1920 .] 
Gifford.—The Origin of New Stars. 
41 
We are therefore justified in saying that the final kinetol, thermatol, and 
velocity are practically identical whether the body starts from rest at an 
infinite distance or at the distance of a Centauri. If the body stands at the 
distance of Neptune we have to subtract from the kinetol 2*9177 X 10 11 ergs, 
and this reduces the final velocity from 381-284 to 381-251 miles per 
second, the difference being approximately one-thirtieth of a mile per 
second. 
When, however, we consider the time occupied on the journey the 
position of the starting-point is most important. The path from a point 
Fig. 4. 
at a finite distance must be taken as half the perimeter of the limiting 
straight-line ellipse of which the distance is the major axis. The time of 
fall is half the periodic time in this ellipse : therefore 
7r 
T = -7= • (Jr) 
v 7 
fi 
IT 
2V2 
= ‘ r 2 . 
/x 
3tt 
That is, the time for the rest of the journey is -j- times as great as if the 
body had fallen from an infinite distance. This increases the time of 
fall from the distance of a Centauri from eleven million to over twenty-six 
million years, and that from the distance of the Earth from twenty-seven 
to nearly sixty-five days. 
The, diagrams given before may be modified to illustrate the effect of 
changes in initial distance or initial kinetol. 
III. Let there be an initial velocity perpendicular to the directioh of 
the force. Let the body be projected from the point A (see fig. 4) in the 
direction AT with a velocity v, and let each gram be acted on by an 
