Abstract
The different weighing methods are reviewed. Three methods of direct weighing may be distinguished: weighing in the gravitational field, measurement of the impulse of an accelerated sample, and measurement of the frequency shift of an oscillating sample. Two basic interactions are applied for weighing: gravitation and electromagnetism. Three types of gravitational balances are used: lever balance, spring balance, electromagnetic or electrostatic balance. Parameters characterising a balance and their determination are described in detail. Adjustment of balances, consideration of influences on weighing, error estimate and its elimination are presented. Advantages of substitution and transposition weighing are discussed. Damping devices and methods for speeding up weighing are presented. A survey is given on standardisation method. The limits of weighing are summarised.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Einstein, Die Grundlagen der allgemeinen Relativitätstheorie. Ann. Phys. 49, 769–822 (1916)
Equivalence principle. http://enwikipedia.org/wiki/Equivalence_principle (2007)
T. Gast, T. Brokate, E. Robens, Vacuum weighing, in Comprehensive Mass Metrology, ed. by M. Kochsiek, M. Gläser (Wiley/VCH, Weinheim, 2000), pp. 296–399
DIN, DIN 1319, Teil 2: Grundbegriffe der Meßtechnik. Begriffe für die Anwendung von Meßgeräten (Beuth, Berlin, 1980)
DIN, DIN 1319 Teil 3: Grundbegriffe der Meßtechnik. Begriffe für die Meßunsicherheit und für die Beurteilung von Meßgeräten und Meßeinrichtungen (Beuth, Berlin, 1983)
DIN, DIN 8120, Teil 3: Begriffe im Waagenbau (Beuth, Berlin, 1981)
DIN, DIN ISO: Internationales Wörterbuch der Metrologie. International Vocabulary of Basic and General Terms in Metrology (Beuth, Berlin, 1984)
DIN, DIN EN 45501: Metrologische Aspekte nichtselbsttätiger Waagen (Beuth, Berlin, 1992)
A.W. Czanderna, S.P. Wolsky, Microweighing in Vacuum and Controlled Environments (Elsevier, Amsterdam, 1980)
OIML, OIML R 76-1 (E). Non-automatic weighing instruments. Part 1: Metrological and technical requirements—Test. OIML R 76-1 (F). Instruments de pesage à fonctionnement non automatique. Partie 1: Exigences métrologiques et techniques—Essais (OIML, Paris, 1992)
BIPM, International Vocabulary of Metrology—Basic and General Concepts and Associated Terms VIM, 4th edn. JCGM 200:2008, ISO Guide 99 by ISO (ISO/IEC Guide 99-12:2007) (BIPM Sevres, 2008)
EN, D., DIN EN 45501: Metrologische Aspekte nichtselbsttätiger Waagen (Beuth, Berlin, 1992)
A.M. Basedow, H.R. Jenemann, Waage und Wägung, in Quantitative organische Elementaranalyse, ed. by F. Ehrenberger (VCH, Weinheim, 1991), pp. 79–108
E. Robens, Bemerkungen zur Charakterisierung der Leistungsfähigkeit von Waagen. Wägen + Dos. 26, 6 (1995)
E. Robens, The characterization of the capability of a balance. J. Therm. Anal. 47, 619–622 (1996)
C. Berg, Grundlagen der Wägetechnik (Sartorius, Göttingen, 1995)
DIN, DIN 55 350 Begriffe der Qualitätssicherung und Statistik; Teil 13: Begriffe der Qualitätssicherung; Genauigkeitsbegriffe (Beuth, Berlin, 1987)
R. Schwartz, Mass determination with balances, in Comprehensive Mass Metrology, ed. by M. Kochsiek, M. Gläser (Wiley/VCH, Weinheim, 2000), pp. 232–295
M. Grabe, Measurement Uncertainties in Science and Technology (Springer, Heidelberg, 2010)
I.G. Hughes, T.P.A. Hase, Measurements and Their Uncertainties: A Practical Guide to Modern Error Analysis (Oxford University Press, Oxford, 2010)
H. Günzler, P. De Bièvre, Measurement Uncertainty in Chemical Analysis (Springer, Heidelberg, 2010)
S.G. Rabinovich, Measurement Errors and Uncertainties: Theory and Practice (Springer, Heidelberg, 2010)
B. Pesch, Messunsicherheit: Basiswissen für Einsteiger und Anwender (Books on Demand Verlag, Norderstedt, 2010)
G. Genta, Methods for Uncertainty Evaluation in Measurement: Statistical Issues in Metrology (VDM Verlag Dr. Müller, Saarbrücken, 2010)
Archimedes, The Works of Archimedes, §7. About Swimming Bodies, vol. 1 (Wissenschaftliche Verlagsbuchhandlung, Frankfurt am Main, 1987)
M. Kochsiek (ed.), Handbuch des Wägens, 2nd edn. (Vieweg, Braunschweig, 1985)
Mettler-Toledo, Mettler Wägefibel (Mettler, Greifensee, 1989)
E. Robens, T. Gast, Errors due to zero uncertainties and buoyancy in the gravimetric measurements of sorption isotherms. J. Vac. Sci. Technol. 15(2), 805–809 (1978)
E. Robens et al., Auftriebsanwendungen und Auftriebsfehler. Vak.-Tech. 36(5), 139–147 (1987)
E. Robens et al., Determination of the amount adsorbed from the gas phase in a porous solid, in Proceedings of the XXVIth International Conference on Vacuum Microbalance Techniques, ed. by M.b.B. Chanaa (Université Cadi Ayyad, Marrakesh, 1995), pp. 219–224
R.A. Pierotti, Gas-solid interactions and buoyancy, in Vacuum Microbalnce Techniques, ed. by A.W. Czanderna (Plenum, New York, 1967), pp. 1–16
A. Lindau, Gravity Information System of PTB. http://www.ptb.de/cartoweb3/SISproject.php. Physikalisch-Technische Bundesanstalt, Braunschweig (2007)
H.H. Willems, Creep Behaviour and Microstructure of Hardened Cement Pastes (Technische Universiteit, Eindhoven, 1985)
J.A. Poulis, J.M. Thomas, Sensitivity of analytical balances and relevance of fluctuation theory, in Vacuum Microbalance Techniques, vol. 3, ed. by K.H. Behrndt (Plenum, New York, 1963), pp. 1–14
C.H. Massen, J.A. Poulis, Sources of error in microweighing, in Microweighing in Vacuum and Controlled Environments, ed. by A.W. Czanderna, S.P. Wolsky (Elsevier, Amsterdam, 1980), pp. 95–123
D. Morse, Lab Balance Handbook (IES Corporation, Portland, 2011). www.iescorp.com/HB.pdf
H.R. Jenemann, The development of the determination of mass, in Comprehensive Mass Metrology, ed. by M. Kochsiek, M. Gläser (Wiley/VCH, Berlin, 2000), pp. 119–163
J.A. Cramer, Elementa artis docimasticae 1739/1744, Lugdunum Batavorum = Leyden
A.L. de Lavoisier, Second mémoire sur la nature d’eau. Histoire de l’Académie Royale des Sciences—avec les Mémoires de Mathématique et de Physique, 1770/3, pp. 90–107
H.R. Jenemann, Zur Geschichte der Substitutionswägung und der Substitutionswaage. Technikgeschichte 49, 89–131 (1982)
A.L. de Lavoisier, R.J. Hauy, Expériences de Lavoisier et Hauy, in Oevres de Lavoisier (Paris, 1793), pp. 683–685
C.F. Gauß, H.C. Schumacher, Briefwechsel, ed. by C.H.F. Peters (Altona, 1861), pp. 34, 61
J. Leupold, Theatrum staticum – das ist: Schauplatz der Gewichtskunst (Theatrum staticum universale, Leipzig, 1726)
L. Euler, Disquisitio de Billancibus. Commentari Acadimiae Scientiarium Imperialis Petropolitanae 1738/1747. 10
C.F. Gauß, Abhandlungen zur Methode der kleinsten Quadrate, ed. by A. Börsch, P. Simon (Vaduz, Berlin, 1886/7)
Error calculation (Universität Basel, 2009)
F.G. Skinner, Weights and Measures—Their Ancient Origins and Their Development in Great Britain up to AD 1855 (Science Museum, London, 1967)
H.R. Jenemann, Die Geschichte der Dämpfung an der Laboratoriumswaage. Ber. Wiss.gesch. 20, 1–17 (1997)
T. Gast, H.R. Jenemann, E. Robens, The damping of balances. J. Therm. Anal. Calorim. 55(2), 347–355 (1999)
W. Felgenträger, Feine Waagen, Wägungen und Gewichte (Springer, Berlin, 1932)
T. Gast, T. Brokate, E. Robens, Vakuumwägung, in Massebestimmung, ed. by M. Kochsiek, M. Gläser (VCH, Weinheim, 1996), pp. 294–399
E. Robens, High-speed weighing. J. Therm. Anal. Calorim. 55, 455–460 (1999)
H.R. Jenemann, E. Robens, Indicator system and suspension of the old Egyptian scales. Thermochim. Acta 152, 249–258 (1989)
C.J. Williams, A new lease on life for gravimetric adsorption. American Laboratory 1969(6)
Y. Kobayashi et al., Prototype kilogram balance II of NRLM. Bull. NRLM 33(2), 7–18 (1984)
Y. Kobayashi et al., Prototype kilogram balance II of NRLM. Bull. NRLM 35(2), 143–158 (1986)
N. Mendelssohn, Beschreibung einer großen und sehr genauen Wage zum Gebrauch für Physiker und Chemiker. Gilberts Ann. Phys. 29, 153–161 (1808)
M. Gläser, Massekomparatoren, in Massebestimmung, ed. by M. Kochsiek, M. Gläser (VCH, Weinheim, 1997), pp. 442–479
C.F. Plattner, Die Probirkunst mit dem Lötrohre (Leipzig, 1833)
F. Arzberger, Luftdämpfung für analytische Waagen. Liebigs Ann. Chem. 178, 382–384 (1875)
H.R. Jenemann, Zur Geschichte der Herstellung von Präzisionswaagen hoher Leistung in Wien. Bl. Tech.gesch. 49, 7–85 (1987)
P. Curie, Sur une balance de précision et à lecture directe des derniers poids. C. R. Hebd. Séances Acad. Sci. 108, 663–666 (1889)
H.R. Jenemann, Paul Bunge und die Fertigung wissenschaftlicher Waagen in Hamburg. Z. Unternehm.gesch. 31, 117–140 (1986), see also 165–183
H.R. Jenemann, Zur Geschichte der Präzisionsmechanik und der Herstellung feiner Waagen in Gießen. Mitt. Oberhess. Geschichtsver Gießen 66, 5–54 (1981)
W. Kuhn et al., Methods of the elimination of weighing troubles due to convection in a microbalance, in Vacuum Microbalance Techniques, ed. by C.H. Massen, H.J. van Beckum (Plenum, New York, 1961), pp. 1–21
W.C. Tripp, R.W. Vest, N.M. Tallan, System for measuring microgram weight changes under controlled oxygen partial pressure to 1800°C, in Vacuum Microbalance Techniques, ed. by P.M. Waters (Plenum, New York, 1965), pp. 141–157
O. Frölich, Die Entwickelung der elektrischen Messung (Braunschweig, 1905)
W. Marek, Aperiodische Wage mit Hilfsfedern. Österreichische Zentral-Zeitung für Optik und Mechanik 1, 5–7 (1906)
R.F. Walker, Microbalance techniques for high temperature applications, in Vacuum Microbalance Techniques, ed. by M.J. Katz (Plenum, New York, 1961), pp. 87–110
E.A. Gulbransen, K.F. Andrew, An enclosed physical chemistry laboratory: the vacuum microbalance, in Vacuum Microbalance Techniques, ed. by M.J. Katz (Plenum, New York, 1961), pp. 1–21
R.J. Kolenkow, P.W. Zitzewitz, A microbalance for magnetic susceptibility measurements, in Vacuum Microbalance Techniques, ed. by P.M. Waters (Plenum, New York, 1965), pp. 195–208
H. Mayer et al., On some modifications of a torsion microbalance for use in ultrahigh vacuum, in Vacuum Microbalance Techniques, ed. by K.H. Behrndt (Plenum, New York, 1963), pp. 75–84
H.R. Jenemann, The early history of balances based on electromagnetic and elektrodynamic force compensation, in Microbalance Techniques, ed. by J.U. Keller, E. Robens (Multi-Science Publishing, Brentwood, 1994), pp. 25–53
H.R. Jenemann, Die Waage des Chemikers—The Chemist’s Balance (DECHEMA, Frankfurt am Main, 1997)
R.L. Schwoebel, Beam microbalance design, construction and operation, in Microweighing in Vacuum and Controlled Environments, ed. by A.W. Czanderna, S.P. Wolsky (Elsevier, Amsterdam, 1980), pp. 59–93
F.A. Mauer, Analytical balance for rapid changes in weight. Rev. Sci. Instrum. 25, 598–602 (1954)
L. Cahn, H.R. Schultz, The Cahn recording GRAM electrobalance, in Vacuum Microbalance Techniques, ed. by K.H. Behrndt (Plenum, New York, 1963), pp. 29–44
W.E. Boggs, The adaption of the Cahn electrobalance control system to the automatic operation of a quartz-beam vacuum microbalance, in Vacuum Microbalance Techniques, ed. by A.W. Czanderna (Plenum, New York, 1967), pp. 45–58
T. Gast, Microweighing in vacuo with a magnetic suspension balance, in Vacuum Microbalance Techniques, ed. by K.H. Behrndt (Plenum, New York, 1963), pp. 45–54
C.H. Massen et al., Automated balances of the second generation. Thermochim. Acta 103, 1–4 (1986)
C.H. Massen et al., Computer simulation of balance handling. J. Therm. Anal. Calorim. 55(2), 367–370 (1999)
J.A. Poulis, C.H. Massen, E. Robens, Verfahren zur Ablesung einer schwingenden Anzeige, insbesondere von Waagen, in Offenlegungsschrift DE 197 30 070 A 1, Germany (1997)
J.A. Poulis, C.H. Massen, E. Robens, Verfahren zur Ablesung einer schwingenden Anzeige, insbesondere von Waagen, in Offenlegungsschrift DE 198 26 438 A 1. Germany (1998)
K. Horn, To make load-cell-scales settle faster, in XI IMEKO Congress, vol. 2 (1988), pp. 217–243
K. Horn, Verfahren und Meßeinrichtung zur Bestimmung mechanischer Meßgrößen, insbesondere eines unbekannten Gewichts, in Patentschrift DE 3743897 C2. Germany (1987)
C.H. Massen et al., Optimizing of balances of the second generation. J. Therm. Anal. Calorim. 55(2), 449–454 (1999)
C.H. Massen et al., Fast electromagnetic balance. J. Therm. Anal. Calorim. 71(1), 47–51 (2003)
J.A. Poulis et al., Schnelle Wägung. Wägen Dos. Misch. 3, 11–13 (2003)
O. Jäntti, J. Junttila, E. Yrjänheikki, Mikropunnitusajan Lyhentämisestä Ekstrapolaatiomenetelmällä. (On curtailing the microweighing time by an extrapolation method). Suom. Kemistil., A 43, 214–218 (1970)
O. Jäntti, J. Junttila, E. Yrjänheikki, On curtailing the micro-weighing time by an extrapolation method, in Progress in Vacuum Microbalance Techniques, ed. by T. Gast, E. Robens (Heyden, London, 1972), pp. 345–353
E. Robens, C.H. Massen, On the applicability of Jäntti’s method of shortening sorption measurements. J. Therm. Anal. Calorim. 94(3), 711–714 (2008)
O. Jäntti, E. Robens, Computerised reduction of the weighing time required for the determination of adsorption isotherms on activated carbons. Thermochim. Acta 51, 67–75 (1981)
C.H. Massen, J.A. Poulis, E. Robens, Criticism on Jäntti’s three point method on curtailing gas adsorption measurements. Adsorption 6, 229–232 (2000)
E. Robens, J.A. Poulis, C.H. Massen, Fast measurements, fast evaluation, fast results, fast richtig. GIT Z. Labortechnik 46(5), 556–559 (2002)
C.H. Massen et al., Extension of the applicability of Jäntti’s method for fast calculation of desorption data. Adsorp. Sci. Technol. 18(10), 853–856 (2000)
J.A. Poulis et al., Fast adsorption measurements on silicium dioxide, in Theoretical and Experimental Studies of Interfacial Phenomena and Their Technological Applications: Book of Abstracts, VIII Ukrainian-Polish Symposium, ed. by Y. Tarasevich et al., September 19–24 2004, Sergijiwka–Odessa, Ukraine (SCSEIO, Odessa, 2004), pp. 258–263
J.A. Poulis, C.H. Massen, E. Robens, Measurement of gas adsorption with Jäntti’s method using continuously increasing pressure. J. Therm. Anal. Calorim. 68(2), 719–725 (2002)
J.A. Poulis, C.H. Massen, E. Robens, The Jäntti approach using a two-layers model. J. Therm. Anal. Calorim. 71(1), 61–66 (2003)
J.A. Poulis et al., The application of Jäntti’s method for the fast calculation of equilibrium in the case of multilayer adsorption, in Characterization of Porous Solids VI, ed. by F. Rodríguez-Reinoso et al. (Elsevier, Amsterdam, 2002), pp. 761–767
J.A. Poulis et al., Jäntti’s method for the fast measurement of adsorption combined with diffusion. Z. Phys. Chem. 218, 245–254 (2004)
J.A. Poulis et al., A fast two-point method for gas adsorption measurements, in Characterisation of Porous Solids, ed. by K.K. Unger, G. Kreysa, J.P. Baselt (Elsevier, Amsterdam, 1999), pp. 151–154
J.A. Poulis et al., The possible use of Jäntti’s method for the explanation of adsorption onto rough surfaces, in Analytical Forum, Book of Abstracts (Warszawa, 2004)
J.A. Poulis et al., The application of Jäntti’s method for the explanation of adsorption onto rough surfaces. J. Therm. Anal. Calorim., 39–42 (2006)
J.A. Poulis et al., Application of Jäntti’s method to volumetric adsorption measurements. J. Therm. Anal. Calorim. 76(2), 579–582 (2004)
J.A. Poulis et al., Evaluation of the applicability of Jäntti’s method to volumetric sorption measurements. J. Therm. Anal. Calorim. 86(1), 43–45 (2006)
E. Robens et al., Fast measurements of adsorption on porous materials using Jäntti’s method. Adsorp. Sci. Technol. 17(10), 801–804 (1999)
E. Robens, J.A. Poulis, C.H. Massen, Fast gas adsorption measurements for complicated adsorption mechanisms. J. Therm. Anal. Calorim. 62, 429–433 (2000)
J.A. Poulis et al., Introduction of new functions to speed up sorption measurements. Adsorption 12(3), 213–217 (2006)
J.A. Poulis et al., General application of Jäntti’s method for the fast calculation of sorption equilibrium. J. Therm. Anal. Calorim. 76(2), 583–592 (2004)
J.A. Poulis et al., A Jäntti approach for quick calculations of sorption equilibria. Z. Phys. Chem. 216, 1123–1135 (2002)
J.A. Poulis, C.H. Massen, E. Robens, Saving time when measuring BET isotherms. J. Colloid Interface Sci 311(2), 391–393 (2007)
I. Jenemann, S. Kiefer, E. Robens, Some intriguing items in the history of scientific balances. J. Therm. Anal. Calorim. (2008)
Anonymus, Weseler Edikte (Wesel, 1324–1600)
DIN (ed.), Internationales Wörterbuch der Metrologie (Beuth, Berlin, 1984)
DIN, DIN 51006: Thermische Analyse (TA) – Thermogravimetrie (TG) – Grundlagen (Beuth, Berlin, 2005)
E. Schneider, Daten zu Eiffelturm. http://www.baufachinformation.de/denkmalpflege.jsp?md=1988017121187 (2010)
M. Kochsiek, M. Gläser (eds.), Comprehensive Mass Metrology (Wiley/VCH, Berlin, 2000)
W.M.F. Petrie, A Season in Egypt (London, 1888)
W.M.F. Petrie, Ancient Weights and Measures (London, 1926)
C.H. Massen et al., Investigation on a model for a large balance of the XVIII Egyptian dynasty, in Microbalance Techniques, ed. by J.U. Keller, E. Robens (Multi-Science Publishing, Brentwood, 1994), pp. 5–12
G.V. Childe, The prehistory of science: archaeological documents, Part 1, in The Evolution of Science, Readings from the History of Mankind, ed. by G.S. Metraux, F. Crouzet (New American Library/Mentor Books, New York, 1963), pp. 66–67
C. Seeber, in Untersuchungen zur Darstellung des Totengerichts im Alten Ägypten, ed. by H.W. Müller, Münchner Ägyptologische Studien, vol. 35 (Deutscher Kunstverlag, München, 1976)
Aristoteles, a.t. (ed.), Questiones mechanicae, ed. by P. Gohlke (Kleine Schriften zur Physik und Metaphysik, Paderborn, 1957)
Al-Chazini, Buch der Waage der Weisheit (Merw, 1120)
L. da Vinci, Codex atlanticus—Saggio del Codice atlantico, ed. by Aretin, vol. fol. 249 verso-a + fol. 8 verso-b (Milano, 1872)
H.R. Jenemann, Das Kilogramm der Archive vom 4. Messidor des Jahres 7: Konform mit dem Gesetz vom 18. Germinal des Jahres 3? in Genauigkeit und Präzision, ed. by D. Hoffmann, H. Witthöfft (Physikalisch-Technische Bundesanstalt, Braunschweig, 1996), pp. 183–213
H.R. Jenemann, Die Werkstatt von Paul Bunge: 100 Jahre Präzisionswaagenherstellung in Hamburg. Beitr. Dtsch. Volks- Altert.kd. 26, 169–188 (1988/1991)
H. Pettersson, A new micro-balance and its use. Diss. Stockholm, Göteborg’s Vet. of Vitterh. Samhalle’s Handlinger (Göteborg, 1914)
H. Pettersson, Experiments with a new micro-balance. Proc. Phys. Soc. Lond. 32, 209–221 (1919)
R. Strömberg, Adsorptionsmessungen mit einer verbesserten Mikrowaage. K. Sven. Vetensk.akad. Handl. III 6(2), 33–122 (1928)
R. Strömberg, Adsorption measurements with an improved microbalance. K. Sven. Vetensk.akad. Handl. III 6(2), 1–12 (1928)
A.W. Czanderna et al., Photoelectrically automated, bakeable, high-load ultramicrobalance. J. Vac. Sci. Technol. 13, 556–559 (1976)
U. Kilian, C. Weber, Lexikon der Physik, vol. 4 (Spektrum Akademischer Verlag, Heidelberg, 2000)
G. Böhme et al., Determination of relative weight changes of electrostatically suspended particles in the sub-microgram range, in Progress in Vacuum Microbalance Techniques, ed. by S.C. Bevan, S.J. Gregg, N.D. Parkyns (Heyden, London, 1973), pp. 169–174
R. Hooke, De Potentia Restitutiva or of Spring, explaining the Power of Springing Bodies. Lectiones Cutleriana or a collection of Lectures: Physical, Mechanical, Geographical, & Astronautical. Early Science in Oxford, vol. VIII (Gunther, London, 1678/9)
H.R. Jenemann, Robert Hooke und die frühe Geschichte der Federwaage. Ber. Wiss.gesch. 8, 121–130 (1985)
E. Robens, D. Möhlmann, Planning of gravimetric investigations on Mars. J. Therm. Anal. Calorim. 76(2), 671–675 (2004)
G. Sauerbrey, Verwendung von Schwingquarzen zur Wägung dünner Schichten und zur Mikrowägung. Z. Phys. 155, 206–222 (1959)
P. Poncheral et al., Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513–1516 (1999)
B. Ilic et al., Attogram detection using nanoelectromechanical oscillators. J. Appl. Phys. 95(7), 3694–3703 (2004)
S. Gupta, G. Morell, B.R. Weiner, Electron field-emission mechanism in nanostructured carbon films: a quest. J. Appl. Phys. 95(12), 8314–8320 (2004)
J. Wood, Mass detection finds new resonance. Mater. Today 4, 20 (2004)
LaHaye et al., Science 304, 74 (2004)
C. Sealy, Probing the quantum world with uncertainty. Mater. Today 6, 9 (2004)
U. Brand, Nanosensor misst gleichzeitig Kraft und Weg. Nachrichten und Presseeldungen aus Labor und Analytik (2013)
S. Arnold, E.-C. Reiff, Kraftmessung in nanoskopischen Dimensionen. LaborPraxis 7/8, 54–56 (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Robens, E., Jayaweera, S.A.A., Kiefer, S. (2014). Weighing. In: Balances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36447-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-36447-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36446-4
Online ISBN: 978-3-642-36447-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)