MR. LUBBOCK ON THE PENDULUM. 
20(5 
The author of this article assumes the equations of the axis of rotation to be 
x, — a Zj -f- a 
&, = **, + & 
and he gives the equation h = — = 
_ >/ + /3“ 
V 1 + <z a + b 2 
this equation is incorrect ; it should be 
✓ {(« 9 + / 3 2 )(1 + a * + b*)-(ax + b(; 3 ) 5 } 
h = 
V (1 + a 2 + 5 s ) 
It is easy by proper substitutions in the equations which I have given, to 
ascertain the influence of any deviation of the knife edge ; and for this purpose 
I shall take the pendulum described in the Annals of Philosophy, vol. iv. 
p. 13/. used by Mr. Baily, of which the length is 62 inches, the width 2 inches, 
and the thickness ‘2/5 inch. One of the knife edges is 5 inches from the extre- 
mity ; and therefore from well known expressions for the moment of inertia in 
a parallelepiped, 
3l 2 + l 
k 2 = 
= 320-6666 
H 2 = g -llJ- 'I . 3752 = 3 2 0 - 339 
k" 2 = 1 - 75 ' = -33964 
If X, o, V and e, = 0, G Ch = 11.2514, G C 2 = 28.5, Ci C 2 = 39.7514 
1 . When S' and e, = 0, the true length of the simple pendulum 
{ sin !} 2 
qu q ii 2 Cj G X C 2 G 
Ci C 2 
= 397514 + -80667 
{siny} 2 
2. When S' and g, = 0, the true length of the simple pendulum 
P - IP 
* V9 
sin o' 
p a p a i 
— T (jc 2 _ GO, 
= 39./5 14 + .013137 sin S 2 . 
