
ITS ERRORS AND CORRECTIONS, ETC. 469 
whereas by experiments with the magnet in the meridian, we find 
6 = oeere x 1-56, =; 29/2, 
7. In this experiment the angles of torsion with the bifilar wire were only 
estimated by means of a fibre attached to the wire below the point of suspension ; 
but other experiments were made with a more perfect apparatus; the ends of 
the wires were passed through holes in a brass plate of such diameter as to allow 
them to turn freely without any lateral displacement, and the ends were soldered 
into two brass pins with points, which indicated the amount of rotation of each 
wire on small circles graduated on the brass suspension plate, having the wire 
holes for centres. In this way some accurate observations were made, of which 
the following is the summary :— 
= (m = 7°7 nearly) ee by one wire in the meridian 6’ for 1° of torsion, = 0433 
two wires at right angles Av... ela, 
the latter fens, for two wires, v = 57° 13’, and v’ — v = 1° 20’; then, 
By equation (7), 6 = 264; 
By experiment, 6 = 24:8. 
Magnet (m = 2: a suspended by one wire in the meridian, 6’ for 1° of torsion, = 1-42; 
two wires at right angles to meridian, Av for 
1 of torsion, : " ; = 0-74, 
the latter as before being for the torsion of both wires, v = 14° 52’, v' —v =11’; 
then, 
By equation (7), 0 = 21"7; 
By experiment, 6’ = 21-1. 
In all instances, the confirmation is as near as could be expected. 
8. Equation (3), however, is on the assumption that the wires are wholly 
without twist before the torsion circle is turned; a supposition wholly gratuitous 
in fact, since the wires have generally been wound on bobbins before use, and the 
twist thus introduced is rarely ever wholly removed. Trials at Makerstoun in 
1841, with all the conditions as equal as possible, showed that the angle » varied 
about 1° (one degree), according as the torsion circle was turned to the right or to 
the left.* 
9. Unit Coefficient —In 1846 I employed a new method, which was free from 
the objections applying to the torsion circle observations, and in which the bifilar 
magnet was deflected by another placed at known distances.+ I have also since 
then employed the following processes. If we make W, a, 0, or / to vary con- 
siderably in the hypothetical equation (1.), and take the differences, a given 
variation of W = +a W, of a=-+aa, of /=-+ a J, will be connected with 
the observed variation of » = a v (u = 90°) by the equations. { 
* See Introduction to Makerstoun Observations, Trans. Roy. oe Ed., vol. xvii, part 1. p. 27 
} Introduction to Mak. Obs., 1848, p. Ixv.; 1844, p- xxviii. ; 1845, ?. XXVil. 
{ I have only lately learned that Mr Brooxe has employed the process by weights for his self- 
Besitoring instruments (Phil. Trans., p. 85, 1850). 
