244 



Dr. C. Chree. 



where u is a constant. As to the value of u, it has been proved that 

 the total viscous resistance to the motion is* 



16-/i^a6c/(xo + c 2 7o), 

 where //'is the viscosity, and 



Xo = abc f " [(a« + X) (6« + X) (e» + 



Jo 



yo = a&c j " [(a 2 + A) (fls + X) (<£ + 

 But this resistance is also equal to g (p - p)~iralc [or to jj/WS], 



« = ^</>-p')"(x»'+^yo)/iV- 



Substituting for f and / in (25), we have 



S = - n - + Mf) + ^ (p - p') a 2 z/c\ : 



M = -Tl-gp\z+ut) + yip-p')b*zlc\ 



£= -n-^+^)-^(p-^')^ h (27). 



*y = o, 



£/aj = p/// = -ig(p-p') 



The corresponding displacements, supposing the material isotropic, 



thus 



are 



1-2^ 



:[n + ^ + «0] + ^H| + ,(i-g} 



= 



1-Hr, 

 E 



,[n + ^^0] + ^^[| + ,(i-J)], 



7 = -l^[nz + gp'utz + ig P '(z*-x*--y*)] 



6E 



f- (28). 



1+7 



-^[.(• 2 + 3, + ^) + W 2 + 3j;+ ^: 



§ 7. The terms inside the first brackets in (28) contain II or gp, and 

 represent displacements which vary only with the depth of the element 

 or its distance from the centre of the ellipsoid. The terms containing 



# Cf. Lamb's < Hydrodynamics,' Art. 296. 



