SPHEROIDS, AND OH THE OCEAN TIDES UPON A YIELDING NUCLEUS. 
3 
-J+vV 3 a+X = (T 
dx 
—|W/?+Y = 0 - 
—& +wV+ z =° 
(i) 
where x, y, z are the rectangular coordinates of a point of the fluid ; a, {3, y are the 
component velocities parallel to the axes ; p is the mean of the three pressures across 
planes perpendicular to the three axes respectively; X, Y, Z are the component forces 
acting on the fluid, estimated per unit volume ; v is the coefficient of viscosity ; and 
o • i x i • . d? d? d? 
V" is the Laplacian operation - ,+ 7 y+ , : ; 
CLX CVlf Cl% 
Besides these we have the equation of continuity = 0 
Also if P, Q, R, S, T, U are the normal and tangential stresses estimated in the 
usual way across three planes perpendicular of the axes 
Now t in an elastic solid, if a, /3, y be the displacements, m —\n be the coefficient of 
dilatation, and n that of rigidity, and if S= ^ + ~; the equations of equilibrium 
are 
+« v m+ X = 0 
niy + nv 2 /3+Y = 0 
dy 
m~ -j- n v 3 y+Z = 0 
dz ' 
J 
(3) 1 
Also 
P=(m-n)S+2n^ Q=(m-w)S + 2n^, R=(m—n)S + 2nJ . . (4) 
and S, T, U have the same forms as in (2), with n written instead of v. 
1 72 / 
Therefore if we put — p=-(P + Q + R), we have p— —(m—~)S, so that (3) may be 
O 
written 
* Thomson and Tait’s ‘ Nat. Phil.,’ § 698, eq. (7) and (8). 
2 B 
