LENZ OX ELECTRO-MAGXETISM. 613 



In order now to find the resistance which the electric current suffers 

 in its passage through the different wires, I first reduce their lengths 

 all to one diagonal, and indeed to that of the wire of the multiplier, 

 on the principle that two wires of the same metal offer then the same 

 resistance to conduction when their lengths are in the same proportion 

 as their diagonals (See Ohms Galvanic Chahi). In this case therefore 

 the reduced lengths of the wires express their resistance to conduction: 

 to have therefore a general idea of the problem, I suppose the mul- 

 tiplier, the conducting wires, and the electromotive spirals (with tlieir 

 free ends) to have tlie three reduced lengths, L, /, and X, and the elec- 

 tromotive power produced in the spirals to be represented by x, then 



^ will be in effect the current which takes place, and we 



L» -J- / -|- A. 



therefore have 



a; = (L + / + \) • j9 • sin. | a (A.) 



If we now consider the electromotive power in a convolution of the 

 wire as unity, representing the unknown deviation produced by a con- 

 volution by £, and its reduced length by (X) ; then granting the pro- 

 bable hypothesis, that at one and the same distance of the convolutions 

 the electromotive force is directly as the number of convolutions, the 

 following relation will take place for the number n, and for the reduced 

 lengths X„ belonging to it (this is not necessarily n X, because the free 

 ends of the spirals need not increase in the same ratio for every num- 

 ber of convolutions) 



1 ^ (L + / + (X))7)-sin.lg 

 n (L + / + X„) ja-sin. \ a 

 therefore 



sm. ia = «• J— j-^_L_^-sm.^H^ . . . (B.) 



In the experiments just mentioned / -f X continued of the same 

 magnitude for every number of convolutions, as the conducting and 

 spiral wire consisted of one piece, besides L remains the same, we 

 therefore have L + / + (X) = L + ^ + X„ and the equation B be- 

 comes changed into the following : 



sin. i a = w sin. \^ (C.) 



If we now put instead of ^ a the values contained in the last column of 

 our table of experiments, we obtain eleven equations, from which after 

 the method of the least square, we shall be able to determine ^, and if 

 we bring this value of ^ into the equation (C), we shall find the devi- 

 ations a belonging to the number n of convolutions, and the differences 

 between this and the observed values will show whether the assumed 



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