58 Mr Green on the Vibrations of Pendulums 
d¢ df , px df dp_ py df dpb_ me df an 
dz Sale abe * abbe da’ dy a@bcdy dz abe dz” a 
© 
and, consequently, at the surface in question, where f= 0, 
I Lin Wits Pdf, pe ba df dp_ py af dp_ pz da 
date a yf @be 0d da’ dy a®Uc¢ dy’ dz a°U'c dz 
r : : c d d 
These values, substituted in (6.), give, when we replace eS s nd a 
with their values at the ellipsoidal surface, 
o= neuf here ee (8.) 
which may always be satisfied by a proper determination of one of the con- 
stants A and yu, the other remaining entirely arbitrary. 
From what precedes, it is clear, that the equation (2.), and condition to 
which the fluid is subject, may equally well be satistied by eve 
p(s 4H fl) vont o= (ran fh 
iv'a) 
provided we determine the constant quantities therein contained by means 
of the equations 
O=5 xen f er +o a vu fer § ae 
respectively. The same may likewise be said of the sum of the three values 
of @ before given. However, in what follows, we shall consider the value 
(3.) only, since, from the results thus obtained, similar ones relative to the 
cases just enumerated may be found without the least difficulty. 
Instead now of supposing the solid at rest, let every part of the whole 
system be animated with an additional common velocity — A in the direc- 
tion of the co-ordinate w. ‘Then, it is clear, that the equation (2.), and con- 
dition to which the fluid is subject, will still remain satisfied. Moreover, if 
x’, y’, 2’ are now referred to three axes fixed in space, we shall have 
a =a — frdt, y=y; a 
