unbaffled Gregorian-cum-eyepiece containing an eye-hole, cf. Pearson, W., (op. cit. ref. 4), plate xxvii, Fig. 2. For the eye-hole of a Newtonian-cum-eyepiece, cf. Fig. 4.2 of the present work.

  212. 212.

    Cf. Coddington, H., (op. cit. ref. 103), p. 40, footnote *: “In applying [an] eye-piece to Gregory’s telescope, it is found necessary to put a cap over the eye-glass, with an aperture just sufficient to let the effective pencils pass out to the eye, this being the only means of avoiding the unpleasant effect of stray light coming through the eye-piece without having been properly reflected at the mirrors.” On the eye-holes (or “eyestops”) of the Great Melbourne Telescope, cf. Robinson, T.R. & T. Grubb, (op. cit. ref. 126), p. 134; and idem et al., Correspondence concerning the Great Melbourne Telescope, iii, (London, 1871), p. 58. For Herschel’s enlarging and repositioning of eye-holes, cf., “A series of observations of the satellites of the Georgian planet, etc.,” PT, cv (1815), 293–362, p. 297 [TSP, ii, 542–574, p. 544]: “The hole through which [light rays] pass in coming to the eye, should be much larger than the diameter of the optic pencils, and considerably nearer the glass than their focus; for the eye ought on no account to come into contact with the eye piece….” For Herschel’s advice to his friend, Alexander Aubert about Cassegrainian or Gregorian telescopes, cf. RAS MS Herschel W.1/1, pp. 27–28: “The lenses will need no guard or cap to screen the eye from light as they are to be used in the night time….” Edwards and Maskelyne also inveighed against eye-holes: cf. Edwards, J., (op. cit. ref. 114), pp. 52–53; and Maskelyne, N., (op. cit. ref. 114), pp. 58 and 60, and Maskelyne noted – already in 1783 – that Herschel did not use them.

  213. 213.

    For a framework tube, cf. William Lassell’s 48-in. Newtonian used on Malta in the 1860s, as shown in King, H., (op. cit. ref. 166), p. 221.

  214. 214.

    Cf. King, H., (op. cit. ref. 166), pp. 125 and 208; Rosse, Earl of, (op. cit. ref. 14), plate xxiv, Figs 5 and 7.

  215. 215.

    Oxmantown, Lord, (op. cit. ref. 13), p. 524.

  216. 216.

    Robinson, T.R, (op. cit. ref. 175), p. 132.

  217. 217.

    RAS MS Herschel W.5/12.1, pp. 7–8.

  218. 218.

    RAS MS Herschel W.5/12.1, pp. 22–23 and 30.

  219. 219.

    For the dictum, cf. ref. 67. For an early use of a stop, cf. RAS MS Herschel W.5/12.1, p. 100, exp. 336.2 (20-Jan-1789): “I tried the [20-ft] speculum in the evening on Jupiter and with 12 inch [sic] open saw that planet better than ever I have seen it before.” Note that the outer 3-inch annulus of this mirror was at the time known to have a defective figure. Thus, when stopped down it gave a splendid image – even better, it seems, than his smaller Newtonians.

  220. 220.

    For Schrader cf. ref. 165; for Schroeter ref. 138.

  221. 221.

    For the letter to Wilson, cf. RAS MS Herschel W.1/1, pp. 255–256. For the 24-inch testing diaphragm, cf. RAS MS Herschel W.5/2.1, p. 124, exp. 392.

  222. 222.

    RAS MS Herschel J.1/9, p. 8. RAS MS Herschel W.4/31.2 contains a large set of diaphragms labelled “10 feet gaging powers.”

  223. 223.

    For John’s observation logbook showing his interest in diffraction patterns, cf. RAS MS Herschel J.1/9, f. 15r-26v, dated from April 1822 to October 1823. For his discussions and illustrations in the Treatises on physical astronomy, light and sound, cf. Herschel, J.F.W., (op. cit. ref. 27), pp. 491–493 and plates 9–10.

  224. 224.

    An hexagonal aperture was mentioned in 1867 by Dawes, W.R., (op. cit. ref. 176), p. 155. In recent times, it has been recommended by Sidgwick, J.B., Amateur astronomer’s handbook, 4th ed., (London, 1979), p. 464; and Jones, K.G. (ed.), Webb Society deep-sky observer’s handbook, vol. 1, (New Jersey, 1979), pp. 18 and 22. The present author routinely uses one on his 8-in. and 11-in. refractors.

  225. 225.

    Cf. Warner, B., (op. cit. ref. 122).

  226. 226.

    One stricken comment of interest in the present context states: “My principal object being the discovery of new nebulae and the determination with greater precision of the places of known ones; when objects of that nature were to be expected, little leisure was allowed for a minute examination of stars, especially on new ground. But in regions which had been once or twice well swept, or where nebulae were comparatively thinly scattered or altogether absent, stars down to the 6th or 7th magnitudes were seldom finally dismissed from the field of view till they had undergone the application of one or more of the diaphragms whether circular or triangular (almost universally the latter) with or without increased magnifying power according to the state of the air. To have executed a review with the 20-feet reflector expressly for the detection of close double stars would have required some additional years.” Cf. Herschel, J.F.W., “Description of the 20-feet reflector [with figures],” Box W0106 -W0195, Folder WO147, p. 29.

  227. 227.

    Warner, B., (op. cit. ref. 122), pp. 101–102.

  228. 228.

    Herschel, J.F.W., “Observations of nebulae and clusters of stars, made at Slough, with a twenty-feet reflector, between the years of 1825 and 1833,” PT, cxxiii (1833), 359–505.

  229. 229.

    Herschel, J.F.W., “Account of some observations made with a 20-feet reflecting telescope, etc.,” MmRAS, ii, part ii (1826), 459–497, pp. 459–460. Cf. also, idem, “Approximate places and descriptions of 295 new double and triple stars, etc.,” MmRAS, iii, part i (1827), 47–63; idem, “Observations with a 20-feet reflecting telescope-third series, etc.,” MmRAS, iii (1829), 177–213; idem, “Fourth series of observations with a 20-feet reflector, etc.,” MmRAS, iv (1831), 331–378; idem, “Fifth catalogue of double stars, etc.,” MmRAS, vi (1833), 1–81; and idem, “Sixth catalogue of double stars, etc.,” MmRAS, ix (1836), 193–204.

  230. 230.

    Herschel, J.F.W., “Extract of a letter from Sir John Herschel to Francis Baily, Esq., dated Cape of Good Hope, October 22, 1834,” The London and Edinburgh philosophical magazine and journal of science, vi (1835), 450–452, p. 452.

  231. 231.

    Equations derived from Wilson, R.N., (op. cit. ref. 45), p. 80.

  232. 232.

    Cf. TSP, i, p. lv.

  233. 233.

    RAS MS Herschel W.5/11.3, pp. 8–9.

  234. 234.

    For the price, cf. TSP, i, p. l.

  235. 235.

    Herschel gave similar instructions to the Russian government of Catherine the Great about the 20-ft front-view that they purchased in the 1790s. Their instrument, however, was not fitted for an aperture stop since they also bought a standard 10-ft Newtonian, and there was little to be gained by the complication of a diaphragm.

  236. 236.

    Cf. Hoskin, M., [op. cit. ref. 4, (2011)], p. 155–156; and Planesas, P., “Elementos ópticos del telescopio de Herschel de 25 pies del Observatorio Astronómico de Madrid,” Observatorio Astronómico Nacional Informe técnico OAN 2001-14, (Madrid, 2001).

  237. 237.

    Dobbins, T.A., “A folded Herschelian reflector,” Sky and telescope, cvii, (March 2004), 132–135, p. 135.

  238. 238.

    E.g., Pawlick, J.R., “An unusual off-axis reflector,” Sky and telescope, xxxii, (1966), 231–232; and idem, “A folded Herschelian off-axis reflector,” Sky and telescope, xxxix, (1970), 191–192.

  239. 239.

    Lampert, G., “Some notes on the performance of a 155mm f/11,75 Herschelian Telescope,” (2009). Report in the author’s possession.

  240. 240.

    Schrader, J.G.F., (op. cit. ref. 15), pp. 17–18.

  241. 241.

    Schrader, J.G.F., (op. cit. ref. 15), p. 18.

  242. 242.

    On Šafařik, cf. Polášek, C., “The 8-inch Alvan Clark object glass at the Ondřejev Observatory,” JBAA, cxi, 3 (2001), 145–149.

  243. 243.

    Anon., “Bericht über die Versammlung der Astronomischen Gesellschaft zu Berlin, 1879 September 4 bis 8; Dritte Sitzung, Montag Sept. 8,” Vierteljahrschrift der Astronomischen Gesellschaft, xiv (1879), 340–356, p. 347: “Was den zweiten Punkt betrifft, so hat der Vortragende zuerst die Herschel’sche Frontview-Construction studirt und gefunden, dass die Verschlechterung der Bilder, welche durch die Neigung des Spiegels gegen die Axe entsteht, und welche bis jetzt diese Construction nur für schwache Vergrösserungen brachbar machte, durch Neigung der Oculare fast völlig gehoben und das Bild ungemein verbessert werden kann.”

  244. 244.

    Schroeder, H., “The oblique Cassegrainian telescope,” English mechanic and world of science, mdcxxviii (June 5, 1896), 353–354, p. 354. On Schroeder, cf. Riekher, R., (op. cit. ref. 29), pp. 201–203 and von Rohr, M., “Zur Erinnerung an Hugo Schröder,” Central-Zeitung für Optik und Mechanik, xlviii (1927), 275–277.

  245. 245.

    Ingalls, A.G., Amateur Telescope Making, (New York, 1935), 450; reprinted in ATM, i, 515.

  246. 246.

    Herschel, W., (op. cit. ref. 5), p. 297–298 [TSP, ii, p. 544].

  247. 247.

    Herschel, W., (op. cit. ref. 5), p. 298 [TSP, ii, p. 545].

  248. 248.

    Cf. Smith, G.H., et al., (op. cit. ref. 24), pp. 323–371 and 564–567.

  249. 249.

    Cf. Taylor, H.D., The adjustment and testing of telescope objectives, 4th ed., (Newcastle, 1946), pp. 18–19.

  250. 250.

    For the monocentric eyepiece, cf. Smith et al., (op. cit. ref. 248), pp. 494–497.

  251. 251.

    Schroeter, J.H., (op. cit. ref. 142), pp. 224–225.

  252. 252.

    For hand manipulation of an eyepiece, cf. TSP, i, p. xlvii.

  253. 253.

    Hoskin, M., [op. cit. ref. 4, (2003)], pp. 19-20; idem, [op. cit. ref. 4, (2011)], p. 171–174; and TSP, i, p. lii–liv.

  254. 254.

    Hoskin, M., [op. cit. ref. 4, (2011)], p. 128. For pores, burs, and polishing defects, cf. RAS MS Herschel W.5/12.1, Exp. 423.2; W.5/12.2, Exp. 103.2.7, Exp. 483, and Exps 527–528, etc. For the machine breaking, cf. RAS MS Herschel W.5/12.2, Exp. 117.2; and W.5/12.3, Exps 5–7; and for problems with the pitch laps, cf. RAS MS Herschel W.5/12.3, Exps 194–214 and 232.

  255. 255.

    Ironically in June 1795 when Herschel’s paper on the 40-ft was read before the Royal Society, the instrument was not in a fit state for use. The mirror was tarnished and had a poor figure, as the polishing log shows. Even though Herschel struggled with it into the fall of 1795, it was no better: cf. RAS MS Herschel W.5/12.3, Exp. 232, 235, 254, etc. For the time needed to sweep the whole sky with the 40-ft, cf. Herschel, W., (op. cit. ref. 170), p. 85 [TSP, ii, 52]. For its mechanical problems, cf. Herschel, W., (op. cit. ref. 5), p. 295–296 [TSP, ii, p. 543–544]; and Herschel, Mrs. J., (op. cit. ref. 155), pp. 210.

  256. 256.

    Already in August 1789, during the first trials of the 2nd, thicker speculum, Herschel privately recorded: “The Speculum gives a pretty sharp image of the stars. The large ones are affected with a very small burr, or rather scattered light, owing to the remaining scratches in the speculum.” Cf. RAS MS Herschel W.2/4, f. 1v. This, however, seems to be hopeful thinking. The log in which it is recorded (“Observations with the 40 feet Telescope”) has been characterized as “a brief to justify the monster’s existence,” and indeed the entries in its remarkably petite compass of eight pages seem tendentiously selected. No other log book for a particular telescope in Herschel’s collection exists. Cf. Hoskin, M., [op. cit. ref. 4, (2003)], p. 15.

  257. 257.

    For Herschel’s “pre-discovery” sighting of Enceladus with the 20-ft, cf. RAS MS Herschel W.3/1.8, p. 63 (28-July-1789): “22h 31′ I now perceive between the nearest satellite [Rhea] and [Saturn] on the following side, a small lucid point like an emerging satellite…22h 37′ The last discovered point not quite half way between the 3d [satellite] and the body [of Saturn]. May be (it is) a 6th satellite.” Cf. also Herschel, W., (op. cit. ref. 170), p. 77 [TSP, ii, 47]: “…both satellites are within the reach of the 20-feet telescope….” The author has often seen Enceladus with an 8-inch refractor. It was seen in ca. 1796 by Giuseppe Cassella in Naples using a 7-ft Herschel Newtonian belonging to Lord Acton. Cf., Cassella, G., “Aus einem Schreiben des Herrn Cassella, König. Astronomen in Neapel,” AJJ 1799, (1796), 244; and Gargano, M., “The development of astronomy in Naples: the tale of two large telescopes made by William Herschel,” Journal of astronomical history and heritage, xv.1, (2012), 31–42, p. 35.

  258. 258.

    The author has seen it several times in a 16-in. f/4.5 Newtonian. On the suspicious history of discovery of both moons by Herschel, cf. Hoskin, M., [op. cit. ref. 4, (2011)], pp. 123–128. That the 2nd (thicker) 40-ft mirror was not yet fully polished can be seen at RAS MS Herschel W.5/12.1, p. 124, exp. 393.4 (22-Aug-1789): “The polish is still very far from being complete but I shall try the speculum on celestial objects before I polish any more.”

  259. 259.

    South, J., (op. cit. ref. 16).

  260. 260.

    The three editions of the first volume of Public characters are: Anon., British public characters of 1798, (London, 1798), 358–366; idem, Public characters of 1798, (Dublin, 1799), 251–257; and idem, Public characters of 1798–9. The third edition, (London, 1801), 384–392. The text quoted comes from the revised 3rd edition, p. 391. For the brisk sales see the advertisement to that edition.

  261. 261.

    Hoskin, M., [op. cit. ref. 4, (2011)], pp. 175–176.

  262. 262.

    Von Zach, MC, v, (1802), 70–77.

  263. 263.

    RAS MS Herschel C.4/5 (between Zach’s pp. 76–77). Caroline’s faulty spellings have been corrected here. The notion that William discovered 6 satellites of Uranus is mistaken, as is the notion that the “quintuple belt” of Saturn was found with the 40-ft. William thought he found four additional satellites (he did not) with the 20-ft; and the quintuple belt was observed with a 7-ft Newtonian. Cf. Hoskin, M., [op. cit. ref. 4, (2011)], pp. 147–148; and TSP, i, pp. 452 and 459–461.

  264. 264.

    Maseberg, H.C., “Versuch einer Lebensbeschreibung Fr. Wilh. Herschels, Doctors der Rechte und Mitglied der königl. Societät der Wissenschaften in London,” Neues Hannöverisches Magazin, xiv (1805), 1009–1030, cols 1011–1012, note *. His full name was probably Heinrich Christoph Maseberg: cf. Hamberger, G.C. & J.G. Meusel, Das gelehrte Teutschland, x (1803), p. 253.

  265. 265.

    Hoskin, M., [op. cit. ref. 4, (2011)], p. xv.

  266. 266.

    Maseberg, H.C., (op. cit. ref. 264), cols 1025–1026: “…so hatte er nun in der Nachbarschaft von Windsor seinen Plan noch erweitert, und ein Teleskop von nicht weniger als 40 Fuß zu Stande gebracht. Doch die Unregelmäßigkeiten des Spiegels, und die Schwierigkeit, die Theile eines so ungeheuern Instruments so mathematisch genau und richtig zu machen, als erforderlich ist, haben es ihm bisher unthunlich gemacht, einige genaue Beobachtungen damit anstellen zu können.”

  267. 267.

    Von Zach, (op. cit. ref. 262), 76: “Man hat [seine Entdeckungen] seiner seltenen Beharrlichkeit und nicht der außerordentlichen Wirkung seines 40 füßigen Reflectors zu danken, welcher eher ein Gegenstand der Neugierde, als von wirklichem Nutzen ist”; and Maseberg, H.C., (op. cit. ref. 264), col. 1028: “Seine Entdeckungen sind einzig und allein seiner lobenswerthen Beharrlichkeit im Beobachten, und nicht der Größe seiner Teleskope zuzuschreiben, welche bisher mehr Gegenstand der Neugier als der Nützlichkeit gewesen sind.”

  268. 268.

    Maseberg, H.C., (op. cit. ref. 264), cols 1027–1028, note i: “Mit Unrecht sagt der Verfasser von Herschels großen, und besonders dem 40schuhigen Teleskope, daß es mehr ein Gegenstand der Neugierde, als der Nützlichkeit gewesen sey, da er doch vorher selbst eingesteht, daß er seine Entdeckungen mit Reflectoren von 10 bis 20 Fuß, und zwar von eigener Arbeit, gemacht habe. Vielleicht schrieb der Verf. seine Biographie so früh nieder, ehe Herschel noch sein großes Teleskop zur größtmöglichsten Vollkommenheit gebracht hatte; da er aber doch die Vollendung desselben vom 28sten August 1789 datirt, und diese Sammlung von Lebensbeschreibungen erst 1798 bis 1801, also 9 Jahre später erschien, so hätte billig diese voreilige Behauptung wegbleiben müssen. Da er überdies wissen konnte, daß er mit demselben 40schuhigen Teleskop den 6ten Trabanten am 28sten Aug. 1789 entdeckte, und die Flecken des Saturns, wie H. selbst sagt, besser dadurch sah, als zuvor.”

  269. 269.

    For the “two other” moons, cf. Maseberg, H.C., (op. cit. ref. 264), cols 1025–10,287, note h); for the Herschelian bibliography, cf. Anon., Public characters of 1798–9. The third edition, (London, 1801), 392, note *.

  270. 270.

    Cf. de Lalande, J., “History of Astronomy for the Year 1806,” in A. Tilloch (ed.), The philosophical magazine, xxviii (1807), 69–79, 121–129, and 234–244, p. 129. For the French original, cf. de Lalande, J., “Histoire de l’astronomie, pour 1806,” in A.L. Millin (ed.), Magasin encyclopédique, ou journal des sciences, des lettres et des artes, (Janvier, 1807), 354–395, p. 379: “Le télescope de 40 pieds, de M. Herschel n’a point encore fourni les résultats extraordinaires que nous en attendions. Je lui ai écrit que j’irois en Angleterre pour voir ce prodigieux instrument, aussi-tôt qu’il m’écrirait qu’il en seroit content; je n’ai point encore reçu cet avis. Comme M. Herschel a 68 ans, je crains qu’il ne puisse se satisfaire et qu’il ne trouve pas un successeur capable de terminer complettement une aussi difficile entreprise.” Cf. also “Simplex,” “Correction of an error in La Place’s System of the world,” European magazine and London review, lxi (1812), p. 183: “La Place…seems to have placed too implicit a reliance on Dr. Herschel’s magnificent telescope; which indeed, has never proved of any service to astronomy.”

  271. 271.

    RAS MS Herschel W.1/13, W.166, 1.v-2.r.

  272. 272.

    Arcturus, “An examination of what Jérôme de Lalande has published, in his History of astronomy for 1806, concerning Dr. Herschel and his 40-feet telescope,” in A. Tilloch, (ed.), The philosophical magazine, xxviii (1807), 339–344, p. 339–340.

  273. 273.

    RAS MS Herschel W.1/1, p. 271.

  274. 274.

    Anon., “British Association,” Athenaeum, dcccxxx, (23-Sept-1843), 866–867, p. 866, col. 3 infra.

  275. 275.

    Hoskin, M., [op. cit. ref. 4, (2011)], p. 202; and Herschel, Mrs. J., (op. cit. ref. 155), pp. 335.

  276. 276.

    Herschel, W., “Account of the discovery of a sixth and seventh satellite of the planet Saturn, etc.,” PT, lxxx, (1790), 1–20, p. 7 [TSP, i, 370–381, p. 373].

  277. 277.

    Herschel, J.F.W., “Sir John Herschel on the reflecting telescope of the late Sir William Herschel,” Athenaeum, dcccxxxi, (30-Sept-1843), p. 884, col. 2.

  278. 278.

    Robinson, T.R., “Dr. Robinson’s reply to Sir John Herschel,” Athenaeum, dcccxxxiv, (21-Oct-1843), 945–946.

  279. 279.

    Herschel, J.F.W., “Sir John Herschel’s reply to Dr. Robinson,” Athenaeum, dcccxxxvi, (4-Nov-1843), 983–984, p. 983, cols 1–2.

  280. 280.

    Herschel, J.F.W, (op. cit. ref. 279), p. 984, col. 1.

Abbreviations

AJ:

Astronomical journal

AJJ:

Bode, J.E., ed., Astronomisches Jahrbuch für das Jahr XXXX, (Berlin)

AN:

Astronomische Nachrichten

Anon:

Anonymous

ApJ:

Astrophysical journal

ATM:

A.G. Ingalls, ed., Amateur telescope making, (New York, 1935–1953; reorganized and reprinted by Willmann-Bell, 1998), i–iii

JBAA:

Journal of the British Astronomical Association

JFI:

Journal of the Franklin Institute

JHA:

Journal for the history of astronomy

MC:

Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde, herausgegeben von Fr. von Zach

MmRAS:

Memoirs of the Royal Astronomical Society

MNRAS:

Monthly notices of the Royal Astronomical Society

NRRS:

Notes and records of the Royal Society of London

Obs:

The observatory

PA:

Popular astronomy

PT:

Philosophical transactions of the Royal Society of London

TCPS:

Transactions of the Cambridge Philosophical Society

TOS:

Transactions of the Optical Society

TSP:

J.L.E. Dreyer, The scientific papers of Sir William Herschel, (London, 1912), i–ii

Acknowledgments

I would like to thank Alan Agrawal, Richard Berry, Owen Gingerich, Michael Hoskin, John Koester, Guntram Lampert, Woody Sullivan, and Walter Stephani for commenting on and helping to proofread this chapter. Especially I would like to thank Woody Sullivan for alerting me to the existence of the letters that passed between John Herschel and T. R. Robinson, and finally Cliff Cuningham and the editors at Springer for bringing the chapter to publication. Whatever errors remain, naturally, belong to me alone.

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  1. Richard F. Caris Mirror Lab, University of Arizona, Tucson, AZ, USA

    Roger Ceragioli

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  1. Austin, Texas, USA

    Clifford J. Cunningham

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Ceragioli, R. (2018). William Herschel and the “Front-View” Telescopes. In: Cunningham, C. (eds) The Scientific Legacy of William Herschel. Historical & Cultural Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-32826-3_4

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