459 
of Edinburgh, Session 1868 - 69 . 
3 . These two equations (5) and (6) contain every possible case 
of the motion, from the most infinitesimal oscillations to the most 
rapid rotation about the point of suspension, so that it is necessary 
to adapt different processes for their solution in different cases. In 
this abstract we take only the ordinary Foucault case, to the degree 
of approximation usually given. 
4 . Here we neglect terms involving to 2 . Thus we write 
ii = 0 , 
and we write a for a„ as the difference depends upon the ellipticity 
of the earth. Also, attending to this, we have 
r 
p = — ~ a + ®r 
r a 
■ ■ ■ ( 7 ), 
where (by ( 6 ) ) 
Saw — 0 , 
• • • (8), 
and terms of the order w 2 are neglected. 
With (7), (5) becomes 
— - Yaw = 2Va=r ; 
a a 
so that, if we write 
II 
e 
... (9) 
we have 
Ya(w + 92 2 w) = 0 . 
Now, the two vectors 
. . . ( 10 ). 
ai - a sin A and Yia 
have, as is easily seen, equal tensors ; the first is parallel to the line 
drawn horizontally northwards from the point of suspension, the 
second horizontally eastwards. 
Let, therefore, 
w = x (ai — a sin A) + y Via (11), 
which (x and y being very small) is consistent with (6.) 
From this we have (employing (2) and (3), and omitting to 2 ) 
zs = x (ai — a sin A) + y Yia — xio sin A Via — yco (a — ai sin A), 
w = x(ai — a sin A) + yYia — 2 xm sin AY ia — 2y« (a — ai sin A). 
With this (10) becomes 
** (at — a sin \) + y Vta — 2xa) sin A Via — 2ya>( a — at sin \) + n 2 x (at — a sin A) + n 2 t/ Via] = o 
