Siemens Mercury Unit of Electrical Resistance. 405 



results; but it is far less considerable than Mr. Rowland seems 

 to expect. More than a year ago, while reading (in MaxwellV 

 * Electricity/ vol. ii. p. 361) the exact theory of Weber's method, 

 adopted by Kohlrausch, I calculated this correction. The data 

 for the earth-inductor I take from a paper of Weber's ( Uebcr 

 die Anwendung d. magn. Induction auf Messung d. Inclination, 

 Gottingen, 1853, p. 53) ; and those for the galvanometer-coil 

 may be calculated approximately from Kohlrausch's description 

 and sketch. I assume the windings of the galvanometer to be 

 of a rectangular form, the innermost being 180 millims. long by 

 70 wide, the outermost 260 by 150, and the number of windings 

 = 250 (it was "about 250 " according to Kohlrausch). Calcu- 

 lating the coefficients of self-induction L by Maxwell's method 

 ('Electricity/ vol. ii. chap. 13), I find L,=9'170.10 8 millims. 

 for the inductor, L 2 =0*822 . 10 8 for the galvanometer; hence the 

 value of L for the whole circuit L=Lj -f L 2 = 9'992 . 10 8 millims. 

 (the distance between the two parts of the system being suffici- 

 ently great to make the coefficient of mutual induction insensible). 

 From this value of L I calculate the period of vibration T of 

 Kohlrausch's magnet (with the circuit closed) by Maxwell's 



GV/i 2 

 equation (15) (/. c. p. 363), the other coefficient 2 in the 



equation being estimated from Kohlrausch's data with an accu- 

 racy quite sufficient for our purpose. The said equation I solve 

 by successive approximations, taking first the right side =0 

 (Kohlrausch's assumption) and calculating T, then putting this 

 value of T in the right side to obtain the second approximation, 

 and so forth. I find T = 34*8636 see., and proceed now to cal- 

 culate the exact value of the resistance R of the circuit, using 

 Maxwell's equation (14). This gives, if we denote by Rk the 

 value of R as found by Kohlrausch, 



R=R K (1 + S)-A, 



where •«. 



8 = 0-00035, A =0-00281 . lO 10 ^^ 



sec. 



Finally, from the three measurements made by Kohlrausch I 



find .„. 



1 Siem. =0-97000. iO 10 ^-, 



sec. 



» 0-97174 „ „ 



„ 0-97242 „ „ 



and the mean result will be 



1 Siem. =0-97139. 10'»==-, 



sec. 



instead of 0*9717 . 10 10 as given by Kohlrausch. 



