MAGNETIC DECLINATION AT BOMBAY. 
365 
and the azimuthal adjusting-screw turned until the star was bisected by the vertical spider- 
line at the proper moment, as taken from the Nautical Almanac : it appeared, from 
observations made in May 1866, and described in detail in the Introduction to the Bombay 
Magnetical Observations for 1864, pages x to xii, that this adjustment was at that time 
very nearly correct. Secondly, a bundle of about forty threads of untwisted silk having 
been prepared with care to avoid entangling the different fibres, a brass bar of the same 
weight as the magnet was suspended and allowed to swing until it took up a position of 
rest ; the arms of the torsion-circle and the attached suspension-pin, to which the upper 
end of this thread was bound, were then turned in azimuth until the brass bar lay at 
rest approximately in the true meridian : the magnet was now substituted in place of the 
brass bar, and a reading of the scale was taken and recorded ; next, the magnet being 
provided with a suspension-hook that allows the bar to be inverted about its own length 
as an axis, without disturbing any of the attachments, this inversion was made and the 
scale again read. Now the position of the magnetic axis of the bar in the direct and re- 
verse positions would be the same, but the scale-reading would be increased in the one 
case and diminished in the other, by an amount corresponding to the deviation of the 
magnetic axis from true meridian ; hence the average of the two readings will give the 
reading that would be found if the magnet lay with its axis in the true meridian, and 
half their difference represents the deviation (in scale-divisions) from that position. 
When the instrument was last adjusted, on the 9th November, 1861, the true meridian 
reading was 28-2733; and the scale being placed in an inverted position it appeared 
erect in the telescope, so that increase of reading represents an easterly movement of 
the north end of the magnet. 
5. One other element, taking account of the magnet being restrained from responding 
fully to the changes of magnetic force by the torsion-force of the suspension-thread, 
enters into the reduction of the observations : — the torsion-force is assumed, as in Cou- 
lumb’s Electrometer, to be proportional to the angle of torsion, that is, to the deviation 
of the magnet from the position of no torsion — in this case the true meridian ; the torsion- 
coefficient, or unity plus the ratio between the torsion-force and the directive force of 
the earth acting upon the particular magnet, is determined by observing the change of 
scale-reading produced when the arms of the torsion-circle are turned through 90°, 
dividing the corresponding angle (a) by (90°— a), and adding unity to the quotient. 
In November 1861 its value was found to be 1-0028, and this has been used without 
alteration over since. 
6. The formula used in the reduction of the observations was 
D=6'-841(/— R) . c, 
where 6'"841 is the adopted value of a unit of the declinometer scale, R the true meri- 
dian reading, c the torsion-coefficient, and D is the absolute easterly declination when 
f is the observed scale-reading. The values of D thus obtained, in which form the 
