BALANCE OR VERTICAL ForcE MAGNETOMETER. XXXV 
plane, and T is the time of one vibration in a vertical plane.* 4 € is obtained from 
the observations in micrometer divisions, one division being = 0’:1003.4 
The time of one vibration in the horizontal plane, T’ = 12*-00.t 
Time of vibration in the vertical plane. 
The needle being in its usual position on the agate planes, the moveable wire 
of the left micrometer is made to bisect the spider-cross ; the needle is then vibrated 
by means of asmall piece of steel, through an angle of about 40 micrometer divi- 
sions or 4’, and the periods of the cross passing the wire, are estimated to a tenth of a 
second (See Table 12, Introd. 1843, p. xxxix.) The are of vibration at the com- 
mencement was measured by means of the right micrometer, it was usually taken 
very small on account of the difference in the times of vibration with difference of 
are (afterwards noticed, 54), although it is now certain that large arcs of vibration 
give a time which satisfies better the previous equation and the true coefficient of 
the instrument. 
The following Table contains the observations for the value of T made in 1845 
and 1846. 
The number of vibrations observed, is given in the column after that contain- 
ing the are of vibration at commencement. 
TABLE 4.—Values of T, the Time of Vibration of the Balance Needle in a Vertical 
Plane, with the Temperature of the Needle, in 1845 and 1846. 
Arc at |Number| Time 
Com- of of one 
mence- | Vibra- | Vibra- 
tions. | tion, i] tion. | Needle. 
res Are at [Number] Time Fd 
Gottingen of Agios Gottingen 
Mean Time, Vibra- | Vibra- Mean Time. 
* See Dr Luoyn’s Account of the Magnetical Observatory of Dublin, p. 38. 
+ Introduction, 1843, p. xxxviii. { Introduction, 1841-2, Table 15, p. xxxv. 
