ON STANDARDS OF ELECTRICAL RESISTANCE. 161 
wire as the coils A and C, and if those coils are formed of about 100 inches 
of wire, and if the observed positions of U differ by a given distance, x, this 
length, w, measured in inches, will express very nearly the difference between 
R and § in a percentage of the whole length of R. Thus, if w be one inch, 
the standards S and R differ by about one per cent. If the point U, when 
adjusted in each case, be found nearer R than §, then R is the smaller of the two, 
and vice versé. The percentage of error in R, thus measured, is not of course 
strictly accurate, inasmuch as the ratio between the two arms is not exactly 
ap but if WX be not more than three or four inches long, the percentage 
of error measured in this way is quite sufficiently accurate to allow the new 
coil to be so exactly adjusted after very few trials, that no greater movement 
of U than (say) ;4th of an inch is required to prevent any deflection on the 
galvanometer when R and S are reversed. We may then be sure that no 
greater error than (say) about 0-1 per cent. exists in the equality between 
the new coil and the standard. Two fresh coils, A,, C,, are then taken, 
containing each about 1000 inches of wire similar to WX, or an equivalent 
resistance. It will then be found that, to maintain the index at zero when 
R and S are reversed, U must be moved about ten times as much as before, 
or (say) one inch. R can then be still further adjusted till U is not moved 
more than />th of an inch, when a new degree of approximation to equality, 
with an error of not more than 0-01 per cent., will have been reached. Then 
the coils A,, C, are changed for a fresh pair, A,, C,, with a resistance equal 
to about 10,000 inches of the wire WX: one-tenth of an inch on WX will 
then represent an error of only 0-001 per cent. By a repetition of this 
process, quite independently of any absolute equality between the pairs A, O, 
A,, ©,, A,, ©,, &c., a gradual approximation to any required extent may be 
ensured. The delicacy of the galvanometer used, and the nicety of the means 
available for increasing or diminishing the resistance of R, form the only 
limits to the approximation. A slight want of equality between any pair of 
arms will simply bring the point U a little to one side or the other of the 
centre of WX, as the final adjustment with that pair is made, but will not 
affect the truth of the comparison between R and S. Each pair must, however, 
be so nearly equal that the addition of part of the short wire, WX, to one side 
will be sufficient to correct the other; otherwise the adjustible point U would 
not bring the index to zero, even when at one end of the wire. 
This arrangement, besides rendering us independent of the accuracy of 
any two arms, has some incidental advantages of considerable practical 
importance. At éach test it gives a measure of the amount by which the 
new coil to be adjusted must be lengthened or shortened. The test is at first 
comparatively rough, or adapted to errors of one or two per cent., and only 
gradually increases in delicacy as the desired equality is more and more 
nearly approached. It is not necessary that the resistance of WX should 
remain absolutely constant, since it is only used (numerically) to give a 
rough approximation to the percentage of error. It is desirable that the 
battery should remain in circuit as short a time as possible; the circuit is 
therefore broken between 1 and 2, figs. 7 and 8, by a key, K, with which 
_ contact should be only momentarily made, when all the other connexions are 
complete. The direction of the jerk of the galvanometer-needle to one side 
or the other need alone be observed ; no permanent deflection is required with 
this arrangement as a guide to the amount of error. This is a considerable 
advantage, inasmuch as it avoids heating the wires, and saves time. The 
om’ of the coils on themselves might lead to some false indications, 
862, M 
