24 J. G MACGREGOR ON THE MEASUREMENT OF THE 
a current at once flows. In fact no adjustment of resistances can be found, with which 
the galvanometer indicates no current. 
If the use of alternating currents reduced the polarization to an amount too small to 
be observed, then with an electrolytic cell in one of the arms of a bridge, it should be 
possible to find some adjustment of the resistances in the arms with which no current 
would flow through the galvanometer branch, whether the source of the alternating cur- 
rents used was an induction machine such as Kohlrausch and his co-workers employed, 
or a Daniell’s cell and commutator as above described. I found, however, as the result of 
a large number of experiments with both forms of apparatus, that no such adjustment of 
resistances could be found. 
If, however, electrolytic cells with equal electrodes are placed in two of the arms of 
a Wheatstone’s bridge in the manner described above, and if the resistances of the arms 
containing the electrolytic cells are equal, the current through the cells must be equal, 
and their electrodes having the same area, the polarization produced in both arms must 
have the same value. As the currents in both cells have the same directions relatively to 
the ends of the galvanometer branch adjacent to them respectively, the potentials of b and 
d must be similarly and equally affected by the polarization. In this case then no deflec- 
tion can be caused by the polarization, and the adjustment of the resistances being such 
as to produce none, there can be no deflection at all. With this arrangement then, it 
should always be possible to find some adjustment of the metallic resistances in the arms 
bc, ed, with which the galvanometer gives no deflection. This I have always found to be 
the case. 
When no deflection is shewn by the needle of the galvanometer, the points, b and d, 
must have the same potential. But the point « is common to the two wires, a b and a d, 
and these wires have the same resistance. Therefore, by Ohm’s law, equal currents flow 
through them. As no current flows in the branch bd, the current in ¢ 6 must, by the first 
of Kirchhoff’s laws, be equal to that in ba. Similarly, the current in ¢ d must be the 
same as that ind a. The currents in ¢ b and € d are, therefore, equal ; and in consequence 
the electro-motive force of polarization is at any moment the same in both electrolytic cells.* 
In both also the electro-motive force is such as to tend to send a current either towards or 
away from c. Hence, these polarizations tend, in the circuit of the mesh c b d of this net- 
work of conductors, to-send currents in opposite directions. Calling these equal polariza- 
tions, p and — p; the equal currents through c b and cd, 7; the resistances of the cells E, 
and E», R, and R, respectively ; that of the box of coils in ed, Rs; that of the wire cf, Ru; 
and that of the wire ce, Rs ; Kirchhoff’s Second Law gives us the equation : 
i (R, + Bs) —7 + B+ Ry) =p —p—0. 
Hence 
Ri +R: = Rk, + RB + R, 
and 
ee ssi see Se, 
The difference of the resistances of the electrolytic cells, therefore, is expressed in 

* This assumes that the polarization varies with the intensity of the current and with the area of the elec- 
trodes, but not with their difference of potential. See Wiedemann’s Galvanismus, (2nd. Ed.), Vol. I., 4 468-469. 
