458 Prof. W. A. Jenkins on 



magnet system deflected 45°, 



2 HZ sin (45 +a) ==* {0-u) + 2 Wl sin 45,. 

 Hsin (45 + a) -—Hsin «=Fsin45 



H = F . ,. si "f . 



sin (4o + a) —sin <x 



_ F . 



cos a-f sin a — v^2 sin a 

 F 



cos a — ( V2 — 1) sin a 



If sin a is of the order •- - then cos a is 1— J 10~ 8 , so 



that cos a can be called 1. 



Therefore H = F (1 — *41 sin a), and in order that the 



torsion can be neglected sin a must be less than n . 



The torsion which will give a deflexion of this order is 36°. 



The torsion was eliminated, as in the previous experiment, 

 by substituting a brass bar equal in weight to the magnet 

 and allowing the system to come to rest. It is not probable 

 that in such a case 36° of the torsion would remain in the 

 fibre. 



The following additional errors are possible : — 



(a) Error in the determination of the angle between the 



mirrors attached to the magnet. 



(b) Error in the determination of the angle through which 



the solenoid is rotated. 



(c) Error in the determination of the coincidence of the 



zero of the scale with the cross-wires of the telescope. 



(a) The angle is an invariable quantity and can easily be 

 measured to 10 seconds. Approximately H = F cot 45 An 

 error of 10 seconds in 45 degrees gives an error of 1 in 10,000 

 in the calculated value of H. If desired the angle could be 

 measured with greater accuracy than that indicated. 



(b) Is similar to (2). 



(c) The distance of the scale from the mirror was 75 cm. ; 

 with care the coincidence could be determined to "1 of a 

 division, i. e. '01 cm. This corresponds to an angle of rotation 

 of the mirror of approximately 15 seconds. 



The actual angle through which the mirror is rotated 

 is about 45°. Therefore we get 



H = Fcot(45 +15"). 

 This gives an accuracy of 1 in 6666, or say 1 in 7000. 



The accuracy of the experiment therefore reduces itself to 



