1919.] 
Astronomical Notes. 
383 
ASTRONOMICAL NOTES. 
The Origin of New Stars (No. 3). 
Partial or Constructive Impact. 
We have seen that a collision between two suns will liberate suddenly a 
supply of energy which, though easily expressed in figures, is inconceivably 
great, and amply sufficient to account for the amazing outbursts that have 
been observed. Whether an impact is direct or of a grazing character, 
the collision will also account for the astonishingly rapid increase of bright¬ 
ness. It is evident, however, that a direct impact—or, indeed, any impact 
that results in the complete coalescence of the two bodies—will fail utterly 
to account for the transient character of most temporary stars. There is 
no doubt that direct impacts, though extremely rare, must sometimes occur, 
but we have no record of any such phenomenon having ever been observed. 
When a direct collision does happen a new star will be formed, not to fade 
to insignificance in a few short months, but to show its light in the heavens 
for untold millions of years. 
Each time a nova is found to have the light curve so characteristic of 
these bodies it gives evidence of a 'partial impact. The steepness of the 
rising curve points to a collision of some kind as the cause of the sudden 
liberation of such vast stores of energy ; and the steep downward slope 
which follows proclaims that the impact was by no means direct. 
That the phenomena associated with grazing impacts should be much 
more common than those which follow complete collisions is exactly what 
we should naturally expect, and the results of observation confirm this 
expectation. Even if there were no such thing as gravity, and if stars 
were spheres moving indiscriminately in straight-line courses through space, 
partial impacts would be far more common than direct ones. To put the 
case numerically, let us imagine a projectile, fired at random and moving 
in a straight line, to hit a distant sphere. Let the sphere be divided into 
a number of shells by spherical surfaces concentric with itself, and equi¬ 
distant from one another. Then, considering the sphere as a target, it 
can be represented by a circular bull’s-eye surrounded by concentric rings 
of equal width. If the radius of the sphere is divided into 100 equal parts, 
the outer ring of the target will have an area of 199 times as great as the 
bull’s-eye. Therefore a particle aimed at random and moving in a straight 
line will be 199 times as likely to pass through the outer ring as through 
the bull’s-eye—that is, it will be 199 o times as likely to pass through the 
sphere within one-hundredth part of the radius from the outer surface as 
to pass within the same distance of the centre of the sphere. If the bullet 
were a sphere similar to the target the two would just graze when their 
centres were two radii apart. The chance of a graze penetrating less than 
one-hundredth of the radius from the outer surface would then be 399 
times as great as that of a collision within the same limits of a direct one. 
If there were 1,000 shells instead of 100 the chances in the two cases would 
be 1,999 to 1 and 3,999 to 1 respectively. 
It is clear then that, even if stars moved in straight lines, grazing 
impacts would be far more numerous than direct ones. The actual propor¬ 
tion, under the law of gravitation, is very much greater still. Two heavenly 
bodies attracting one another describe conic sections with their common 
centre of gravity as one focus. They approach more nearly than they 
would do if moving in straight lines. To revert to our last illustration, 
many shots that would have missed the target had the motion been straight 
