Febriaby 8, 1895.] 



SCIENCE. 



147 



by Hipparcluis. Tliq . law of gravitation 

 supplied a reason for this phenomenon ; 

 but to understand it fully the properties of 

 rotating bodies had to be elaborately stud- 

 ied by Euler and d'Alembert. Observa- 

 tional astronomy liegan far earlier than the 

 era of Ilipparchus ; but precise observa- 

 tional astronomy was not possible before 

 Iluyghens' invention of the penduhmi clock 

 and before XewtonV law led the way to 

 separating the motions of the earth from 

 those proper to the stars and to light. 



The earlier part of the period in question 

 was also characterized by the varietj- of 

 special processes used in the applications of 

 mechanics. This peculiarity is due partly 

 to the fact that the great method of investi- 

 gation now known as the differential and 

 integral calculus was not duly understood 

 and appreciated. Newton, as we have seen, 

 devised and used this method under the 

 name of fluxions, but dared not bring it into 

 jtrominence in his Principia. Indepeudenth" 

 of, though a little later than Newton, 

 Leibnitz discovered substantially the same 

 method. Priority of publication of the 

 method by Leibnitz led to one of the most 

 remarkable and bitter controversies in the 

 history of science ; proving amongst other 

 things that scientitic men are no better than 

 other folks, and giving color to Benjamin 

 Franklin's allegation that mathematicians 

 are prone to be conscientiously contentious. 

 IJut this war of words, in which personal 

 and national prejudice figured shamefullj- 

 enough, did not long disturb the minds of 

 continental mathematicians. The Leib- 

 nitzian form of the calculus, by reason of its 

 intrinsic merits, came into general use. The 

 BernouUis, Euler, Clairaut, and d'Alembert, 

 who were the leading mathematicians of the 

 time, adopted the calculus as their instru- 

 ment of research and paved the way to the 

 age of extraordinary generalizations which 

 began nearthe end of the eighteenth century. 



The varietj- of problems considered and 



the diversity of methods employed during 

 this period served to call attention to the 

 need of more comprehensive mechanical 

 principles. Before the publication of 

 d'Alembert"s treatise on djniamics in 174.3, 

 each problem had heeja considered by itself, 

 and although many important results were 

 attained, the principles employed did not 

 appear to have any close connection with 

 one another. There was thus an oppor- 

 tunit}' for rival schools of mechanicians, and 

 they fell into the habit of challenging one 

 another with Mhat would now be called prize 

 problems. The first step toward a unifica- 

 tion of principles and processes was made 

 by d'Alembert in the treatise just mentioned. 

 This treatise announced and illustrated a 

 principle, since known as d'Alembert's prin- 

 ciple, which put an end to rivalry by show- 

 ing how all prol)lems in dynamics can be 

 referred to the laws of statics. By the aid 

 of this principle, d'Alembert showed how to 

 solve mechanically not only the splendid 

 problem of the precession of the equinoxes, 

 but also that more recondite question of the 

 nutation of the earth's axis. The fact of 

 nutation had Ijeen discovered a year and a 

 half earlier Ity the astronomer Bradley ; but 

 d'Alemberfs exi)lanation of this fact, ac- 

 cording to Laplace, is not less remarkable 

 in the history of mechanics than Bradley's 

 discovery in the annals of astronomy. 



The work of the devotees to mechanics in 

 the times of which we speak is not gener- 

 ally fully appreciated. Their fame is, in- 

 deed, eclipsed by that of Newton and by 

 that of their innnediate successoi-s. But 

 their contributions were important and sub- 

 stantial. Clairaut gave us the fii"st mathe- 

 matical treatise on the figure of the earth ; 

 while his colleague, Maupcrtius, in the 

 famous Lapland expedition, announced the 

 the jirinciple of ' least action " and the ' law 

 of repose,' both of which have proved fruit- 

 ful in later times. The BernouUis, a most 

 distinguished family of mathematicians, of 



