146 



Louis Schwendler — On Differential Galvanometers. [No. 2, 



the resistance of each coil should always be the third part of the resistance to 

 be measured. 



This relation is so exceedingly simple that at first I thought it must be a 

 well known one, and that I only was unacquainted with it. However, I have 

 since carefully read the literature on the subject, and I find the above law no- 

 where stated, and as a further proof of its being new, I may add that none of the 

 differential galvanometers with which I have had occasion to deal, fulfil it. 

 That this relation is of the greatest importance in the construction of differ- 

 ential galvanometers cannot be doubted, and I have accordingly thought it 

 worth while to bring my investigation before the Society. 



Solution of the Problem in its most general form. 



Fig. 3 gives the diagram of a dif- Fig. 3. 



ferential galvanometer in its general 

 form, to and to' are the two resistances to 

 be compared and which we suppose to 

 be given. E is the given electromotive 

 force of the testing battery, and f the 

 total resistance in the battery branch ; — 

 g and g' are the resistances of the two 

 coils, and their values are to be deter- 

 mined under the condition that the 

 reading, when near balance, is most de- 

 licate, i. e. that the slightest variation in 

 w or to' causes the greatest possible 

 variation in the deflection of the needle. 



The magnetic moment of the coil 

 g, when a current Gr passes through 

 it, may be designated by Y, and the mag- 

 netic moment of the coil g', when 



a current G' passes through it, may be called Y'. Both these magnetic 

 momenta are taken with respect to the same needle, or system of needles, and 

 we may suppose that neither Y nor Y' alter perceptibly, when the needle, or 

 system of needles, slightly alters its position towards the coils, which are 

 supposed to be fixed. (This condition will be fulfilled as closely as possible 

 near balance, when the needle is approximately always in the same position 

 with respect to the coils, and it is only for such a case that the following 

 investigation is of any practical interest) . 



According to the principle of the differential galvanometer, we have — ■ 

 a° oc Y — Y' 

 where a represents the deflection of the needle, before balance is arrived at, 



