Note on the preceding Paper. 443 



the part played by radial forces as that from which the error 

 in the boundary conditions arises. 



The rest of the work is the same as in Love's book, and thus 

 it is unnecessary to give it here. 



The erroneous theory and my theory give exactly the same 

 results for an incompressible sphere, but there is a difference 

 in the results for a compressible solid. I will give here the 

 correct result when a disturbing force, which has a potential 



W 2 , acts on a sphere and the value of the ratio - is unity. 



The radial displacement is 



n 2253 W 2 



where 



275 + (9yf)S g 



\ 



& 



The result given by the incorrect theory (Love's ' Elasticity,' 

 Art. 183) is 



: lQo— c 



225S W 2 



275 + 933 g 



V 



XLII. Note on the preceding Paper. By A. E. H. Love *. 



MR. PRESCOTT'S criticism of my solution is to the 

 effect that I have not used correct expressions for 

 the body forces. The right way to obtain expressions for the 

 components of the body force at a point, say P, is to express 

 the potential at Pin terms of the coordinates of P and differ- 

 entiate the expression so obtained with respect to the co- 

 ordinates of P. What Mr. Prescott does is to differentiate 

 (with respect to the coordinates of P) the potential at that 

 point Q to which the particle that was initially at P is 

 displaced. I do not know of any justification for this 

 procedure. 



Mr. Prescott's argument in the paragraph of his paper 

 beginning " Now there is a second meaning to «v, y, z" seems 

 to me to be unsound. Whenever, as in this problem, it is 

 necessary to distinguish the forces that act upon the body in 

 the strained and unstrained states, the coordinates a, y, z that 

 occur in the equations of equilibrium must be taken to be the 



* Communicated by the Author. 



