1920.] 
Gifford.—The Origin of New Stars. 
35 
If we take the gravitational force acting on 1 gram at the Equator 
as 978-024 dynes, the mass of the earth as 5-98 x 10 27 grams,* and the 
equatorial radius of the earth as 6-378294 X 10 8 cm.,* and substitute in 
the equation, we find 
G = 6-6536 X 10~ 8 . 
Abbot, in The Sun , gives the value 
6*6607 X 10~ 8 , 
and Kaye and Laby give 
6-658 X 10“ 8 . 
We use the last value in what follows. 
To find /x in the equation 
d 2 x 
Tt 2 ' 
fJL 
X 
where y is the attractive force on 1 gram at unit distance from a mass M, 
we have 
/X = G x = GM. 
In the case of a body drawn towards the Earth 
/*= 3-98148 x 10 20 , 
and in the case of one drawn towards the Sun 
/x= 1-31146 X 10 
26 
Let us take the Sun as a typical star and draw to scale the following 
curves to represent the details of the motion of a body drawn towards 
it from a very great distance. 
(1.) The curve of force. The equation is 
y 
/JL 
X 
2 > 
where y is the force on unit mass at unit distance. The abscissa represents 
the distance from the centre of attraction, and the ordinate the force on 
each gram at that distance. 
(2.) The curve of work. The equation is 
y 
[A 
x 
This is a rectangular hyperbola. The work done on each unit mass of 
the body, up to the time it arrives at any point on its path, may be found 
by summing the area enclosed between the curve of force, the ordinate 
at that point, and the axis of x. This work is stored in the mass as kinetic 
energy; so the ordinate at any point of the curve of work represents the 
kinetic energy of each unit mass of the body when it is passing that point. 
Bickerton has given the convenient name “ kinetol ” to this quantity. 
It can be measured conveniently by the number of ergs possessed by each 
gram of the moving body on account of its velocity. The kinetic energy 
of a body of mass m moving with velocity v is 
\mv 2 
its kinetol is kv 2 . If 
* These are the means of Helmert’s 1906 and U.S. Survey 1906 numbers as given 
by Kaye and Laby in Physical and Chemical Constants. 
