10 The N.Z. Journal of Science and Technology. [Mar. 
progression. If, however, the planetary nebulae are third bodies produced 
by stellar grazes these velocities are easily explained. 
In the case of the partial collision of two stars of equal mass and 
volume the third body is, of course, left without any motion of translation 
except that due to original proper motion of one or both of the stars. 
There is, however, rapid rotation even in this case. If the bodies are of equal 
volume but different densities there is still no resultant velocity of trans¬ 
lation. 
For example, if one of the colliding suns, which we may call A, is nine 
times as dense as the other, B, then B has T % and A has ^ of the relative 
velocity, which we shall suppose is 400 miles per second. Thus B is 
moving 360 miles per second and A 40 miles per second. 
But, the diameters being equal, the volume struck from A is equal to 
that struck from B. The mass from A is therefore nine times that struck 
from B. The momenta of the two portions are equal, and the third body 
is left spinning in space without appreciable velocity of translation, whilst 
A leaves it with an initial velocity of almost 40 miles per second, and B 
starts away with a velocity of about 360 miles per second. 
Fig. 1. 
If, however, the diameters of the stars differ appreciably, the trans¬ 
lational motion will be considerable. It is indeed surprising what a large 
velocity results from an exceedingly small irregularity in size. 
As soon as there is any inequality in the diameters of the bodies their 
density also becomes of great importance in determining the final velocity 
of the third body. With stars of given volume the relative velocity of 
impact is directly proportional to their density, and the initial velocity 
of the third body varies in the same ratio. 
If we make a numerical estimate of the velocities to be expected in the 
case of encounters of stars like our Sun it will be easy to allow for variations 
in volume and density. 
When unequal stars collide the limpet-like portions struck from the 
two have the same maximum area of cross-section APBQ (fig. 1), but 
their lengths are different, being equal respectively to 2AK and 2BL. 
Let us assume as a rough approximation, which is quite close enough 
for our purpose, that the respective volumes of the limpets are in the ratio 
of these lengths. 
Let M 1? M 2 be the masses of the stars; d 1 , d 2 their diameters; v ± , v 2 
the velocities with which they meet; m 1 , m 2 the masses of the portions 
