in Fimd Media. 59 
and if X’ represents the co-ordinate of the centre of the ellipsoid referred 
to the fixed origin, we shall have 
Adding now to ¢ the term —) 2 due to the additional velocity, the ex- 
pression (3.) will then become 
d 
p= Led = 
and the velocities of any point of the fiuid will be given, by means of the 
differentials of this last function. But @ and its differentials evidently va- 
nish at an infinite distance from the solid, where f= «©; and consequently, 
the case now under consideration is that of an indefinitely extended fluid, 
of which the exterior limits are at rest, whilst the parts in the vicinity of 
the moving body are agitated by its motions. 
It will now be requisite to determine the pressure p at any point of the 
fluid mass. But, by supposing this mass free from all extraneous action 
V =0, and if the excursions of the solid are always exceedingly small, com- 
pared with its dimensions, the last term of the second member of the equa- 
tion (1.) may evidently be neglected, and thus we shall have, without sen- 
sible error, 
dp 
= 3es- 1. €. b eta Fe 
or, by substitution from the last value of ?, 
d 
p= px ft 
a 
Having thus ascertained all the circumstances of the fluid’s motion, let 
us now calculate its total action upon the moving solid. Then, the pressure 
upon any point on its surface will be had by making f=0 in the last ex- 
pression, and is 
ga df 
= dt be 
HQ 
