40 The N.Z. Joubnal of Science and Technology. [Feb. 
From the diagrams or the table we see that a- body which starts at an 
infinite distance from the Sun, and is drawn towards it by gravitation, when 
at the distance of a Centauri has still 11,082,050 years to complete its 
journey. The force acting on each gram is only 7-5 billionths of a dyne, 
and its thermatol is only § of a calorie. 
Nearly eleven million years later its distance from the Sun has been 
reduced to a billion miles, and its energy increased to 20 calories per 
gram. 
When all but three hundred years of the vast journey are accomplished 
the body is still far outside the limits of the solar system. Its velocity is 
over a mile and a "half per second, and its thermatol 1,000 calories per 
gram. It is already a formidable body to encounter, and its energy is 
increasing every moment. 
When only twelve years and a half remain it is crossing the orbit of 
Neptune. That of Uranus is reached six years later. When it reaches the 
orbit of Saturn less than two years and a quarter are left. The vast dis¬ 
tance from the orbit of Jupiter to the Sun is traversed in 327 days. Four 
months before the final catastrophe the Asteroids are left behind. Any 
message the body carries from the orbit of Mars reaches the Sun in fifty- 
two days, nearly half of which time is spent outside the orbit of the Earth, 
and another ten days between that and the orbit of Venus. The final rush 
of thirty-six millions of miles from the orbit of Mercury to the Sun is 
accomplished in less than a week. 
When the visitor reaches the Sun’s surface every gram of its mass 
carries energy equal to more than 45 million units of heat, the velocity 
being about 381 miles per second. 
In the case of approach to a more massive sun the velocity acquired 
is correspondingly greater. 
II. Let the body start from rest at a finite distance a from the sun. 
Then, as before, 
We must now distinguish between the actual and the parabolic kinetol. 
The actual kinetol \v 2 is the kinetic energy per unit mass which the 
body actually possesses in virtue of its velocity. The parabolic kinetol 
is the kinetic energy per unit mass which it would have possessed at this 
point if it had fallen from an infinite distance. That is the same as the 
energy per unit mass required to carry it to an infinite distance in spite 
of the action of the force. 
The parabolic kinetol at the distance x from the Sun is -. The equation 
30 
is therefore a statement of the fact that when a body starts from rest at 
a finite distance its kinetol at any point is less than the parabolic kinetol 
there by the parabolic kinetol at the starting point. 
For example, if a body starts from rest at the distance of a Centauri 
instead of at an infinite distance, to find its kinetol at any other point we have 
to subtract 3-1498 X 10 4 ergs per gram from the parabolic kinetol at that 
point. As the parabolic kinetol at the Sun’s surface is 1-8825 X 10 15 ergs 
per gram, the subtraction does not affect the first ten significant figures. 
