The N.Z. Journal of Science and Technology. 
36 
[Feb. 
we divide the kinetol in ergs per gram by 4T8 X 10 7 we express the energy 
per gram in calories. 
The heat equivalent of the energy per unit mass is called the 
“ thermatol.” 
The same curve gives the values of the kinetol and thermatol; but 
the number expressing the kinetol in ergs per gram is 4T8 X 10 7 times 
as great as that expressing the thermatol in calories per gram. 
(3.) The curve of velocity. The equation is 
The ordinate at any point represents primarily the velocity in centimetres 
per second. By dividing this number by 1-6093 X 10 5 we express the 
velocity in miles per second. 
(4.) The curve of duration. The equation is 
This curve is a parabola. The ordinate at any point represents the time 
that the body would take to traverse unit distance with the velocity it 
has at that point. 
(5.) The curve of time. The equation is 
V2 * 
y= X-. 
3 V fi 
The ordinate at any point represents the summation of all the elements of 
area enclosed between the corresponding ordinate of the curve of duration, 
the portion of that curve from the ordinate to the origin, and the axis of x. 
We can read off from it the whole time taken from any point to the origin 
by a body which started from an infinite distance. 
The Diagrams. 
In order to be able to read off the details of the motion at any distance 
from the centre of force it is well to have a number of diagrams drawn to 
different scales. In the case of a body approaching the Sun the following 
are convenient :— 
(1.) One representing the last ten million years of the journey, during 
which the body comes from a distance of nearly four light-years, 
or rather less than that of the nearest star. The distance of 
a Centauri is given as 4-4 light-years. From this diagram the time 
can be read off in millions of years, the velocity in decimals of a 
mile per second, the kinetol and thermatol in terms of their 
values at a billion (= 10 la ) miles from the sun, or, if preferred, 
directly in ergs and calories. 
(2.) One representing the last three hundred years of the journey. From 
this we can read the time in years, the velocity in miles per 
second, the distance in thousands of millions of miles, and the 
thermatol in thousands of calories. 
(3.) One representing the last three months of the approach, during 
which the body is within the orbits of the Asteroids. During this 
stage the velocity reaches hundreds of miles per second, and the 
thermatol millions of calories per gram. 
