272 Mr. Earnshaw's Answer to Prof. Moseley's 



balance the forces A ; but those of the latter are solely em- 

 ployed in balancing each other; and with regard to this set 

 i have to observe : — 



1st, That they are propagated by the forces of the system C, 

 since no horizontal force can be propagated by the system A. 



2ndly, That, though in equilibrium amongst themselves, 

 they cannot be removed by the principle of the superposition of 

 forces ; for the forces C are oblique, and consequently pro- 

 duce these horizontal pressures of necessity: that is, no change 

 in the magnitudes of the forces C can ever remove these hori- 

 zontal pressures. It is not allowable to remove them in any 

 other way than by changing the magnitudes of C ; and any 

 other method would change the directions of C, which cannot 

 be admitted, because the directions are given. Wherefore it 

 is impossible to remove them at all. 



As I rest my objections to Mr. Moseley's theory principally 

 on this point, I will vary the argument a little, lest Mr. 

 Moseley should take some objection (though I certainly do 

 not see one myself,) respecting the propagated pressures being 

 horizontal, and not in the directions of the forces C. 1 sup- 

 pose it will not be denied that a body cannot press with a force 

 greater than its own weight. Now, as before shown, the weight 

 of the body = the sum of the resolved parts of the forces C 

 in a vertical direction ; and as the forces C are oblique, their 

 sum is greater than that of their resolved parts ; and therefore 

 the sum of the forces C is necessarily greater than the weight 

 of the body. If, then, the forces C have to support a greater 

 pressure than the weight of the body, whence comes the 

 excess ? I think there can only be this answer: — " That the 

 forces C must of necessity mutually propagate pressures." I 

 consider that Mr. Moseley has erred in his argument on this 

 point in two particulars — 



1. In assuming that each of the forces C can be divided 

 (not resolved) into two parts, one of which is solely employed 

 in sustaining the pressures propagated by the system A, and 

 the other in sustaining the pressure mutually propagated by 

 the system C : 



2. In supposing that these latter forces can be removed by 

 the principle of the superposition of equilibrium. 



I come now to speak of the principle itself, that " the sum 

 of the forces of the system B, each being considered a function 

 of the coordinates of its point of application, is a minimum." 

 It is very usual (and 1 believe the method has never been ob- 

 jected to,) when a general principle is proposed, to try it in 

 particular cases, the results of which are known beforehand 

 from some independent source, and if it fail in any of these 



