182 Rev. P. J. Kirkby on Union of Hydrogen and Oxygen 



From this equation it is easy to ascertain what errors 

 arise when the fall of pressure is considerable. 



For if: rk is written instead of — ¥ , it integrates at 



once and gives 



Q £=log^JI, 

 10 & 3X ? 



where, X being constant, the passage of Q coulombs of 

 electricity through the hydrogen and oxygen lowers the 

 pressure from p to p 1 — all the water- vapour being absorbed. 



If we put p + — j- for p and p— — ^ for p 1 we get 



10 _ 3X i 12/ 3XV (" 



^ > + 80DC (/ + SoJ) 



nearly. Now the second term inside the bracket is negli- 

 gible compared with unity for practically all values of A/?» 

 X being always about 400 or more. Therefore equation (1) 

 holds good for all values of Ap, AQ, so long as X is constant. 

 It may in fact be written 



Po — Pi _ (po±J\}P 3X 

 Q ~ 20 + 800- 



Again, it was observed during the discharge that the 

 glow between the plates at the higher pressures consisted of 

 a small luminous cylinder of very slight diameter compared 

 with the breadth of the electrodes, while at the lower pressures 

 the discharge filled the whole space between the surface of 

 the electrodes left exposed by the guard-rings. Therefore 

 the last equation must be independent of the size of the 

 parallel plates. 



Now the capacity of the apparatus was 1130 c.c. nearly, 

 hence the equation 



Po-Pi _ 1130 f( po+ Pl )D 3X1 

 Q 8 L 20 800 J 



should apply to discharges between parallel conductors in a 

 vessel of S c.c. capacity. 



As for the limits below which p must lie if this equation 

 is to hold, that has not been determined. One experiment 

 in which p was 39 mm., p 1 34, and X 500, was in close 



