300 LORD RAYLEIGH AND MRS. H. SIDGWICK ON THE ABSOLUTE 
§ 9. In actual work, however, it is not necessary, or even desirable, to hit off the 
balance with great accuracy. An unmistakable difference of readings when the 
battery key is put over, is rather an advantage than otherwise, as giving an indication 
that the circuits are properly closed. The plan adopted was to take a series of 
readings of the effect (E—W) of reversing the battery current with an effective 
resistance R 15 not very different from It. Single readings were liable to considerable 
irregularity in consequence of change in the friction at the sliding contacts, and of 
momentary variations in the speed. These errors cannot possibly be systematic, and 
are in great measure eliminated in the mean of a series. Having thus obtained the 
difference of galvanometer readings (E—W) corresponding to R l5 we altered the 
resistance in multiple arc so as to change R 1 into R 3 , the difference being some such 
fraction as T ^o of the whole, and in such a direction that the sign of E—W is changed. 
The two series give by simple interpolation (after correction for the direct effect) the 
true value of It, that is the effective resistance corresponding to the balance. In 
order to get the best result relatively to the time occupied, the number of observa¬ 
tions of E—W in each set was taken roughly in inverse proportion to the values. 
To diminish the influence of a progressive change in the strength of the battery 
current, the observations with IE were interspersed between those with R 1 as 
effective resistance. The readings were usually taken continuously, with no mere 
delay than was necessary to allow the vibrations of the needle to become of moderate 
extent after each change. When they were completed, the driving cord was reversed, 
as well as the commutator, I, and a similar set of observations was taken with 
rotation in the opposite direction. 
§ 10. In the earlier experiments the resistance coils composing the effective 
resistance were arranged as in fig. 1, in which A, B, C may be supposed to represent 
mercury cups, the bottoms of which were formed of amalgamated copper discs. On 
these discs rested the amalgamated terminals of the various resistance coils and 
connecting wires. The shunt a consisted of two unit coils in multiple arc, between 
which the greater part of the main current was equally divided. The magnitude of 
the main current was less than ampere. The resistance b between the points of 
derivation was a unit, while the third resistance c was alternately 105 and 106. 
In reckoning the resistance of the galvanometer circuit we have to include b* The 
remainder scarcely exceeds the ^ ohm due to the galvanometer itself. It appears 
therefore that the deflections obtained with the arrangement described are only one- 
third part as great as they would be if a quite small resistance were substituted for 
the unit in b. As the sensitiveness appeared likely to be inadequate, we afterwards 
replaced the unit by yq, using for c a coil of ten units. As in this case the addition 
or subtraction of a whole ohm in c would make too great a difference, the adjustment 
was obtained by varying a comparatively large resistance placed in multiple arc 
with a. 
In the light of subsequent experience it is doubtful whether this change was an 
