12 The N.Z. Journal of Science and Technology. [Mar. 
have the following results, the resultant velocity of the third body being 
V miles per second :— 
di 
do 
m 2 
m 1 
m 2 
v i 
V‘2 
V. 
VO 
1-000 
1-000 
200 
200 
0 
1-1 
1-331 
1-054 
171-6 
228-4 
25 
1*2 
1-728 
1-106 
146-6 
253-4 
43 
1-3 
2-197 
1-155 
125-1 
274-8 
60 
1-4 
2-744 
1-202 
106-9 
293-1 
75 
1-5 
3-375 
1-247 
91-4 
308-6 . 
86 
1-6 
4-096 
1-291 
78-5 
321-5 
96 
1-7 
4-913 
1-333 
67-6 
332-4 
104 
1-8 
5-832 
1-374 
58-5 
341-5 
110 
1-9 
6-859 
1-414 
50-9 
349-1 
115 
2-0 
•8-000 
1-453 
44-4 
355-6 
119 
2-5 
15-625 
1-630 
24-1 
375-9 
128 
3-0 
27-000 
1-800 
14-3 
385-7 
129 
3-5 
42-875 
1-940 
9-1 
391-9 
127 
4-0 
64-000 
2-080 
6-2 
393-8 
124 
4-5 
91-125 
2-210 
4-3 
395-7 
121 
5-0 
125-000 
2-330 
3-2 
396-8 
117 
6-0 
216-000 
2-560 
1-8 
398-2 
111 
7-0 
343-000 
2-770 
1-2 
398-8 
105 
8-0 
512-000 
2-960 
0-8 
399-2 
100 
9-0 
729-000 
3-150 
0-6 
399-4 
96 
10-0 
1000-000 
3-320 
0-4 
399-6 
92 
Variation in the depth of penetration in moderate grazes has only a 
slight effect on the velocity of the third body. Thus when 
the velocity has the following values :— 
Depth of Penetration. 
V. 
0-05 
23-4 
0-1 
23-1 
0-15 
22-8 
0-2 
22-5 
Thus we see that if the stars are about the size of our Sun and have 
diameters which differ only in the ratio of IT to 1 the resultant velocity 
of the third body is over 23 miles per second, and that by increasing 
the inequality of the diameters up to a ratio of 2 to 1 a velocity of nearly 
120 miles per second is attained. 
It is highly improbable that the colliding stars should have exactly 
equal diameters, and so in most cases the third body will have considerable 
velocity of translation. In the case of denser bodies the velocities will be 
proportionally higher. 
If, then, the planetary nebulae are third bodies produced by the impact 
of stars of very great mass and volume, the observed velocities, which 
average about 48 miles per second, are easily accounted for. 
