326 Prof. G. H. Darwin. [Apr. 30, 



If we put A for stress- difference, then between the centre and the 

 ellipsoid — 



19A=24a 2 -18r 2 -9r 2 cos2^ + 3v/{64(a 2 -r 2 ) 2 +r 4 -16(a 2 -r 2 )r 2 cos2^} 



• • • (A 



and between the polar surface regions and the ellipsoid — 



19A=6v/{64(a 2 -r 2 ) 2 + r 4 -16(a 2 -r 2 )r 2 cos20} . . (g). 

 This last also holds for the whole polar axis, along which — 

 19A = 6(8a 2 -9r 2 ) or 6(9r 2 -8a 2 ). 



[In the paper the form (g) for A was taken as applicable to the 

 whole sphere ; the maximum value of A arises from the form (g), and 

 was therefore correctly computed.] 



In order to find the actual value of A in any special case, we have 

 to multiply the expression for A by appropriate factors, determined in 

 the paper. For the present it will be convenient to omit these 

 factors. 



We may now from (/) and (g) determine the distribution of 

 stress-difference throughout the sphere. 



By computation and graphical interpolation I have drawn the 

 annexed figure, showing the curves of equal stress- difference through - 



Diagram showing curves of equal Stress-difference due to the weight of 2nd 

 harmonic inequalities or to tide -generating force. 



