144 
[No. 2, 
On Differential Galvanometers, 
by Louis Schwendler, Esq. 
There is one very interesting question connected with the construction 
of these instruments which, as far as I know, has not yet been answered, and 
which is of sufficient practical importance to form the subject of an investi- 
gation. 
This question may best be put as follows : 
A certain battery of given electromotive force ancl given internal re- 
sistance has to supply the two coils of any differential galvanometer with a 
current ; what must be the resistance of either coil in order to obtain the 
most delicate reading when measuring a given resistance ?* 
The solution of this problem in its most general form would naturally 
be extremely intricate, and could not be effected without tedious calculation, 
but there is one special case where it is comparatively easy to determine the 
law which connects the resistance of the coils with the external resistances 
to be compared, in order to have the greatest sensitiveness of the instrument. 
Suppose for instance that the two coils of a differential galvanometer 
have equal resistances and equal magnetic momenta, and further that the 
battery which supplies the two coils with current has an internal resistance 
sufficiently small to allow of its being neglected against the resistances to be 
compared. Then, on account of the battery resistance being so small, it 
follows that the current through one coil is entirely independent of the total 
resistance in the other, and as the two coils are supposed to have equal 
magnetic momenta and equal resistances, balance can only be established by 
the currents becoming equal, that is to say at or near balance each coil must 
receive a current 
g + w 
where g is the unknown resistance of either coil, 
w the resistance to be measured, and which is supposed to be known, 
and E the given electromotive force of the testing battery. 
At balance the diagram of this differential galvanometer is, therefore, 
represented by Fig. 1. 
* In tie Philosophical Magazine of May, 1866, and January, 186V, I solved a 
similar question, viz. the proper resistance of the galvanometer to be employed when 
testing by Wheatstone’s balance, and the result of that investigation has led me to 
examine the present question. 
