MR. LUBBOCK ON THE PENDULUM. 
207 
3. When X, S and s / = 0, the true length of the simple pendulum 
7.2 _ 7JI2 S/2 
= C/' C 2 " + g - 07-^C, sin ^' 2 - 2 G c . sin -V 
§/3 
= 39.7514 + 18.5712 sin S' 2 — 22.5028 sin 
4. When X, & and S' = 0, the length of the simple pendulum 
= c L c ? 
COS Ey ' 
The following table shows the increase in the number of vibrations in a day 
due to different values of X, h, h', and t r 
A. 5 if 
30' .62 .00 1.08 1.85 
1° 2.66 .00 4.20 6.54 
So that if, for example, X — 1°, the number of vibrations in a day is increased 
by 2 -66, and a deviation S' in altitude of 1° has the effect of making the distance 
between the knife edges less than the true length of the simple pendulum by 
.00394, and of increasing the apparent number of vibrations by 4.20 in a day. 
I shall now consider the case in which the plane is 
moveable with the pendulum, and rests upon the 
knife edge, which is fixed. 
Let D E F be a section of the knife edge, F O = r 
the angle D O F = 0. 
A G = y, OA = 2 ,GH = « 
y = B C + C G, ultimately when 0 is small 
y — B C sin 0 + r 0, O A = O B ultimately 
z = BC cos 0. 
It may easily be shown that 
A \ % + M {§ + %] +*M g z = Mh 
(See Poisson, Trait6 de Mecanique, vol. ii. p. 189.) 
d y •=: {a cos 0 + r} d 0 
d 2 = — a sin 0 d 0 
dfl 2 
{ k 2 + (a + r) 2 } + 2 g acos 0 — h 
The length of the simple pendulum is F + (a + rf 
