202 
MR. HOPKINS’S RESEARCHES IN PHYSICAL GEOLOGY. 
By a precisely similar investigation applied to the moon’s action we obtain 
(A 4 ) = h A 4 , 
(B 4 ) = AB 4 , 
(D 4 ) = h D 4 . 
d~ v 
7. It remains for us to determine the approximate value of 
Since the exact position and form of any surface of equal pressure and density in 
the internal fluid will depend on the disturbing forces of the sun and moon, as well 
as on the mutual attractions of the different particles of the whole mass, it will be 
constantly varying with the positions of those luminaries. The hypothesis I shall 
Q y. 
make for the purpose of determining an approximate value of j^is this — that the in- 
stantaneous position and form of any surface of equal pressure and density are the same 
as those it would have in its position of equilibrium under the action of the forces at 
the proposed instant, and supposing the whole mass fluid. Each fluid particle would 
then move with the surface to which it belongs, and in a direction at least very ap- 
proximately normal to it, and therefore passing very nearly through the centre of the 
earth, as previously stated (Art. 3.). The extreme slowness of the absolute motion of 
each particle will render this hypothesis quite approximate enough for our purpose. 
We must first determine the surface of equal pressure, supposing it one of equili- 
brium ; and in doing this we may restrict the investigation to the case of the sun’s 
action. From the results thus obtained those depending on the moon’s action will 
be immediately deducible. 
Let X, Y, Z be the whole of the forces on the fluid particle (x, y, z) parallel to the 
coordinate axes, arising from the attractions of the other particles of the mass, the 
centrifugal force, and the disturbing force of the sun. Then 
^^Xdx + Ydy + Zdz; 
d\ d Y dV 
and if ^ 7 ? > and be the attractions on the particle x, y, z, 
X = S + " 2 x + 7* { (t “ 4" cos 2 a) x + T sin 2 A • * } 
v ^ A 1 o ^ 
Y = — + cu 2 y- r~y, 
dy 
13 
Z = S + ${4sin2A.* + (4- + fcos2A) 2 }. 
substituting the values of X', Y' and Z' given in the preceding article. 
Consequently we have for the surface of equal pressure 
c = v + \ (^ 2 + y 2 ) 
+ 27^ {(Y-¥ cos2A )^-3/ 2 +(l+|)c°s2A.z 2 + 3sin2Axzj 
