On the Oscillation of the Pendulum. 241 
tween the total circumferences of the two small earth’s circles, 
just mentioned. 3. 
Let Pmc be a meridional 
section, EO the equator, ® 
latitude of C, and half 
the angle subtended by the 
chord of vibration Cm, and 
R the earth’s radius. 
‘and R” are the radii. 
of the circles of rotation of 
the points C and m; then R/ 
=Rcos#,R”= Ros (+4) 
and 
ww. 
SS, 
~ x 
x 
circumference R’ =27R cos 
‘ R”=2-R cos(®+ %’), 
We have proved that the length of the arc of the dial moved over 
by the pendulum in 24 hours is equal to the difference between 
these circumferences . 
cire R’—cire R”=2aR (cos 6— cos (P+) )= 
22R (cos S— cos ®cos o + sin Hsin &) 
Where ® (as is actually the case) is extremely minute, cos’ 2 is 
sensibly =1 and the above expression becomes 
circ R’/—cire R’=22R sin @sin &, 
Bat Rsin #=Cm and 22R sin is therefore equal to the 
circumference of the dial circle. bt 
*R sin ® sin @ is therefore equal to the dial circumference, 
or 360° multiplied by the sine of the latitude. : 
In other words the plane of oscillation will move in 24 hours 
through an angle equal to 360° x a piprinal nn o8 a result 
arrived at by other methods and prove y observation. as 
he foreyroies dein oneeseeit is rigid; it is based epee sim- 
Ple fact that the pendulum has (with its point and axis . ca 
sion) a rotary motion of its own, around the axis of the Kew a 
and that while this rotary movement is preserved unchang > € 
oscillation of the pendulum is governed by the same laws in re a 
ence to its axis of suspension as if both were motionless in pe 
4 Supposition on which all the investigations of the emule 
Sravitation, as applied to the earth and heavenly bodies, alg ieee 
t assumes nothing unless it be, that the mere one mo 
which the direction of the axis of suspension and 0 age - 
gether undergo, will not permanently alter the direction of t 
chord of the arc of oscillation.* 
Srconn Serres, Vol. XX, No. 59.—Sept., 1856. 31 
