330 Theory of the Magnetic Balance of Hughes. [Feb. 14, 



has been turned ; and is proportional within 1 per cent, for angles 

 less than 45°. For the practical purposes for which the magnetic 

 balance is designed there will therefore be no need of a special 

 calibration table. 



4thly. As it is inadmissible to obtain a great range of compensation 

 for both large and small magnetic forces by diminishing or increasing 

 the distance of the compensator from the indicating needle, it is pro- 

 posed to obtain this range by placing over the compensator a second 

 magnet, capable of rotating round the same axis and having the same 

 length between its poles. A third magnet may be added, similarly, to 

 increase the magnetic moment of the compensator. 



Fig. 4. 



5thly. In the preceding investigation it has been assumed through- 

 out that the length of the indicating needle was small relatively to 

 r and £, so that the terms of the second and higher orders due to its 

 length might be neglected. This was not the case in the original 

 instrument of Hughes, in which the needle was 5 centims. in length. 

 The use of a very small needle is open to the objection that it is not 

 so sensitive as an index. It is therefore proposed to substitute as an 

 indicating needle one of the type sometimes termed " unipolar," that 

 is to say, having one pole set in the axis of rotation, so that only one 

 pole has a moment of couple about the axis of suspension. A steel needle 

 about 5 centims. long has about 1*5 centims. of its length turned up 

 at right angles, the suspending fibre of silk being attached to the 

 turned-up end; a counterpoise is added behind, and a small addi- 

 tional weight is placed below on a brass wire attached immediately 



