ELECTROMOTIVE FORCES OF THE ELECTRIC ARC. 339 



observed P.D.'s is very marked, the error in the calculated result being no less 

 than 32 '6 volts for an arc length of 30 millims. At the same time this is not due to 

 any difference in the nature of the carbons, since the actual experimental values 

 obtained by Mrs. AYRTON,* and on which her equation is based, fit the Curve VII. 

 with considerable accuracy. The whole of this large difference between Mrs. AYRTON'S 

 equation and the experimental results is due to the fact that the equation is based on 

 the range of arc lengths of from 1 millim. to 7 millims., and that the equation no 

 longer represents the facts if we extrapolate any considerable amount. Even over 

 the range of from 1 millim. to 7 millims. the connection between the P.I), and length 

 for constant current is not accurately a straight line, as can be seen either in 

 Curve VII. or by a careful examination of Mrs. AYRTON'S experimental results. 



If the arc length was kept constant and the current varied, a similar difficulty was 

 found with very small currents of 1'5 amperes and lower, namely, that the observed 

 P.D. was less than the calculated P.D., so that Mrs. AYRTON'S equation can only he 

 considered as approximately representing tlie facts within tJte limits site used, and 

 must not be applied to very small currents or long arc lengths. 



Taking, in the present case, as limits from 1 '5 amperes to 12 amperes, and from 

 1 millim. to 6 millims., then the results obtained with the arc between 11 millims. 

 solid " Conradty Noris" carbons can with a very fair approximation be represented 

 by the equation 



V = 39-G 4- 17/ + (15-5 + H'5/)/A, 



which is in very close agreement with the equation given by Mrs. AYRTON for solid 

 "Apostle" carbons, 11 millims. and 9 millims. diameter, for the range 1 millim. to 

 7 millims., viz. : 



V = 38-88 -f 2-077 + (H'GG + 10'54/)/A. 



APPENDIX II. 



On the Resistance of an Electrolyte. 



In measuring the resistance of an electrolyte by the ordinary Koblrausch method, 

 using alternating or induced currents, it is usually assumed that the influence of 

 polarisation of the electrode is avoided, and that the frequency of the alternating 

 current used is unimportant, provided that it is moderately high, say a few hundred 

 periods per second. If an appreciable polarisation of the electrodes is produced by 

 the testing current very soon after its application in any given direction, then the 



* ' Electrician,' vol. 35, p. 635. 



2x2 



