198 



it being not generally true that the sum of three squares, multiplied 

 by the sum of three squares, is a sum of three squares. 



But whatever be thought of the principles of the Calculus of 

 Quaternions, its advantages as an instrument of Mathematical 

 Thought will undoubtedly be judged by the simplicity and ease 

 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 ap- 

 plication, — 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 Jlnahjt'uiue of Lagrange, 

 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 com- 

 posed of an indefinite number of acting molecules, situated inde- 

 finitely near each other), seems to have been first applied to the 

 problem of elastic bodies by M. Navier, who determined by that me- 

 thod the laws of equiVihrium of a homogeneous uncrystallized solid. 



