1200 
and shall call p the impulse corresponding canonically to », m 
and M/ the masses, e, # the charges of the a-particle and nucleus 
respectively, and finally v the initial velocity of the «-particle, the 
atom being originally supposed at rest. The equation to the orbit 
then assumes the simple form 
1 uel 
i= [ecos (pp) Ty vers ont An, mall 
p 
1 1 Beare: 
ae aes AE + (2) 4 sG 
Hence the angle p between the axis and the asymptote of the 
relative hyperbolic orbit of the «-particle is given by 
where 
cos Pp = — 
€ 
or 
Det 
p= wilt (goes et cana wike 
Ip = Ee (12) 
We can now change to the absolute motion by considering, that 
the centre of gravity of the two bodies must move uniformly; 
originally this point moves in the direction of the « particle with 
the velocity ™’/(474m) and this motion has therefore to be superposed 
on the relative motion.” A simple calculation gives the following 
result'): after a sufficient time both bodies have assumed a uniform 
rectilinear motion. The direction of the final motion of the «-particle 
encloses an angle ® with the initial direction (through this angle 
the a-particle is deflected by the collision) 
tgp 
ty D= ok 2s ade, oar 5 Ava 
(m—M) + (M + m) tq’? p 
the velocity V obtaining the value 
v= Vise Mie Dim Menai aa.) .. (A 
M - m 
The angle between the direction in which the atom is propelled 
and the original direction of the @-particle is exactly equal to the 
angle p of equation (12). The velocity of the atom is 
w= 2v— cong, . ee), eee ee die 
According to the view set forth in § 4 certain special motions of 
') Comp. C. Darwin. Phil. Mag. 27, p. 499, 1914. 
