146 Louis Sckwendler — 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- 
ferential galvanometer in its general 
form, w and w' 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 
iv or w' causes the greatest possible 
variation in the deflection of the needle. 
The magnetic moment of the coil 
g, when a current G 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 tire dilferential galvanometer, we have — 
«° OC Y — Y' 
where a represents the deflection of the needle, before balance is arrived at, 
Fig. 3. 
