150 HENRY A. KOWLAXD 



two as taken from the table published by the British Association Com- 

 mittee. If R is the true resistance, 



1 1 



We shall then find approximately 



n _ 1 + tan v' ; ' tan a _ I tan <l'" tan a 



~ /., sin a V- tan a 

 -ft 1 



tan f/ \ sin ^"/\ tan 



When a is small compared with </'" or 0', and when these are also small, 

 we have 



R = R, (1 + a 2 (a 2 - | 0) + &c.). 



So that by taking the mean of positive and negative rotations, the 

 effect of torsion is almost entirely eliminated. Now a is the angle by 

 which the needle is deflected from the magnetic meridian by the torsion 



1 / /?' \ 

 and its value is ( 1 -^ ) nearly, when a is small, and this, in one 



Kr \ ** I 



or two of their experiments, exceeds unity or a exceeds 28. 6, which 



Tf 



is absurd. Taking even one of the ordinary cases where -> = 102 



and (p is about ^V we have a= 12 - nearly, which is a value so large 

 that it would surely have been noticed. Hence we may conclude 

 that no reasonable amount of torsion in the silk fibre could have 

 produced the difference in the results from positive and negative 

 rotation, as has been stated by Mr. Fleming Jenkin in his ' Keport on 

 the New Unit of Electrical Eesistance/ r 



The greatest value which we can possibly assign to a which might 

 have remained unnoticed is y 1 ^, which would not have affected the 

 the experiment to any appreciable extent. 



Another source of error which may produce the difference we are 

 discussing is connected with the heavy metal frame of the apparatus, 

 in which currents can be induced by the revolving coil. The coil 

 passes so near the frame-work that the currents in it must be quite 

 strong and produce considerable magnetic effect. Kohlrausch has 

 pointed out the existence of these currents, but has failed to consider 

 the theory of them. Now, from the fact that after any number of 

 revolutions the number of lines of force passing through any part 

 of the apparatus is the same as before, we immediately deduce the 



1 ' Reports on Electrical Standards,' London, 1873, p. 191. 



