ON STANDARDS OF ELECTRICAL RESISTANCE. 167 
to b and ¢ to d by F and F,, rods of no sensible resistance, This exact equality 
between R and § could never be obtained, owing to slight changes in tempera- 
ture which affected the two coils very differently. The object of the modifica- 
tions introduced was to allow the ratio between S and R, differing by a 
small amount only, to be measured with great accuracy. 
For this purpose a number of German-silver coils were adjusted, represent- 
ing 1, 2, 4,8....512in the arbitrary units, equal to the hundredth part of A 
or C. These coils were so arranged that any one or more of them could be 
introduced between the bars HH, andJJ,. A single coil, equal to 1 in the 
same arbitrary unit, could be introduced between the bars LL, and MM,. 
In the diagram this coil is shown in its position and the rod F, withdrawn, 
Similarly F is withdrawn from between H and G, and the coil 1 joins a, and 
6, in the bars HH, andJJ,. If no other coils were placed between H H, and 
JJ,, the arms of the balance would now be 101 and 101 respectively, instead 
of 100 and 100; but the ratio would still be that of equality. Let us now 
suppose that, when the circuit with the battery is completed, the galvanometer 
by its deflection shows that R is bigger than S, we can reduce the resistance 
of the arm between D and Y by various small graduated and definite amounts 
by introducing the coils 2, 4, 8, &c. between HH, andJJ,. Let us first 
suppose the coil 2 introduced. The resistance between H and J will be the 
reciprocal of 1-5 or 0°6667; for where various resistances are added in 
multiple arc, the resistance of the compound ar¢ is the reciprocal of the 
sum of their conducting-powers, and the conducting-power of a wire is the 
reciprocal of its resistance. The ratio between the two arms will now be 
101 ; 100-6667. Let us suppose that on completing the circuit the galvano- 
meter still deflects in the same direction as before, the arm between D and Y 
must be still further reduced by including fresh coils between H H, and J J,. 
It is very easy by trial to find the combination which maintains the galvano- 
meter at zero when the circuit is completed. Let us suppose that, as in the 
diagram, the coils included were 1, 2, 4, 8, and 64. The reciprocals of 
these numbers are 1, 0-5, 0:25, 0-125, and 0:015625. The conducting-power 
between H and J is therefore 1-890625 the sum of these numbers. The 
resistance between H and J is 052893, the reciprocal of the last number, and 
the ratio between the arms will be 101 : 100°52893. A little consideration 
will show that with the coils named any ratio between 101 to 100-5, and 101 
to 101 can be obtained by steps not exceeding 0:00195, the reciprocal of 512, 
the largest coil or smallest conducting-power which can be included between 
the copper bars HH, and JJ,. By substituting the rod F for the coil 1 be- 
tween LL, and M M,, the observer can obtain a fresh series of ratios with the 
same steps between 101 to 100 and 100-5 to 100. In this way it will be seen 
that unless the coils R and § differ by more than one per cent., their ratio 
can be measured in the manner described within 0-002 per cent. 
It should further be observed that extreme accuracy in the coils 1, 2, 4, 
&c. is not necessary, since an error of one per cent. in the sum of these, as 
compared with their true relative value to the coil C, would only affect the 
final result 0-01 per cent. 
The position of R and § in the balance relatively to A and C, &c. is of course 
interchangeable. 
The diagram is not intended at all to represent the practical arrangement, 
but simply to show the connexions. The electric balance described in Ap- 
pendix H of last year’s Report (Plate I. figs. 1 to 6, Report 1862) was used 
with a stout copper rod between the cups ¢ ¢,, and two additional boards with: 
the copper bars H H,,JJ,, LL,, and M M,, fitted as in the above diagram. The 
