44 



SCIENCE. 



[N. S. Vol. XI. No. 263. 



In the latter he took up the more recondite 

 question of rendering a clear account of the 

 motion of a rigid body. This problem had 

 been treated already by the illustrious 

 Euler, d'Alembert, Lagrange, and Laplace, 

 and it seemed little short of temerity to 

 hope for any improvement. But Poinsot 

 entertained that hope and his efforts proved 

 surprisingly successful. His little volume 

 of about one hundred and fifty pages is 

 still one of the finest models of mathematical 

 and mechanical exposition ; and his repeated 

 warning, " gardons-nous de croire qu'une 

 science soit faite quand on I'a r6duite a des 

 forraules analytiques," has been fully justi- 

 fied. He gave us what may be called the 

 descriptive geometry of the kinetics of a 

 rotating rigid body, the ' image sensible de 

 cette rotation '; he clarified the theory of 

 moments of inertia and principal axes ; he 

 made plain the meaning of what we now 

 call the conservation of energy and the 

 conservation of moment of momentum of 

 systems which are started off impulsively ; 

 and he surpassed Laplace himself in ex- 

 pounding the theory of the invariable plane- 

 Another elementary work of prime im- 

 portance in the progress of mechanics was 

 Poisson's Traite de M6canique. Poisson 

 belonged to the Lagrangian school of ana- 

 lysts, but he was so profoundly devoted to 

 mathematical physics that almost all his 

 mathematical work was suggested by and 

 directed towards practical applications. 

 His facility and lucidity in exposition ren- 

 dered all his works easy and attractive 

 reading, and his treatise on mechanics is 

 still one of the most instructive books on 

 that subject. He was one of the first to 

 call attention to the value of the principle 

 of homogeneity in mechanics,* a principle 

 which, as expanded in Fourier's theory of 

 dimensions,! has proved of the greatest 



*See Article 23, Tome I., Tfaitd de Mecanique, 2d 

 ed., Paris, 1833. 



t 'Throne Analytique de la Chaleur, ' Paris, 1822. 



utility in the latter half of the century. The 

 influence of Poisson's work in mechanics 

 proper, very widely extended, of course,by his 

 memoirs in all departments of mathematical 

 physics, is seen along nearly every line of ' 

 progress since the beginning of the centurjr. 



Of other works which paved the way to 

 the present advanced state of mechanical 

 science, it may sufiRce to mention the Cours 

 de M6canique* of Poncelet (1788-1867), the 

 Traite de Mecanique des Corps Solides et 

 de I'Effet des Machinesf of Coriolis, and 

 the Lehrbuch der StatikJ of Mobius. To 

 the two former of these authors we owe the 

 fixation of ideas and terminology concern- 

 ing the doctrine of mechanical work, while 

 the suggestive treatise of Mobius fore- 

 shadowed a new type of mechanical con- 

 cepts since cultivated by Hamilton (Sir W. 

 K., 1805-1865). Grassmann (1809-1877), 

 and others under the general designation of 

 vector analysis. 



Following close after the development of 

 the elementary ideas whose history we have 

 sketched came the important improve- 

 ments in the Lagrangian analysis due to 

 Hamilton. § With these additions of Ham- 

 ilton, amplified and clarified by the 

 labors of Jacobi, Poisson, and others, || 

 analytical mechanics may be said to have 

 reached its present degree of perfection so 

 far as mathematical methods are concerned. 

 By these methods every mechanical ques- 

 tion may be stated in either of three char- 

 acteristic though interconvertible ways, 

 namely : by the equations of d'Alembert, 



- Metz, 1826. 



t Paris, 1829. 



X Leipzig, 1837. 



§ ' On a general method in dynamics. ' Philomphical 

 Transactions, 1834-35. 



II For an account of these additions and for a com- 

 plete list of papers bearing on the subject (up to 

 1857), one should consult the admirable report of 

 Cay ley on ' Recent progress in dynamics,' published 

 in the Eeport of the British Association for the Ad- 

 vancement of Science for 1857. 



