160 REPORT—1862. 
stand for the index of the balance. Then all the above statements, with 
respect to the weights and arms, hold good for the electrical arrangement 
(except that the proportion between the electrical arms and weights is direct 
instead of inverse). The writer therefore calls this arrangement an electric 
balance—aA and C the arms, § the standard, and R the resistance measured*. 
In the adjustments of resistance-coils or copies of a standard, the object is to 
produce a second coil, R, exactly equal to the first or standard, 8; andthe 
arms, A, C, must therefore be absolutely equal before, by this arrangement, 
an exact copy can be made. Hitherto it has often been the practice to use 
for the arms, A, C, two coils made as equal as possible, and placed so close as 
to remain at sensibly equal temperatures; so that the equality between 
R and S is dependent on the equality between A and C, and cannot be deter- 
mined with greater accuracy than that between these coils. This limit to the 
accuracy is a defect for our present purpose, and the writer has moreover 
found it undesirable to depend on the permanent equality of two coils. It is 
by no means certain that, without very extraordinary precautions, the two 
arms will remain unaltered in their original equality. A slight molecular 
change, or a slight chemical action on the surface of the wires, disturbs this 
equality permanently; and even if the coils are so constructed as to remain 
really equal at equal temperatures, the accidental passage of a current through 
one arm, and not through the other, for a very short time, will disturb their 
accuracy very sensibly for a considerable time. There are various devices by 
which the equality to be established between R and S may be rendered 
independent of the absolute equality between A and C, and the writer has 
adopted a plan, now to be explained with the aid of the diagrams (figs. 7, 8). 
This plan allows the approximation to equality between R and § to be almost 
indefinitely increased. 
It will be seen that fig. 7 does not differ from fig. 9, except by the addition 
of a wire, WX, of sensible resistance, between the two coils A and C. The 
point U is no longer fixed, but can be moved along WX. The arms of the 
balance are therefore no longer A and C, but A+ XU and C+WU. Thus 
the moveable point U affords the means of slightly altering or adjusting the 
ratio of the twoarms. A and C are made as equal as possible, independently 
of WX, which is a very short wire. 
The test is made as follows:—When the standard and coil to be measured 
have been put in their places as in fig. 7, the point U is moved along the 
wire WX until the galvanometer-index is not deflected when the circuit is 
closed. The position of the point U is noted by a scale. R and § are then 
reversed, so as to occupy the position relatively to A, C shown in fig. 8. The © 
point U is again moved until the galvanometer-needle remains undeflected on 
the circuit’s being closed. The new position of U is again observed by a 
scale. If the point U does not require to be moved at all, we may be quite 
sure that R is exactly equal to S, and that A+ XU=C+ WU, since it would 
be quite impossible that the ratio et au should be equal to both 2 and ) 
WU 
unless this ratio were equal to 1. Moreover, if WX be made of the same 
* The name of parallelogram, sometimes given to the arrangement, is objectionable, 
inasmuch as the relation obtaining between the four conductors is not that which exists 
between the four sides of any parallelogram, except in the one case of equality between all 
four conductors. The connexions are, however, most easily followed in a drawing when 
arranged as the four sides of a quadrilateral figure. Professor Wheatstone’s original name 
of Differential Resistance Measurer does not, as it seems to the writer, sufficiently distin- 
guish this arrangement from other differential methods. 
