492 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A 
and this by means of (30) and (31) reduces to 
{— 40? +(e —y')} —B. 
Hence the complete value of y, is 
amet f— 40? 4+ 2 — yy} + Byry + Bowe’ + Boyz’ 
= Bi [—Wep oy} + Bay +2 wef Eye ape, (32!) 
where B,, B,, B; are given in terms of 6’), 6’, 6’; by equations (32), (33). 
From equations (6), (34) it will be seen that, in the motions with which we are 
dealing, w, v, w are linear functions of x, y, z. Hence the components of molecular 
rotation of the fluid, which involve first differential coefficients of w, v, w, will be inde- 
pendent of x, y, z. This justifies the assumption made in § 1 of the paper. 
§ 7. Calculation of Couples on the Shell due to Fluid Pressure. 
At any point of the fluid the pressure is given by (1); we have, viz. :— 
P = pilV, + 30° (2 + y')} — pil 
Let us now refer to a new set of rectangular axes, Ox,, Oy,, Oz,, coincident with 
the principal axes of the ellipsoid in its displaced position. The direction-cosines of 
one set of axes relatively to the other are given by the scheme 






mH | Y 21 | 
i if —6, 0, | 
= (35). 
| y 0; 1 —6, 
= | | 
| Zz vere 6, 6, | 1 | 
| | 

v= XL, — Y,9, + 2%, 
Y= 9, — HO, + 24s, 
2% — ©O,+ WF) 
