January 12, 1900.] 



SCIENCE. 



43 



be simplified and systematized by Poinsot 

 (1777-1859), Poisson, MSbius (1790-1868), 

 and Coriolis (1792-1843), who were all at 

 this time under twenty-five years of age. 

 The undulatory theory of light, in which 

 Young (1773-1829), Fresnel (1788-1827), 

 Arago (1786-1853), and Green (1793-1841) 

 were to be the most conspicuous early 

 figures, was just beginning to be considered 

 as an alternative to the emission theory of 

 Newton. The theory of elasticity, or the 

 theory of stress and strain as it is now called, 

 was about to be reduced to the definite- 

 ness of formulas at the hands of ISTavier 

 (1785-1836), Poisson, Cauchy, and Lame 

 (1795-1870). Planetary and sidereal as- 

 tronomy, to which so much of talent, time, 

 and treasure have since been devoted, was 

 soon to receive the fruitful impetus im- 

 parted to it by the German school of Gauss, 

 Bessel, Encke (1791-1865), and Hansen 

 (1795-1874). 



The advances that have been made dur- 

 ing the past century in analytical mechanics 

 must be measured from the elevated stand- 

 ard attained by Lagrange in his Mecanique 

 Analytique. To work any improvement 

 over this, to simplify its demonstrations, or 

 to elaborate its details, was a task fit only 

 for the keenest intellects. Lagrange had, 

 as he supposed, reduced mechanics to pure 

 mathematics. Geometrical reasonings and 

 diagrammatic illustrations were triumph- 

 antly banished from this science and re- 

 placed by the systematic and unerring 

 processes of algebra. " Ceux qui aiment 

 I'Analyse,"' he says, " verront avcc plaisir 

 la Mecanique en devinir une nouvelle 

 branche, et me sauront gre d'en avoir 

 etendu ainsi le domaine." The mathemat- 

 ical world has not only accepted Lagrange's 

 estimate of his work, but has gone further, 

 and considers his achievement one of the 

 most brilliant and important in the whole 

 range of mathematical science. " The me- 

 chanics of Lagrange," as Mach has well 



said, " is a stupendous contribution to the 

 economy of thought."* 



Nevertheless, improvements were essen- 

 tial, and they came in due time. As we 

 can now see without much difiSculty, La- 

 grange and most of his contemporaries in 

 their eagerness to put mechanics on a 

 sound analytical basis overlooked to a 

 serious extent its more important physical 

 basis. The prevailing mathematical opin- 

 ion was that a science is finished as soon as 

 it is expressed in equations. One of the 

 first to protest against this view was Poinsot, 

 though the preeminent importance of the 

 physical aspect of mechanics did not come 

 to be adequately appreciated until the latter 

 half of the present century. The ani- 

 mating idea of Poinsot was that in the 

 study of mechanics one should be able to 

 form a clear mental picture of the phenom- 

 ena considered ; and that it does not sufBce 

 to put the data and the hypotheses into the 

 hopper of our mathematical mill and then 

 to trust blindly to its perfection in grinding 

 the grist. In elaborating this idea he pro- 

 duced two of the most important elemen- 

 tary treatises on mechanics of the century. 

 These are his Elements de Statique pub- 

 lished in 1804, and his Th^orie Nouvelle 

 de la Rotation des Corps published in 

 1834. -|; In the former work he developed 

 the beautiful and fruitful theory of couples 

 and their composition, and the conditions 

 of equilibrium, as they are now com- 

 monly expressed in elementary books. 



" The Science of Mechanics, by Dr. Ernst Maoh. 

 Translated from the German by Thomas J. McCor- 

 mack. Chicago, Open Court Publishing Co., 1893. 



t Outlined to the Paris Academy in 1834. In 

 the introduction to the edition of 1852 he says, 

 "Voioi une des questions qui m'ont le plus souvent 

 oocupe, et, si I'on me permet de parler ainsi, une des 

 choses que j'ai le plus desire de savoir en dynamique. 



"Tout le monde se fait une idee claire du mouve- 

 ment d'un point, * * * Mais, s'il s'agit du mouve- 

 ment d'un corps de grandeur sensible et de figure 

 quel-conque, il faut convenir qu'on ne s'en fait qu'nne 

 id^e tres-obscure. " 



