Determination of Resistances in Absolute Measures. 345 



attention, is that it is possible so to proportion the quantities 

 that the error of mean radius of the coil does not afect the result, 

 which accordingly depends only npon the diameter of the disk 

 and the distance of the coil's mean planes. How this may- 

 come about will be readily understood by considering the de- 

 pendence of M upon A when a and b are given. It is clear 

 that M vanishes, both when A is very small and when it is 

 very large ; from which it follows that there must be some 

 value of A for which the effect is a maximum and therefore 

 independent of small variations of A. 



In carrying out this idea it is not necessary to approach the 

 above-defined state of things very closely ; for of course we 

 have in reality a good approximate knowledge of the value 

 of A. In my apparatus the distance of mean planes was about 

 30 centim., so that b = about 15 centim. With the actual 

 proportions a calculation of the effects of the various errors 

 shows that 



SM 8A 86 8a. 



-m =-12-r •yb^- + l , b— > 



M A b a 



so that the error of A enters in quite a subordinate degree. 

 The positive coefficient of SA shows that with the given coils 

 and disk the separation was somewhat too great to secure the 

 greatest independence of SA. 



The success of this arrangement depends principally upon 

 the degree of accuracy with which b can be determined. The 

 two rings on which the wire is coiled are separated by distance- 

 pieces; and, as in 1., by reversing the rings relatively to the 

 distance-pieces the result may be made to depend upon the 

 mean length of these pieces and the mean thicknesses of the 

 rings at the places of contact. The three distance-pieces were 

 held together in one length and measured under microscopes; 

 and the thicknesses of the rings were taken with verified cal- 

 lipers. There can hardly be a doubt but that this determina- 

 tion is much more accurate than that of the mean radius of a 

 coil; and, what is also of some importance, it admits of repe- 

 tition at pleasure with comparatively little trouble. 



The value of the B.A. unit resulting from the measurement 

 with this arrangement was '9869 x 10 9 C.Gr.S.* 



There seems no reason why a further increase of accuracy 

 should not be obtainable by enlarging the scale of the appa- 

 ratus. If we suppose the scale doubled, the number of turns 

 in the coil and the angular speed of the disk being unaltered, 

 the value of M would be doubled; and thus with the same 



* The reductions not being yet finally completed, these numbers are 

 liable to a change of one or two units in the fourth place of decimals. 

 Phil. Mag. S. 5. Vol. 14. No. 89. Nov. 1882. 2 A 



