Determ ination of the Earth's Horizontal Magnetic Force. 407 



Taking the data for the Kew unifilar in 1892, we find 

 Bu = 23 x 1CT 6 (or about 48"). 



Xow 8u is the error, in circular measure, in the observed deflection w, 

 and the consequent error in the horizontal force, deduced from the 



Thus the error is nearly one unit in the last significant figure. As 

 the error varies as y 2 + z 2 , it would become of very sensible magni- 

 tude if y and z were twice or thrice as large as in the Kew unifilar. If 

 I may judge from the figures recorded of unifilars under examination at 

 the Observatory, such large values of y and z really exist. 



The source of error just considered alters the observed deflections 

 at 30 and 40 cm. in the same sense, and seems unlikely to exert an 

 appreciable influence on the value of P. 



§ 43. Causes of Asymmetry. — A collimator magnet ought to be ad- 

 justed in its stirrup until it is exactly horizontal in the vibration 

 experiment. The magnetic forces acting on it tend, in this magnetic 

 hemisphere, to pull the [north pole down, and consequently the centre 

 of gravity of the composite body composed of magnet and appendages 

 must be out of the vertical, which is the prolongation of the suspend- 

 ing fibre, and on the same side of it as the south pole. If the stirrup 

 Is symmetrical, and if the lens and scale of the magnet are equal in 

 weight and symmetrically situated, then the C.G. of the magnet itself 

 must, in this hemisphere, lie on the same side of the suspending fibre 

 as the south pole. 



Now the suspending fibre in the vibration experiment, if produced, 

 should cut the magnetic axis at the same point as it is cut in the 

 deflection experiment] by the vertical plane which is perpendicular to 

 the magnet, and contains the fiducial mark on the sliding frame. 



Thus in a perfectly symmetrical magnet the middle point of the 

 magnet's length, and so the middle point of the line joining the " poles " 

 (assuming magnetic symmetry) must lie on one side of the fiducial 

 mark, and so of the graduation on the bar which coincides with it. 



Calling the error thus introduced in the distance r between the 



of 8m, a quantity "whose physical significance is easily grasped. Bat a sufficiently 

 exact value of 5X can be obtained more simply from the relation (r + Sr) 3 (X + 5X) 2 



(14). 



whence 



X = 0-183, cotw = 3-61, 

 SX = - 0-0000075 C.G.S., approx. 



= r 3 X 2 (see (4)). 

 VOL. I. XV. 



2 H 



