240 
MESSRS. R. T. GLAZEBROOK AND J. M. DODDS ON THE 
The time of a complete vibration was measured in the usual way by noting the 
times of 8 or 10 transits of the resting point over the cross wire of the telescope, 
then waiting for the period occupied by some 10 or 12 oscillations and again observing 
the times of 8 or 10 transits. The value thus determined requires reducing to that 
for an infinitely small arc. 
Now we know that if during the observation the arc of oscillation change from 
cq to a,, and if T be the observed time of oscillation, then 
T = T '{ 1 -§( SinS 4 +Si ' ia ?)} 
neglecting higher powers. 
In the observations the value of cq was about 3°, that of oq about 1 0 ‘30the 
correction thus amounts to '000025 and is quite inappreciable. 
The value of X was obtained by setting the needle vibrating, the secondary circuit 
being closed, and observing a series of resting points. If p x , p n be the amplitudes of 
the first and n th vibration we have 
Two independent observations of 17 vibrations gave 
Whence 
— = 1’2913 and 1-2909 
Pn 
X=-0159 
It is the absolute resistance of the secondary circuit; this is very nearly but not 
quite equal to R, the resistance of our standard coil, and the difference between the 
two can be expressed in terms of the resistance of the wire of the B A bridge. This 
wire is 1 metre in length, and is divided into millimetres; let p be the resistance of 
1 millim. The wire is graduated from E to F, (fig. 1); let G L be the position of the 
sliding contact piece when there is no current through the galvanometer, P P', Q Q', 
and M N being connected. 
Let 
EG 2 =£c millim. FG^^ millim. 
R is the resistance of the circuit Q' Q G B N M P P'. 
Hence 
K+£P_W 
R + yp U 
Now interchange U and W, and let x y' be the new values of x and y. 
