54 Mr. C. Chree. Isotropic Elastic Solid Ellipsoids under 

 To a closer degree of approximation we have, for the stress system, 



zxjzx = yz/yz = zzl(c z z 2 ) = |R/> ........ (52), 



and for the strain system, in addition to s x , s y , and s z , in (51), 



.............. (53), 



where n is the rigidity. 



An analysis of (52) gives, on a plane perpendicular to z, a 

 stress Rp (c 2 z 2 ) parallel to z, and a shearing stress jR/zr 

 along r, the perpendicular on the axis of z ; on a plane perpendicular 

 to r a shearing stress, %~Rpzr, parallel to z ; on any plane containing 

 the axis of z, no stress. 



Even in the general case with P, Q, R all existent, and secondary 

 terms retained in the coefficient of R and in II, we get for s z the 

 simple formula 



-,(a'+ &')}].. (54). 



When the bodily forces are perpendicular to the long axis, the 

 stretch parallel to that axis is thus appreciably constant over a cross 

 section ; these perpendicular forces tend to shorten or to lengthen 

 the long axis according as they act outwards from it or towards it. 



Elongated Ellipsoid Rotating about the Long Axis 2c. 

 11. Putting in (46) to (49) 



P = Q = w\ R = 0, 

 we get 



ay]., (MX 



(i-*)(s 



f { 2 a 4 + a 2 6 2 + 6 4 + r/ (a 4 Z> 4 ) }?/ 2 



