196 Prof. Moseley's Reply to Mr. Earnshaw's 



C" those equal and opposite to the pressures mutually propa- 

 gated in C. 



Now it is manifest that if the system 0' be withdrawn, the 

 equilibrium will remain. And yet the forces of the system 

 mutually propagate no pressure ; and are equivalent, se- 

 verally, only to the pressures propagated to their points of ap- 

 plication from the forces of the system A. It is therefore 

 possible, &c. &c. 



Were this not, as I hold it to be, a demonstration that the 

 forces of the system C may, under any conceivable circum- 

 stances, sustain those of A, and yet mutually propagate no 

 pressures, yet I should decidedly object to Mr. Earnshaw's 

 position that any portion of a system of forces not parallel 

 must of necessity mutually propagate pressures. 



Suppose we apply to a solid body any number of equal 

 and opposite forces ; these may certainly have directions how- 

 ever oblique to one another, and yet not mutually propagate 

 pressures. Or, to take a case bearing more immediately upon 

 the point at issue, suppose that to the different points of ap- 

 plication of the system A, we apply forces having for their 

 resultant one of the forces C, and then to the same points 

 forces having for their resultant another of the forces of the 

 system C, and so on until we have thus obtained all the forces 

 of the system C. Now, under these circumstances, the systems 

 of forces concerned will have become precisely analogous to 

 the systems A and C; but by the principle of the superposi- 

 tion of forces, it is manifest that no pressures will be mutually 

 propagated among the forces of C. 



Mr. Earnshaw admits that he has urged this objection with- 

 out much confidence in its validity. The explanations given 

 above will, I think, induce him to yield to me this much of 

 my demonstration. 



And here I would call his attention to the fact, that this ad- 

 mitted, the principle for which 1 contend is established. It 

 follows rigidly that each pressure is a minimum subject to the 

 conditions imposed by the equilibrium of the whole. What 

 remains has reference, not to the demonstration of the principle 

 of least pressure, but to the expression of its conditions in the 

 language of analysis, and to its application. 



This remark bears especially upon Mr. Earnshaw's next ob- 

 jection. He states that he is " unable to comprehend why 

 we are to consider the forces as functions of the coordinates 

 of the points at which they are applied." 



My answer to this is, that there appears to me the same 

 reason for fixing upon these as the variables upon which those 

 functions depend, as for assigning the variables to any other 



