.. lONIZATION BY NEGATIVE IONS 83 



with respect to p and equating -= to zero. The 



following condition for a maximum value of a is thus 

 obtained : 



/(?)-?/(!)=' 



It is obvious that P is proportional to X since the 

 equation involves only the ratio X/p. In order to find 

 the value of X/P which satisfies this equation it is not 

 necessary to know the form of the function / as the 

 required ratio may be found for each gas from the 

 curves (figures 6 and 7). The x and y co-ordinates of any 

 point on one of the curves being X/p and a/p respectively, 



it follows from the above condition that yx~- at 



dx 



the point corresponding to the maximum value of a. 



The equation / r^= shows that the tangent to the 

 dx x 



curve at the point (x,y) must pass through the 

 origin, so that x and y are obtained by drawing a 

 tangent to the curve from the origin. In the curve 

 for air the point of contact of the tangent is near 

 the point where X/p has the value 370, and this 

 value is in good agreement with the result obtained 

 by Stoletow. It is not easy, however, to judge the 

 exact point at which the tangent touches the curve, 

 so that the following method is perhaps more 

 satisfactory. 



1 See paper by the author, Philosophical Magazine, February, 

 1901; also J. J. Thomson, "Conduction of Electricity through 

 Gases," 1903 edition, pp. 233, 342, where the same result is given 

 in a different notation. 



I.G. D 



