VALUE OF THE BRITISH ASSOCIATION UNIT OF RESISTANCE. 
297 
of derivation is - — y. The quantity —-— thus takes the place of R in the 
simple formula, and is called the effective resistance. By taking for instance a=-|, 
b—l, c=I00, we get an effective resistance of about - 20 ^-; and the resistances 
employed may be those of ordinary resistance coils, capable of accurate comparison 
with the standards. 
§ 4. In designing the apparatus we were influenced by the fact that we had at our 
disposal two very suitable coils of large radius, wound some years ago by Professor 
Chrystal, the same in fact as were used by Mr. Glazebrook in his investigation by 
another method. By bringing the two coils close to one another and to the plane of 
the disc, the inductive effect is rendered a maximum. This arrangement accordingly 
was the one first experimented with, as being the most likely to prove successful. 
The diameter of the disc is limited by two considerations. If it be too small, the 
whole inductive effect, and with it the sensitiveness of the arrangement, suffers. On 
the other hand if it be too large, the circumference enters the more intense region of 
magnetic force which lies near the wire, and the coefficient of induction changes its 
value rapidly when any alteration occurs in the mean radius of the coils, or in the 
diameter of the disc x and thus the final result becomes too sensitive to errors in the 
magnitudes of these elements. In the Phil. Mag. for November, 1882, the reader 
will find a calculation of the values of M for various cases, and a general comparison 
of the principal methods for determining absolute resistance especially in respect of 
errors arising in connexion with the fundamental linear measurements. For the 
experiments now to be described, the diameter of the disc was chosen so as to be 
somewhat more than half that of the coils (§§ 22, 23). 
§ 5. The disc was of brass and turned upon a solid brass rod as axle. This axle 
was mounted vertically in the same frame that carried the revolving coil in the 
experiments described in a former communication to the Society* (see Plate 48), an 
arrangement both economical and convenient, as it allowed the apparatus then 
employed for driving the disc and for observing the speed to remain almost undis¬ 
turbed. The coils were supported horizontally upon wooden pieces screwed on the 
inner side of the three uprights of the frame. 
During the earlier trials, extending over the month of May, 1882, the edge of the 
disc was bevelled, and contact was made with it by means of a brush of fine copper 
wires held in a nearly vertical position. No sufficiently regular results could be 
obtained until the sliding surfaces were amalgamated, and even then there were 
discrepancies between the work of one day and that of another, whose cause was not 
discovered until a later period. It soon became manifest, however, that the bevelled 
edge would not answer the purpose, for it cut its way by degrees into the wares of the 
brush in such a manner as to render the effective radius uncertain. The substitution 
of a cylindrical for a bevelled edge promised better results. The width of the edge 
* phil. Trans., Part II., 1882. 
MDCCCLXXXIII. 2 Q 
