396 Dr. A. Macfarlane on the Disruptive 



the single discharge, but also that for the continued discharge. 

 As in the case of variable distance, so here, the equation of the 

 curve is similar to that for the single discharge, and is 



V= -03503 \f{f + 205-6>}, 



giving a = 102*8 millims. and b = 3'602 C.G.S. units. Here the 



ratio of the value of the - for the continued discharge to that for 



the single discharge is *75 ; in the former comparison it is *69. 

 For a '5-centim. spark through air we have 



V = '04579,/{/> 2 + 203 j p}; 

 hence 



R= -02289 V{p 2 + 203p}, 

 and 



p' = -00002085{^ 2 + 203/?}. 



The above equation evidently does not hold for pressures 

 lower than that for the minimum electric strength; it is cer- 

 tainly true for the range between that point and the atmo- 

 spheric pressure ; for Messrs. De La Rue and Miiller* have 

 obtained the same result; and I find that Prof. Rontgen'sf 

 numbers give the difference of potential equal to a hyperbolic 

 function plus a constant. The existence of this constant may 

 be due to the fact that the discharge was taken between a 

 point and a plate, and was convective in nature. The hyper- 

 bolic law is probably true up to a limit much greater than the 

 atmospheric pressure. 



By expanding the function for V, first in descending powers 

 of jo and secondly in ascending, we obtain 



and 



r.wm{ r *\^»-....}. 



Hence when p is large compared with 203 ; we have 



V = A{^ + 101}, 



which agrees pretty well with Knockenhauer'sJ formula, 

 namely 



V=l-406{> + 61'2}'. 



When the third term is added, we obtain the formula which 

 agrees best in form with that of Wiedemann and Ruhlmann§. 



* Phil. Trans, vol. clxxi. p. 78. t Phil- Mag. Dec. 1878, p. 443. 



\ Mascart's Electricite, t. ii. p. 95. § Pogg. Ann. cxlv. p. 253. 



