¥12 Prof. Moseley in Answer to Mr. Earnshaw's Remarks 



circumstances, the systems of forces concerned will have be- 

 come precisely analogous to the systems A and C; but by the 

 principle of the superposition of forces it is manifest that no 

 pressures will be mutually propagated among the forces of C. 

 This is one of those arguments which Mr. Earnshaw states to 

 have had the effect of strengthening rather than of removing 

 his previous objections to my theory. Will he do me the 

 favour to answer it ? Here is a case of two systems of forces 

 in equilibrium, A and C, of which the latter are oblique to 

 one another, and yet mutually propagate no pressures. The 

 pressures propagated from the different forces of A to each 

 point of application of C are exactly sustained by the force 

 applied to that point; and the case is precisely analogous to 

 that in which the forces C are supplied by the resistances of 

 as many fixed points. 



Now it might easily be shown that by varying the magni- 

 tudes and directions of the forces C these might each of them 

 be made to satisfy the conditions supposed above, whatever 

 were the forces A. The general case, therefore, that the 

 forces C may be so taken in magnitude and direction as, al- 

 though oblique to one another, yet mutually to propagate no 

 pressures, is proved. Now this general case is what Mr. Earn- 

 shaw in his first paper particularly objected against, making at 

 the same lime an exception in favour of the particular case of 

 parallel resistance; yet, strangely enough, he in his last paper 

 seems to yield the general proposition, and flies at the parti- 

 cular case. Here, however, I am happy to meet him. He 

 supposes the system A to be supplied by gravity, and the 

 forces C to be resolved, each horizontally and vertically. The 

 horizontal parts of the forces C must, he says, mutually 

 destroy, since the forces A are vertical; and it is thus proved 

 that the forces C mutually propagate horizontal pressures. 

 True ; but what hinders that the forces C should in this case be 

 taken vertically'! My argument is that they may be so taken 

 as mutually to propagate no pressures ; and if taken vertically, 

 they will propagate none. I have all along assumed that in the 

 case of gravity, in which the points of resistance are capable of 

 supplying it in any direction, that direction will be vertical*. 

 My proposition is that the forces C may be so taken in mag- 

 nitude and direction as mutually to propagate no pressures, 

 and yet sustain the forces A. Mr. Earnshaw's case of parallel 

 forces does not in the least shake this conclusion, in as much 

 as it turns entirely upon the hypothesis that the direction of 

 the forces C are given, and are not parallel to those of the 



* Mr. Earnshaw will see this by reference to my paper published in the 

 Lond. and Edinb. Phil. Mag. for December last : vol. iii. p. 431. 



