where K' is the moment of inertia of the magnet and appendages, and 

 fi the induction coefficient at temperature t. 



If 9 be kept small enough this gives an isochronous vibration whose 

 half period T x is given by 



mX 1 1 m 



whence mX = (t^K'/T^) 1 + _- gf - 2 7 2 + C= ) (7). 



Unless be kept very small, a correction becomes necessary for 

 " finite arc " of vibration ; and we then encounter the difficulty that 

 the torsion couple is ®9 and not © sin 9. 



This is rarely, however, of practical importance, except at places where 

 X is specially small, supposing one avoids coarse suspension fibres. 

 At Kew 0/mX very seldom reaches 0*001, and# need never exceed 2° ; 

 and under such conditions ® sin 9 may be freely written for 0(9. The 

 correction for " finite arc " then presents no peculiarity. 



A second criticism that may be passed is that (6) makes no allowance 

 for air resistance ; in the absence of experimental data I have nothing 

 to say on this point. 



§ 26. In the deflection experiment the deflecting and deflected 

 magnets are at right angles, the latter making an angle u with the 

 magnetic meridian. 



Supposing t' the temperature, // the induction coefficient of the colli- 

 mator magnet during this experiment, and X' the horizontal force, we 

 have — 



X'/m = 2r~ 3 cosec u { 1 - qt' - qt" 2 - (fx'X'/m) sin u} (1 + Pr~ 2 ).. . (8), 



assuming the term Qr~ 4 negligible. 



Here r is the actual distance at temperature t' between the centres of 

 the two magnets. 



Unless a large magnetic storm is in progress — in which case an abso- 

 lute observation of horizontal force is worthless — we may regard X 

 and X as equal in the small terms of (7) and (8), and so may write 

 these equations as 



mX - (t^K'/T^) 4- {1 + (0/mX) -qt- +2[ir-* eoseot*}, 



X'/m = 2r~ 3 cosec u (1 + Vr 2 ) (1 - qt' - qt' 2 - 2//7- 3 ). 



Thence, eliminating m, we have 



XX - 2?r2K ' CQSec u ( 1 + Pr~ 2 ) (1 - qt' - qt' 2 - 2//r~ 3 ) . , 



r 3 Ti 2 1 + (®/mX) -qt- q'f 2 + 2fir~ s cosec u'" { ' } ' 



This differs from (4) in several respects; but some of these possess 

 little real significance. 



2 G 2 



