1884.] Theory of the Magnetic Balance of Hughes. 329 



Writing, as before, r=nl, this becomes : — 



T=™cos0( I + I ) . (3). 



p * 1 ( w 2 + l_2^sin0)f (w» + l + 2»sin0)t/ ' 



Assuming that the balance is adjusted for the case n=&, we get the 

 following values for this complex function of : — 



0=0, T=^x -01508. 



V 



0=30°, T=^x -01402. 

 0=60°, T=^-x -00938. 



0=90°, T=^x0. 



Z 2 



The needle, therefore, if nearly astatised when 0=0, will still be 

 nearly astatised when does not exceed 30° ; but beyond this value 

 the meridional component of the force falls off greatly, and the 

 sensitiveness alters correspondingly. 



[5.] Suggested Modifications in the Magnetic Balance. — The preceding 

 investigation has led to the following suggestions : — 



lstly. The compensator should be set so as to revolve against a 

 vertical circle placed at right angles to the magnetic meridian, having 

 its centre on the same level as the indicating needle, and magnetically 

 east or west of it. In this position, which was that chosen for the 

 experiments in which the values of P were observed for the purpose 

 of comparison with the calculated values in the preceding part of 

 these notes, the magnetic force of the compensator has no resolved 

 part in the magnetic meridian at the point where the indicating 

 needle is placed. The sensitiveness of the needle is, therefore, the 

 same in all positions to which the compensator may be turned in its 

 own plane. 



2ndly. A small magnet lying magnetically north and south of the 

 indicating needle is used to astatise it to the required degree. 



3rdly. The compensator is placed so that the distance between its 

 centre and that of the indicating needle is about 4- 6 times the half- 

 length between the poles of the compensator. If the latter be a not 

 very thick flat straight magnet, it may be approximately assumed 

 that the poles are about one-tenth of the whole length from the ends, 

 so that no very important error can arise if a distance equal to five 

 times the half-length between the ends of the magnet is selected. 

 When this is done it is safe to assume that for all positions of the 

 compensator within 55° on either side of zero, the magnetic force 

 which it exerts on the pole of indicating needle is proportional within 

 2 per cent, to the degrees of the scale through which the compensator 



