112 



lest absurdity existing in his discussion of the second law of motion, to which 

 we have alluded in our paper. If this explanation will be of any service to 

 the author, we will give him the advantage of it. 



" The excess of energies makes the resultant, and this must thus divide the 

 angle between the directions of the forces according to their degrees of excess 

 of energy inversely. This is not saying that the resultant is in the ratio to 

 the partial ayigles in question, but that it is in the ratio to the respective ex- 

 cess of energies ; and, as a geometrical fact, this does divide inversely as the 

 angles. To say then, as in the first edition, that in ' unequal excess of ener- 

 gies their composition must give the line dividing their angle in the inverse 

 ratio of the excess of energy,' is equivalent to saying in the second edition, 

 1 that in unequal energies the resultant must be on the side of the greater, 

 making the forces inversely as the sines of the angles.' The first is according 

 to the philosophy of the forces ; the last is according to the geometry of the 

 lines." 



We had always supposed that the lines were the representatives of the 

 forces, and whatever was proved about the one was true of the other. That 

 the philosophy of the forces could lead to a different result from the geometry 

 of the lines, seems an absurdity more palpable than any before perpetrated in 

 the work. 



