Forces derivable from a Potential of the Second Degree. 49 

 *} (l-a*/o) 



x i- 



zz, it should be noticed, is negligible compared to yz and zx, and 

 these in turn negligible compared to xx, yy and xy. The values of 



xjc, yy, and xy bear to the corresponding first approximations in the 

 case of an elliptic disc* of semi-axes a and b, rotating about its 

 cylindrical axis with the same angular velocity w, the common ratio 



(41). 



This ratio also applies to the first approximations to A, s x , s y , s zt 

 and a xy ; while the other strains are in both cases negligible compared 

 to these. It applies further to aja and 6/6. Thus the great 

 majority of the results worked out for the rotating disc can be 

 simply modified so as to apply to the flat ellipsoid by means of the 

 following table which proceeds to three places of decimals. 



Table I. Values of (3a 4 +2a6 2 +36 4 )-:-{4a 4 +(3 + i 7 ) a. 2 8 +4& 4 }. 



On either the " greatest strain " or the " maximum stress- difference " 

 theory of rupture, the limiting angular velocity in the flat ellipsoid 



* 'Phil. Mag.,' July, 1892, pp. 70100; see results (17), (18), (19), p. 75. 



