Determination of Resistances in Absolute Measure. 339 



in the aggregate they must be allowed to have some weight, 

 they are far from preponderating over the advantages which 

 the method possesses in comparison with II. 



If we take the view that the method itself is trustworthy, 

 the principal error will arise in connexion with the mean 

 radius of the coil ; and it becomes an interesting question to 

 consider whether advantage may be expected from a further 

 increase in the dimensions of the apparatus. For this purpose 

 we may regard tan cj> as given. The total resistance E, will be 

 proportional to rc 2 a/S, where S denotes the aggregate section 

 of the copper, from which it follows that &)S may be regarded 

 as given, while a is left undetermined by the consideration of 

 sensitiveness. Thus, if we retain co and S unaltered in a mag- 

 nified apparatus, we shall have the same sensitiveness as before, 

 while the increased diameter of the coil and the relatively de- 

 creased dimensions of the section will conduce to a more accu- 

 rate determination of the mean radius. 



The angular deflection being given, the correction for self- 

 induction is nearly constant whatever may be the proportions 

 of the coil. 



If we are of opinion that there is danger in the operation of 

 self-induction, the case becomes strong for the introduction of 

 a second coil in a plane perpendicular to that of the first *. By 

 this means the relative correction for self-induction would be 

 reduced to one quarter, while the deflection remained unaltered. 

 It scarcely needs to be remarked that this use of a second coil 

 would not, as in II., increase the uncertainty depending upon 

 the linear measurements, the two mean radii entering into the 

 result as parts, and not as factors. 



This combination would lend itself especially well to low 

 speeds of rotation; for the deflecting force, being uniform in 

 respect to time, w T ould not give rise to forced vibrations of the 

 needle. The latter would have nothing further to do than to 

 indicate the direction of a constant field of force. 



IV. 



This method, which was proposed by Foster |, and more re- 

 cently by Lippmann, and to a certain extent executed by the 

 former, is a modification of III., in which the electromotive 

 force generated during the rotation of the inductor is balanced 

 by an external electromotive force, and thus not allowed to 

 produce a current. The external electromotive force is due to 

 the passage of a battery-current through certain resistance- 

 coils; and the current is compared with the earth's horizontal 



* Proc. Roy. Soc. May 1881, p. 123. 

 t Brit. Assoc. Report, 1881. 



