the elementary Relations of Figure and Forces. 199 



— 4- '^''' 

 ~ — "2" 



— -if — 



— — 2 



_ (2 ra + 1 )ir 



"■ — 2 



These indicate the factors of the cosine : hence 



<J> fl = a cos fl 

 and z = a jT cos fl 



Again, when 6 =■ z = 2 x 



Hence finally z = 2 x . cos 9 



It will be seen that this is the immediate result of the com- 

 bination of the elementary ideas contained in the laws of mo- 

 tion. I am aware that it is the practice to preface the de- 

 monstration of this theorem with a set o( physical axioms : but 

 if the inertia of matter has previously been stated in its pro- 

 per extent, the necessity of this is avoided. The investigation 

 1 have now given differs somewhat from those in celebrity. 

 It differs from them probably in possessing superior simplicity, 

 but in principle it is essentially the same. Poisson in disco- 

 vering the equation f jr. (px = ip (jt — 2;) + 4> {^ + z) and in 



the evaluation of a, and Laplace in rejecting the forces — 



and -^, and in evaluing k and g, involve all the physical ideas 



which I have now combined. The theorem of the composi- 

 tion of forces bears to these experimental facts precisely the 

 same relation that the principle of gravitation bears to Kepler's 

 empirical laws — they are both merely condensed expressions. 



Although I consider that Professor Leslie has in both these 

 questions been misled by an unaccountable dislike with which 

 he seems to regard the approaches of analysis, and that in 

 the latter question this dislike has drawn from him an inade- 

 quate exhibition of an important elementary truth, I cannot 

 go along with Dis-Iota in the full extent of his censure. I 

 cannot allow that Mr. Leslie has not been eminently success- 

 ful in illustrating many elementary subjects ; and were proof 

 wanting, I would simply refer to his neat, or rather elegant 

 exposition of the physical characters of fluids in the volume 

 which has drawn forth a portion of these remarks. In this 

 paper I have used those liberties with his name to the use of 

 which an anonymous writer is entitled ; but I have not laid 



aside 



