12 Captain Sabine’s experiments to determine the 
The force acting on the needle in the latter case is reduced, 
according to the principles of the resolution of forces, in the 
ratio of the radius to the sine of the dip ; whence calling M the 
time in which a certain number of vibrations are made in the 
meridian, P the corresponding time in the perpendicular 
plane, and D the dip, = sine D. 
In all the subsequent experiments, the needles were re- 
tained and released at an angle of 40° with the meridian, by 
an apparatus for that purpose fitted to the instrument, and 
were suffered to oscillate until the arc of vibration was 
reduced to 30° before the account was taken up, and the 
observation commenced. 
Exp. 1. Sept. 3d, with a dipping needle, the centre of gravity 
of which was rendered nearly coincident with the axis of 
motion, by a slider of silk advanced towards the end which 
was previously too light, until the needle in the meridian 
stood at 70° nearly, and became vertical when the instrument 
was moved 90° in azimuth. 
