Determination of Resistances in Absolute Measure. 337 



be doubted that the advantage of III. in respect of sensitive- 

 ness is very considerable. 



Experience has shown that there is no difficulty in controlling 

 and measuring the rotation of the coil ; but of course some 

 auxiliary apparatus is required for the purpose. Against this 

 may be set the escape from observations of the time of vibra- 

 tion, and from any uncertainty which may attach to the bal- 

 listic use of a galvanometer-needle. The suspended magnet 

 may easily be made of such dimensions that no appreciable 

 error can arise from supposing it to be infinitely small. 



On the other hand, some new complications enter in method 

 III. which I desire to state in full. In the first place we have 

 to take account of the fact that the inductor moves in a field 

 of force due not only to the earth, but also to the suspended 

 magnet itself. I do not think that the correction thus ren- 

 dered necessary (about 4 parts per thousand in my experi- 

 ments) adds in any appreciable degree to the uncertainty of 

 the final result ; but we may take note of the fact that an 

 auxiliary determination must be made of the ratio of the mag- 

 netic moment of the suspended magnet to the earth's hori- 

 zontal force. 



If the metal ring on which the wire is wound be on a large 

 scale and sufficiently massive for strength, currents may be 

 developed in it, even although it is divided into two parts by 

 ebonite insulation. In my experiments the effect of these 

 currents was very sensible, and had to be allowed for by careful 

 observations of the deflection produced when the ring was 

 rotated with wire circuit open. In any future repetition it 

 will be worthy of consideration whether the ring should not 

 be formed of less conducting material. It does not appear, 

 however, that the final result can be prejudicially influenced ; 

 and the effect produced by secondary closed circuits allows us 

 to verify the insulation of contiguous layers or turns of the 

 wire by comparing the deflections obtained before the wire is 

 wound with those obtained after winding, but with main cir- 

 cuit open, any difference being due to leakage. 



But the most serious complication in method III., and one 

 which in the eyes of some good judges weighs strongly against 

 it, is the disturbing influence of self-induction. With respect 

 to this., the first point to be noticed is that the action is per- 

 fectly regular, and that the only question which arises is 

 whether .its magnitude can be determined with such accuracy 

 that the final result does not suffer. Now the operation of 

 self-induction is readily submitted to calculation if a certain 

 coefficient (L) be known. We find 



B = ttV-W cot $ { 1 - U tan 2 </> - U 2 tan 4 <f> } , 



