a- Particles with Hydrogen Nuclei. 497 



A good approximation will be obtained by neglecting the 

 change in the curves of fig. 3 and also taking 



lp(«J)=^P(«,-AiJ) 



for all the values of 6 in the rather short range of integra- 

 tion. Then 



f 1 |p(0, V)- i i V^P^o-A,, V)/j. dm 



=p(0 o -a i ,v)-|^^p(0 o -a 1 .v) :| 



=p(^ -a 1 ,v(i-|;-,)) 



= P(0 o -A ]) V), (3-9) 



where V is the mean velocity of the a-particles in their 

 passage through the gas. 



Thus we see that a complete determination is possible for 

 the collision relation between P, 0, and V. If at any time 

 really accurate experiments should be carried out on the 

 present principles, then it mi^ht be worth while to carry 

 out in detail the processes sketched, but the labour would be 

 very considerable, and it is to be hoped that it will be found 

 possible to cast future experiments in a more tractable form. 

 In view of the inaccuracy of the present ones I have contented 

 myself with the simpler reduction previously described, 

 together with the correction given in (3*9). 



4. Tlie Reduction of the Experiments. 



The reduction of Rutherford's experiments then took the 

 following course : (The pages mentioned in this section refer 

 to the pages of his paper already cited.) Values of £/4r were 

 taken at every unit decimal between and 1. The values 

 of were calculated for these, and also the (#, 0) curves, 

 illustrated in fig. 3. By mechanical quadrature the areas 

 and moments were found, so as to give A 1 and A 2 . A table 

 of the function O — Ai in terms of t/Ar was thus drawn up, 

 so that any value could be found by interpolation. 



The experimental curves of p. 550 were then measured up. 

 They are drawn in arbitrary units, different for each curve,, 

 and require to be brought to the same scale by means of the 

 table on p. 553. This process was carried out by reducing 

 the latter numbers with the help of the curves of p. 550 to 

 a standard range of 7 cms. The absolute size is determined 



