THE ROYAL IRISH ACADEMY, 1848. 473 



with which it may be applied. In this the author has already done 

 enough to establish its power. He has applied it with great success 

 to many problems of the geometry of Surfaces ; and he has given a 

 sketch of its application to the problem of the Three Bodies, and to 

 the Mechanics of the Heavens generally. These instances of its 

 application, whether we look to the elegance and simplicity of the 

 method, or to the beauty and symmetry of the results, are abun- 

 dantly sufficient to demonstrate the power and pliancy of the in- 

 strument. 



Still, however, more will be required from its author, before the 

 weapon which he wields with a giant's grasp may be touched by 

 feebler hands. It will be necessary that the principles and funda- 

 mental rules of the calculus should be rendered familiar by elemen- 

 tary exposition, and their certainty tested by ordinary applications, 

 before the violation of known analogies which some of them present 

 will be universally acquiesced in ; and I am happy to be able to 

 say that the large debt, which Science already owes at his hands, is 

 likely to receive ere long this addition, and that, like a genuine 

 lover of Truth, he will not rest content until the difficult path 

 which he has cut for himself into her tangled and obscure recesses 

 shall become a highway for all. 



I now proceed to the consideration of Mr. Haughton's memoir 

 *' On the Equilibrium and Motion of Solid and Fluid Bodies." 



The object of this memoir, as stated by the author himself, is 

 " to deduce, by the method of the Mecanique Anatytique of La- 

 grange, the laws of equilibrium and motion of elastic solid and 

 fluid bodies from the same physical principles, and to discover by 

 the same method the conditions at the limits." The method of 

 Lagrange (which is so peculiarly adapted to the mechanics of a 

 system composed of an indefinite number of acting molecules, situ- 

 ated indefinitely near each other) seems to have been first applied 

 to the problem of elastic bodies by M. Navier, who determined by 

 that method the laws of equilibrium of a homogeneous uncrystallized 

 solid. The late Mr. Green, of Cambridge, applied the same me- 

 thod to the more difficult di/nnniical question of the movement of 

 the molecules of the Iiuninifcrous ether; in which application he 

 was followed by the distinguished mathematician whose name is 

 imperishably connected with the records of this Academy. 



Mr. Haughton has judiciously adopted the same mathematical 



