Force in the Voltaic Arc. 357 



of 34 divisions was obtained as the mean of fifteen observations, 

 with a probable error of +3*7. From this the resistance in 

 the disappearing luminous arc may be calculated. If the re- 

 sistance in the German-silver wire is p, and that in the luminous 

 arc and the magnetometer together is called B, we have 



B:B + p = 34:40, 

 from which B = 5*67/9. 



Experiment 4. With thirty elements, but without introducing 

 the sulphate of copper into the circuit, fifteen observations were 

 made as in experiment 2. The battery was increased from twenty- 

 six to thirty elements, because the luminous arc was so feeble with 

 twenty-six elements that it was often spontaneously extinguished, 

 in consequence of which the experiments had to be frequently 

 repeated. The mean of these fifteen observations was 64 divi- 

 sions, with a probable error of +6*5. The resistance in the 

 battery was found on measurement to amount to 1*7 p. The re- 

 sistance in the luminous arc with the use of twenty-six elements 

 was found to be 5*67p ; when thirty elements are used the resist- 

 ance becomes somewhat smaller, for it diminishes as the inten- 

 sity increases. The resistance in the entire circuit was somewhat 

 smaller than 1*7/9 + 5*67/9 = 7*37/9. If the resistance had been 

 equal to that in experiment 3, the deflection of the magnetometer 

 would at most have been 



64x7-37 a „o> • ■ 

 — — — - — =8o*2 divisions. 

 5*67 



Hence we have 



83*2:40 = E-^:^ 



from which sc = 9'7 elements. 



We see from this that the electromotive force in the extinguish- 

 ing luminous arc between carbon points cannot be less than that 

 of 9*7 Bunsen's elements. 



The data furnished by this and by previous experiments may 

 be used to calculate the electromotive force of the luminous arc 

 from experiments 1 and 2. 



If the resistance in 30 elements is l'7p, 



It may be assumed that in 50 elements it is Jg l'7p, or 2*83/9 



If the resistance in one inch of the solution of sulphate 



of copper be called r, a special investigation showed 



that p=2'06r; 

 Hence in five inches of the solution of sulphate of "\ n.An 



copper the resistance was J P 



Hence the total resistance in the battery and in the rheostat 

 together is 5*26/9. Assuming that the resistance in the lumi- 

 nous arc and in the magnetometer, as in experiment 3, amounts 



