208 
MR. LUBBOCK ON THE PENDULUM. 
If the two knife edges are isochronous, and n = r 2 
k 2 + K + r ) 2 _ k 2 + (Qq + rf 
a x c 2 
7 2 _ ci K + r ) 2 — a 2 (g! + r ) 2 
^ ~ C 2 — 
The length of the simple pendulum = <? 2 + «i + 2 r = the distance be- 
tween the planes which vibrate on the knife edges. 
Index to the notation. 
0x,0y,0 z rectangular coordinate axes meeting in the point O. G the centre 
of gravity, G.r ; , G y,, Gz,, their principal axes which intersect each other in the 
point G. C the point in the axis Ox, where a perpendicular let fall upon it 
from the centre of gravity G cuts it, C' the point when the plane (zy) cuts the 
axis Ox ; C" the point where one of the surfaces of the pendulum cuts the same 
knife edge, G" the point in this surface where a perpendicular from G cuts it. 
g the force of gravity 
y t = x t tan h -f- /3 
tan S . 
Z. = X, z i, + 7 
1 1 tan S' 1 ' 
the equations to the axis O# referred to the coordinate axes G^, Gy t , G z p so 
that h and l' may be considered as the deviations of the knife edge in azimuth 
and altitude. 
G C = a, G C' = a'. 
M = the mass of the pendulum. 
A, B, C the principal moments of inertia. 
A = d/A-2, B = M k' 2 , C = Mk"2. 
e, s', s" the angles which the line 0.r makes with the coordinate axes, Gx p 
Gy,, G z r 
t = half the thickness of the pendulum. 
(3 = a! sin X, y = a' cos X. 
x, y, z the coordinates of the centre of gravity. 
r the radius of curvature of the knife edge. 
