108 Mr. H. Hilton on van der Waals 3 Equation. 



probably due the high temperature of the spark. This high 

 temperature in turn is favourable to the production of fresh 

 ions, and to this fact the comparatively steady state of the 

 damping in circuits with large capacities may probably be 

 attributed. In such a case the current is so great that a 

 large number of ions are produced, the recombination of 

 these produce a high temperature by means of which fresh ions 

 are formed to take the place of those that have recombined, 

 and the field is thus kept comparatively uniform. 



I wish to express my obligation and gratitude to Professor 

 Rutherford for his kind assistance at every stage of the 

 investigation. 



Macdonald Physics Laboratory, McGill University. 

 Feb. 12th, 1901. 



V. A Further Note on van der Waals 1 Equation. 

 By Harold Hilton*. 



IN a previous note f I collected the various mathematical 

 facts connected with the family of curves obtained 

 by considering the temperature a variable parameter in 

 van der Waals' equation (the Isothermals) ; in the present 

 note I propose to complete this work by doing the same for 

 the curves of constant volume and the curves of constant 

 pressure. 



We take the same equation as before/ 



t dyx d -(y + 80)x 2 + 9x-3 = («) 



We will first consider the family obtained by considering 

 x as an arbitrary parameter. The family is a series of straight 

 lines such that two consecutive members meet in the point 



_ 3x-2 ('dx-l) 2 



y ~ x % ' °- ±x d ' 



Eliminating x from these two ^equations, we have as the 

 equation of the envelope 



(y + 80-9) 3 + 81(z/-40 + 3) 2 = O, 

 which has a cusp at the point (1, 1), the tangent to the cusp 

 being y — 40 + 3 = 0; cuts the axis o£ where = §, and 

 touches it where = 0; cuts the axis of y where y = 0, and 

 touches it where y=—27; and goes off to infinity in the 

 direction of y + 80— 9 = 0. A series of points on it are given 

 in Table 1. 



* Communicated bv the Author. 

 t Phil. Mag. May 1901. 



