Between Mathematics and Experimental Philosophy: Hydrostatics in Scotland About 1700

Abstract

Many years ago J.B. Conant contrasted Pascal’s and Boyle’s approach to hydrostatics and pneumatics in terms of “two traditions,” one mathematical, the other experimental. Peter Dear has brilliantly recast Conant’s suggestion by linking Pascal’s (so-called) mathematical approach and Boyle’s experimental approach to their contrasting theological views. In a more general way, there is a broad consensus that the experimental approach was the distinguishing feature of the teaching of natural philosophy in Britain from the late seventeenth century on. In the early Enlightenment in Britain, Larry Stewart and others have shown, the utilitarian, manipulative, visual, experimentalist side of natural philosophy was favored and stressed to the point that the mathematical content almost disappeared. It was an approach in which hands-on experience and observation not only helped to overcome difficulties in concept-clarification and in mathematical arguments, but appeared as real alternatives to them. Although there is much truth in those accounts, we present here evidence that a British mathematical approach to hydrostatics and pneumatics was successfully developed by John Wallis, James Gregorie (or Gregory), Newton, and others. In a sense that we will specify here, their approach is more deeply and more genuinely mathematical than Pascal’s. Finally we also present evidence that such a mathematical understanding of hydrostatics and pneumatics occupied a prominent place in the teaching of natural philosophy in Scottish universities from the late seventeenth century on.

Sources and Authorship of Aberdeen University Library (Aul) Ms 2206/7

The University of Aberdeen keeps the only copy now extant (as far as we know) of a manuscript on hydrostatics and pneumatics titled “Hydrostatica” and which title page attributes authorship to “James Gregory, professor of mathematics in Edinburgh University.” It is contained in one fair, 41-page long copy dated 1740 and neatly written by an unknown amanuensis hand.⁸⁹ The manuscript catalog of Aberdeen University Library further identifies the author by calling him “Professor of Mathematics at St. Andrews.” Although two James Gregories (or Gregorys, in what was then a characteristic English spelling) occupied the Mathematics professorship in Edinburgh, only the senior James (1638–1675) had also been professor of mathematics at St Andrews. As we shall see, there are good reasons to assume the two James were involved in the authorship of this manuscript, although the major role must have corresponded to the senior James. Upon James Gregorie’s death in 1675, his friend and colleague William Sanders wrote down a list of the mathematical papers Gregorie left in a finished form. According to Sanders, Gregorie left among other things “The Theory of the whole Hydrostaticks comprehended in a few definitions and five or six Theorems.”⁹⁰ The present manuscript fairly agrees with the foregoing description. It exactly contains four definitions and eleven propositions, the first six of which concern hydrostatics proper, while the last five propositions apply the former ones to explain “Torricelli’s” experiment and pneumatics.

Internal references make the contents of the “Hydrostatica” manuscript mostly consistent with a date of composition around 1670 or shortly thereafter, the years in which James Gregorie the elder must have written his hydrostatical mini-treatise. As set forth above, “Hydrostatica” is a free paraphrase of Wallis’ “De hydrostaticis.” It simplifies and improves its original, but it is a paraphrase nonetheless. Mersenne and Boyle are more than once quoted, in particular with reference to the quantitative limits these authors provided for the atmospheric air’s condensation and rarefaction. The references can be traced back to Mersenne’s “Hydraulica [et] Pneumatica” (published within his Cogitata physico mathematica of 1644) and to Boyle’s Hydrostatical paradoxes of 1666. As explained above, in 1671 Gregorie wrote to John Collins asking for a copy of Wallis’ Mechanica.⁹¹ There is therefore both internal and external evidence not to be easily dismissed that makes the senior James Gregorie author of this manuscript.

On the other hand, we know that the first two propositions of the manuscript along with their long lists of corollaries and the definition of fluid (on the whole some eight pages of text out of the 39 written pages of the manuscript) come almost verbatim from Newton’s Principia, Book II, Section 5, Propositions 19 and 20 and their corollaries. The borrowing is explicitly acknowledged on page 10 of the manuscript: “we bring over [these two propositions] from the principles of the most illustrious Newton.” The grafting of Newtonian hydrostatics into Gregorie’s manuscript suggests that someone was still using it after 1687. The candidates are many, but among the most likely ones two nephews of the senior James Gregorie stand out, David Gregorie (1661–1708) and the junior James Gregorie (1666–1742), both of whom were professors of mathematics at the University of Edinburgh. We do know that David appropriated his uncle James’ manuscripts without properly acknowledging his sources. If he had used his uncle’s hydrostatics, it is likely that the manuscript would have reached us under David’s name. Furthermore, he left Edinburgh for Oxford in 1691, before he had time to fully acquaint himself with the Principia. It is likely, therefore, that it was the younger James who amended and perhaps expanded the hydrostatical manuscript.⁹² The younger James, of whom no written production is known, was professor of philosophy (not of mathematics) in St Andrews from 1686 to 1691 and then professor of mathematics in Edinburgh from 1692 to 1742.⁹³ The name in the title page of “Hydrostatica” might have been meant for him—in this case the library catalog does not identify him properly.