398 COMPARISON OF RESISTANCES. 



It is more advantageous to determine by experiment the metal 

 resistance r, which, substituted for the liquid, and not itself intro- 

 ducing any coefficient of self-induction, gives the same intensity 

 for the same velocity. We have in that case 



E 2 F 2 



A 2 ~P 



In order that the resistances x and r shall be equal, we must have 



/27rL T\ 2 ^ 

 \ T m) ~ 



T 2 ' 

 or 



that is to say, the period should be equal to T v^2. For a greater or 

 less value of the period than T \/2, we shall have r^x. 



In this case, again, it would be often difficult to determine and 

 realise a convenient velocity. Professor Kohlrausch gets over this 

 difficulty by using very weak currents with platinised electrodes of 

 very large surface that is to say, whose capacity is very large. If 

 the capacity c is pretty great, and the period so small that the term 



ry\ -- 



- may be neglected in comparison with - , the equation of 

 2Trc F 



condition is satisfied, and the two resistances are equal, whatever 

 T may be. It can then be established that the equivalence of 

 resistances between x and r is independent of the velocity. This 

 verification will serve as control for the exactitude of the experi- 

 ments. 



995. Professor Kohlrausch also used Wheatstone's bridge with 

 sinusoidal currents. The inductor and the coil, fixed to an electro- 

 dynamometer, are placed in the branch R of the battery. The 

 movable coil occupies the ordinary place of the galvanometer. The 

 two arms a and a' of the parallelogram are taken as equal. By 

 means of a commutator the two other resistances b and b' may 

 be interchanged, one of them being the resistance of the liquid. 

 If the four branches have neither mutual induction nor self in- 

 duction, the deflection of the movable coil does not alter, when 

 the two resistances b and b' are interchanged, provided they are equal. 



