1921.] Gifford.—Variations in Size of a Comet’s Head. 253 
at this distance is inversely proportional to the square of the distance. 
Therefore the heat received in passing over unit distance at a distance x 
from? the Sun is proportional to xy'x 2 —that is, to x~ Therefore the 
total heat received in passing outwards from a distance to a distance 
= fkx~ ? ‘dx = k I""— 2x~^ + cV 2 = 2 k(-= -tq. 
L Jrj \Vr, VrJ 
That is, the total heat received whilst going from a distance r to an infinite 
distance, or in coming from an infinite distance to a distance r, is propor¬ 
tional to 1/r^ 
For example, let us compare the quantity of heat received by Encke’s 
Comet whilst passing between its perihelion distance and the orbit of the 
Earth with that recevied by it during its journey from the distance of the 
Earth’s orbit to aphelion. Taking its nearest distance from the Sun as 
0*36 astronomical unit approximately, and its greatest distance as 4 astro 
nomical units, we have, denoting the two quantities by H : and H 2 , 
H t v\ a 
jTITX ~~ 1 -i ~" 
VI v 'i 
That is, the heat received by the comet from the Sun whilst within the 
distance equal to the radius of the Earth’s orbit only exceeds by one-third 
that received whilst beyond that distance. 
Of course, the rate at which heat is received by the comet when at peri¬ 
helion is about nine times as great as when its distance from the Sun is 
one astronomical unit, whilst at aphelion the rate is only one-sixteenth 
part of the latter. But the radiation falls on one side only of each meteorite, 
and although profound effects are produced in the outer layers, the main 
portion of each meteorite appears to be little affected. 
We thus reach the following tentative conclusions :— 
(1.) That the primary cause of the diminution in size of a comet’s head 
as it approaches the Sun is the convergence towards perihelion 
of the orbits of the meteorites of which it is composed. 
(2.) That the diminution thus brought about allows the mutual attrac¬ 
tion of the particles to reduce still further the space occupied by 
the swarm. 
(3.) That the diminution caused by gravitation is a function of the 
distribution of density within the swarm, and is less the greater 
the condensation of the materials of the swarm towards its centre. 
(4.) That observations of changes in diameter will afford a clue to the 
distribution of density in the head of any comet. 
(5.) That the rate of oscillation of the particles of the swarm is probably, 
in the case of most periodic comets, sufficiently rapid to prevent 
or retard the spreading of the materials of the head along the 
orbit, which the difference of the periods of revolution round the 
Sun of the separate meteorites would otherwise lead to. 
(6.) That comets’ heads are not completely vaporized even at perihelion. 
