MEASUREMENT OF VERY SMALL RESISTANCES. 379 



as the potentials are linear functions of the currents, we may also 

 write 



Vj = C + a^ + * 12 I 2 + * 1S I 8 + * 14 I 4 , 



V 2 = C + tf oil], + tf 2 o! 2 + ^23*3 + ^24^4 > 

 (4l) 



V 3 = C + flf^Ij + tf 32 I 2 + 33 I 3 + 34 I 4 , 

 V 4 = C + d^Ij + tf 42 I 2 + 43 I 3 + 44 I 4 . 



The quantity C and all the coefficients a are constants; there 

 are relations of condition between these n 2 coefficients, and they 

 may be referred to - independent coefficients. 



Taking into consideration equations (40), we deduce 



V 2 - V 3 = (a 2l - a sl - 24 + 34) Ij + (# 22 - # 32 - # 23 + # 33 ) I 2 , 

 an expression which we put in the form 



(42) v 2 -v 3 =* 



The factor x\ Represents the difference of potential V 2 -V 3 , 

 when I 2 = 0, that is, when the 'circuit of the two electrodes 2 and 

 3 is not closed, and that l l = t' ) this then is the resistance of the 

 conductor between these two electrodes. It will be seen that two 

 equations like the preceding are sufficient to determine the value 

 of x ; experiment giving the difference V 2 - V 3 and the currents 

 Ij and I 2 . 



It has been supposed that the electrodes are equipotential 

 surfaces. This- condition is realised if contacts are made by points 

 so fine that the surface of contact may be considered infinitely 

 small in comparison with a small sphere, which itself is infinitely 

 small compared with the dimensions of the conductors. 



In the case of a cylindrical bar, we might take the electrodes 

 i and 4 on the two bases, then the electrodes 2 and 3 on a 

 generating line, at such a distance from the ends that the equi- 

 potential surfaces may be regarded as normal sections in the 

 interval of the points 2 and 3. In these conditions, the measured 

 resistance x is precisely that of a cylinder comprised within two 

 perpendicular sections passing through the points of contact 2 

 and 3. 



