3 8o 



COMPARISON OF RESISTANCES. 



978. According to Prof. Kirchhoff,* in the case of a homo- 

 geneous bar in the shape of a parallelopipedon with a square 

 base of length /, and side #, if we take the four electrodes at the 

 summits which correspond to the same lateral face, each of them 

 may be considered as bounded by the eighth of a sphere; if cr is 

 the specific resistance of the bar, and y a coefficient equal to 

 07272, the resistance measured is expressed by 



This resistance is equal then to that of a bar of the same 



section, the length of which is merely / - ya. It has in fact been 



a 



supposed in the calculation that the ratio - is infinitely small ; but 



Fig. 200. 



even if this ratio were equal to 0-5, the error does not amount 

 to 0*0003. 



The preceding discussion defines accurately the conditions 

 within which we must work. All the experimental artifices should 

 be directed to diminishing the surfaces of contact of the electrodes, 

 and eliminating the corresponding resistances. 



979. Sir W. Thomson! has used the double bridge mentioned 

 in 975 for measuring small resistances. 



Let us suppose that the object is to compare the resistances 

 a and b (Fig. 200), the first comprised between the points A 

 and A x , and the second between the two points B and B r The 



* KIRCHHOFF. Berliner Monatsbericht, 1880 ; Gesammelte AbhandL, p. 71. 

 GREENHILL. Proc. Camb. Phil. Soc., p. 293. 1879. 



t Sir W. THOMSON. Phil. Mag. [4], Vol. xxiv., p. 149. 1862. 



