Kohlrausch on the Electroscopic Properties of the Voltaic Circuit. 329 



the resistance in every portion of the circuit to be referred to a 

 certain unit, and. that the distances along the datum line from 

 which the tensions are plotted are measured off with reference to 

 this unit ; that, for example, if an inch of the fluid portion ex- 

 hibit a fall three times as great as an inch of the solid portion, 

 the said fluid portion shall, on the datum line, be expressed by 

 a distance three times as great as that which expresses an equal 

 length of the solid portion ; it is evident that when the resist- 

 ances are thus referred to a common standard, the line which 

 expresses the tension must be one uniform gradient from begin- 

 ning to end. Ohm calls the length of a circuit referred to such 

 a standard its reduced length. 



It has already been stated, that when any point of the circuit 

 is perfectly discharged, the tension at this point is null, and in- 

 creases in tension right and left, showing positive electricity on 

 that side of the point from which the current proceeds and ne- 

 gative electricity at the other side; the length of the circuit 

 which shows the one fluid or the other will depend upon the 

 position of the point ; if exactly central, as at a", fig. 5, the 

 lengths will be alike. If the point be nearer to the zinc pole 

 than to the copper pole of the arrangement, as at a', the length 

 of wire exhibiting positive electricity will be greater than the 

 length exhibiting negative electricity ; and if the point be chosen 

 contiguous to the zinc plate, as at a, the whole circuit will ex- 

 hibit positive electricity. 



Having the electromotive force be, and the reduced length of 

 the circuit, we are taught by the theory of Ohm to deduce by 

 simple calculation the electroscopic state of every single point. 

 Let the scheme in fig. 6 represent the state of things in a circuit 

 where the discharged point a is contiguous to the zinc pole. 

 The reduced length, ab, and the electromotive force, be, being 

 given, let d be any point whose tension, de, we wish to ascertain. 

 Let bc=a, de = u, ab = l, ad=\; then by similar triangles, 



u: a=-\: I, or u= —. . a; 



or, expressed in words, if the reduced length of the circuit be- 

 tween the discharged point and the point whose.tension is sought 

 be divided by the reduced length of the entire circuit, the quo- 

 tient, multiplied by the electromotive force, gives the tension at 

 the required point. 



In submitting this formula to an experimental test, M. Kohl- 

 rausch made n~c of the wooden trough before alluded to. The 

 Copper and zinc plates were united, as in one of the experiments 

 already described, by a lung fine wire, bent from side to side of a 

 wooden frame in a zigzag manner. The tensions of the points 



