252 
The N.Z. Journal of Science and Technology. 
[Nov. 
411 million miles. If its greatest diameter at aphelion were 1,000,000 
miles, and if T 1 and T 2 were the periods of two extreme particles, then 
T] /412\! 
T 2 
t 2 - t 2 
-±-z =— = -00365. 
= Un7 = 1-00365. 
Taking T 2 as 3-29 years, T a — T 2 = 4-38 days. 
If, then, the orbits were of the same excentricity, and if there were no 
mutual attractions between the particles, those starting simultaneously at 
aphelion from opposite ends of that diameter of the swarm which when 
produced passes through the Sun would reach perihelion 2-19 days apart. 
To see whether this could result in spreading the comet out along its 
orbit we must find the period of oscillation of a particle in the swarm. 
When a particle is moving with simple harmonic motion its acceleration 
is u) 2 r, where r is the amplitude of vibration and u> the angular velocity 
of the corresponding point moving uniformly in a circle. The period of 
complete oscillation 
277 • -— 
= —— 2tt vr/a. 
to 
Now, if M is the total mass, and r the radius of a meteor-swarm of uniform 
density, G being the constant of gravitation = 6-658 X 10 -8 , 
MG 
The period of oscillation of a particle through it = 27r ^ (r 3 /MG). That 
is, the period varies as \/(r 3 /M). 
Taking first the case of an imaginary particle oscillating in a tube 
through the centre of the Earth, its period is 
2/r- Vr/g. 
Taking r — 6-367 X 10 8 cm., g — 980, the period = 84-41 minutes 
= -0586 day = -00016 year. If the mass of the meteor-swarm is T ouoo 
of that of the Earth, and its radius 100 times as great, the period will be 
increased 10 5 times, and will be about 16 years. If, however, the diameter 
of the swarm is reduced to that of the Earth the period will be reduced to 
•016 year. 
It seems, then, that the oscillations within the swarm take place rapidly 
enough in this case to prevent the orbital spreading of the materials. 
The Physical State of the Material of a Comet's Head .—The fact that 
the head of a comet expands again as it passes away from the Sun appears 
to prove that it is not completely vaporized even at perihelion. If it were 
reduced to a single uniform vaporous mass it is difficult to see how it 
-could regain the characteristic properties of a comet, which appear to be 
those of a swarm of very small, widely separated, solid particles. It is 
important, therefore, to inquire as to the amount of radiant energy received 
by a comet during different stages of its journey round the Sun. 
The time required to pass over unit distance when at a distance of 
x units from the Sun = A/ The heat received per second by radiation 
* N.Z. Jova\ Sci. & Tech., vol. 3, p. 36, 1920. 
