1921.] 
Astronomical Notes. 
11 
struck of!; and t the thickness AB of the maximum section. Also, let the 
relative velocity 
v i + v 2 = v. 
Then, d t 3 1 
M 2 d 2 3 
— = AK = VAB]AC = = V*E? approximately. 
m 2 BL AB.BD BD d 2 -t 
Neglecting, for the time, the effects of original proper motion in one or 
both of the stars, we have 
Mi — M 2 v 2 ; 
Mj _d / 
M 2 d 2 3 ’ 
Mo 
Vl ""Mi + M~ * 
The velocity of the third body produced by the impact (if we neglect 
the loss of energy expended in shearing the stars, which is an infinitesimal 
part of that available) is given by the formula 
m 2 v 2 — m 1 v 1 
m 1 + m 2 
v 2 ~ 
m. 
m. 
V ; 
— + l 
m 0 
Numerical Illustration .—Let us take the diameter of the smaller star as 
unity, and consider the resultant velocity of the third body when different 
diameters are given to the larger star. 
Let the densities of the stars be equal, and the total mass such that 
the relative velocity at the moment of impact is 400 miles per second, and 
let the impact penetrate to of the diameter of the smaller. Then we- 
