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of the earth, is to cause a separation between the axis of rota 
tion of the external shell, and the axis of rotation of the in- 
ternal fluid. ; 
The effect of such a separation will plainly be to develop 
a force of friction between the fluid and the shell. It becomes, 
then, a question of considerable importance to ascertain whe- 
ther this friction, which of course exercises a retarding force 
upon the velocity of rotation, produces any appreciable effect 
upon the length of the day. 
For very small relative velocities, as in the present case, 
the force of friction may be taken to be proportional to the 
velocity. If, then, w represent the velocity of rotation of the 
earth, y the distance of any point on the inner surface of the 
shell from the axis of rotation of the shell, and a the angle 
between this axis and the axis of rotation of the fluid, it is 
easy to see that the moment of the friction round the axis of 
rotation will be 
kw (1 - cos a) [ yd 8, 
k being a constant depending upon the nature of the fluid, 
and dS the element of the surface. Assuming the shell to be 
spherical, which is very nearly true, and extending the inte- 
gral through the entire surface, this becomes 
Srkw 
a‘ (1 — cosa), 
a being the internal radius of the shell. The equation of ro- 
tation of the shell will be, therefore, 
,, dw Sirhaw4 
ey eee ee _ 
Mk i 3 (1 - cos a), 
Mk? being the moment of inertia of the shell. 
The author then proceeds to perform the calculation, on 
the supposition that the earth is filled with a fluid, whose force 
of friction is such that it would in 1’ reduce to its ;45th part, 
the velocity of a sphere composed of a material similar to that 
