Length of the Needle in Tangent-galvanometers. 347 



apprehension that the moment which arises is of a higher order 

 of small quantities than those included in the rest of the inves- 

 tigation, whereas it is of the same order. Accordingly another 

 term, with $ for its coefficient, and therefore of the second order, 

 needs to be added to the general equation numbered (5) in 

 my paper. This term is easily calculated : but, without being at 

 the pains of going through the work, it is easy to see that it will 

 behave exactly as the other small terms which have been included. 

 In fact the new term arises from the difference of the action of the 

 current on the two poles of the needle ; and as this difference 

 would gradually decrease to nil if the centre of the needle 

 were moved from the position it occupies in Gaugain's galvano- 

 meter into the position it has in the ordinary galvanometer, it is 

 plain a priori that the most considerable term of the series ex- 

 pressing the moment (which is of the second order of small 

 quantities) vanishes as the needle approaches the latter posi- 

 tion. 



Hence no term of the second Order needs to be added to for- 

 mula (6), which has reference to the common galvanometer; but 

 a new term of that order should be added to formula (7), which 

 relates to Gaugain's instrument, — thus leaving the conclusion at 

 which I arrived undisturbed, that, " though in Gaugain's galva- 

 nometer we get rid of the trouble of applying a correction for 

 the length of the needle, it is necessary to attend carefully to 

 the position of the needle in its cradle, and to the horizontal 

 adjustments of the point of suspension, lest errors should creep 

 in of which it would be impossible to make any exact estimate ; " 

 and that " in conducting investigations in which accuracy is a 

 point of much importance, the ordinary form of tangent-galva- 

 nometer is to be preferred." (Phil. Mag. February 1858, p. 139.) 



It may be well to add that the small moments arising from 

 the other defects of adjustment which could exist (such as a slight 

 lateral displacement of the axis of rotation from the line joining 

 the poles, or a slight dipping of the needle, either when at the 

 meridian, or from the state of equipoise ceasing when it deviates 

 from the meridian) all yield to a precisely similar treatment, 

 and all corroborate the same conclusion. 



This remark maybe extended to the effects of small deviations 

 of the current-wire from the circular form, which therefore do 

 not ever sensibly disturb the law of the common tangent-galva- 

 nometer, but might be such as would render Gaugain's instru- 

 ment inaccurate. 



