198 On the Use of Analysis in investigating 



tellectual process, the less must be the chance of error. The 

 use of experiment is merely to completely define the objects of 

 contemplation. When the relation termed a triangle, for in- 

 stance, is once defined by experiment, the evolution of its dif- 

 ferent forms is accomplished by reasoning alone, and it would 

 be next to ludicrous were an editor of the Eletnents to offer ex- 

 perimental proofs of them. The experimental principles of 

 every department of science should be reduced to the Jewest 

 possible; and the processes that furnished them ought not to 

 be again introduced (excepting tor mere verification), until the 

 occurrence of some physical action ?iot already involved by 

 them. Does the composition of forces then involve any phy- 

 sical pliaenomenon not included amongst those susceptibilities 

 of matter already defined by the laws of motion F The simul- 

 taneous action is quite analysable, and its analysis will in- 

 stantly answer the question. One of the forces may be supposed 

 to have already acted upon the body, and set it in motion. 

 At a point in its course it is affected by the other force. Now 

 this second force may be conceived decomposed into two others, 

 one of which acts equally and oppositely to the force which 

 has impressed the motion. At the instant of this action, then, 

 the first force will be annihilated, and the body will be con- 

 strained by a new force acting upon it in another direction. 

 The physical phaenomenon of the joint action thus involves 

 nothing new. The body merely loses one tendency to motion 

 and receives another; and the determination of the resultant 

 should be obtained by contemplating the physical truths «/- 

 ready known. That it does follow from a combination of them 

 will instantly appear. Let two equal forces x act upon a 

 point M, making an angle 2 fl. The inertia of matter deter- 

 mines that the resultant z shall bisect the angle. Here 



2 = <J) (jr, 9, y) 

 which is converted by the law of homogeneity into 



* z _ f 



X ~ y 

 or conceiving 9 the ratio 



z = X . (^ 6 

 but z, and consequently f 9 become when, and only when 



* This transformation is accomplished in the same manner by Poisson . 

 It is a blemish in Francoeur's little treatise, that he has chosen to deduce 

 it otherwise, and more circuitously, Laplace's investigation is very diffe- 

 rent from either Poisson's or Francoeur's. The English student who can- 

 not refer to the first section of the Mechanique may find it in Dr. Thomas 

 Young's Illustrations, &c. 



