92 
NATURE 
[ NovEMBER 22, 1906 
given length is inversely as the square of the wave-length, 
so that a’c’s’ has four times the energy and momentum 
that acB has in the same length, or the wave a‘c’s’ has 
twice the energy and twice the momentum of the wave 
AcB sent out in the same time, and the pressure against 
A’ is twice that against a. 
When the speed of the source w is small compared with 
that of light, the increase of pressure in forward motion, 
or decrease in backward motion, is practically the fraction 
u/u (more exactly it is altered to u/u+u of the value 
when at rest). We may call this the Doppler emission 
effect. 
Coming back to the pressure on a source at rest, that 
pressure depends on the rate at which the source is pour- 
ing out radiant energy, and that rate depends on the 
temperature of the source. If the body is a black body 
or a full radiator, the rate of radiation is as the fourth 
power of the absolute temperature, a law no longer depend- 
ing on precarious hypotheses, but the result of direct 
experiment. Here is a table showing the energy radiated 
and the pressure back against the radiating surface at 
three important temperatures :— 
Radiation from and Back Pressure against a Radiating 
Surface. 
Energy emitted Back pressure 
Absolute in ergs per second in dynes 
temperature per sq. cm. is sd. cm. 
fo) = mee (o) ata 
300° (Earth) 4°3 x 101 te 9° Gx TOme 
6000° (Sun) 6°9 x 10° sae Lot 
A black surface on the earth, then, is pushed back with 
a force of 1/100,000 mgm. per sq. cm. by its own radi- 
ation, while the surface of the sun is pushed back with 
a force of a milligram and a half on the square centi- 
metre. This table helps us to realise the exceeding 
minuteness of the forces with which we have to deal. 
While we are considering ‘the connection between radi- 
ation and temperature, it will be useful to see how the 
temperature of an absorbing particle depends on its distance 
from the sun. Take first such a particle, at the distance 
of the earth from the sun. If the sky were completely filled 
with suns it would be at the temperature of the sun, and 
give out the corresponding radiation. But the sun only 
fills 1/200,000 of its sky, so that the particle only re- 
ceives and gives out 1/200,000 of that radiation. Its 
temperature is therefore 4/200,000, say about twenty times 
less than that of the sun. We can form a tolerably good 
estimate of the temperature of the particle, since the rota- 
tion of the earth and its circulating atmosphere make its 
mean temperature, which is nearly 300° absolute, the 
same as that of the particle. So that the temperature of 
the sun is probably about 6000° absolute, or at any rate 
gives out as much radiation as a full radiator at that 
temperature. 
If we move the particle in to, say, one-quarter the 
distance, a little within the nearest approach of Mercury, 
the heat from the sun is sixteen times as great, so that 
the temperature of the particle is twice as great, say 600° 
absolute, about the temperature of boiling quicksilver. Out 
near Jupiter it will be half as great, say 150° absolute, the 
temperature varying inversely as the square root of the 
distance. 
Now we have the data from which we can trace some 
of the consequences of light pressure in the solar system. 
The direct pressure of sunlight is virtually a lessening 
of the sun’s gravitation, for, like it, it varies as the 
inverse square of the distance. As we can by direct 
measurement find, or at any rate form an estimate of, 
the energy per c.c. in sunlight, we can calculate the 
pressure which sunlight exerts on a square centimetre ex- 
posed directly to it at the earth’s distance, and it works 
out to about 0-6 mgm. per square metre. On the whole 
earth it is only about 75,000 tons, a mere nothing com- 
pared with the sun’s pull, which is forty billion times 
greater. 
But if we halved the radius of the earth we should have 
one-eighth the gravitation, while we should only reduce 
the light pressure to one-quarter, or one would be only 
twenty billion times the other. With another halving it 
NO. 1934, VOL. 75] 
would be only ten billion times as great, and so on until, 
if we made a particle a forty-billionth of the radius of 
the earth, its gravitation would be balanced by the light 
pressure if the law held good so far. 
This effect of diminution of size applies to the radiating 
body as well. If we halved the radius of both earth and 
sun, the gravitative pull would be one sixty-fourth, while 
the light pressure would be one-sixteenth, or we should 
in each halving reduce the ratio of pull to push twice as 
much, and should much sooner reach the balance between 
the two, and, of course, the balance would be reached 
sooner the hotter the bodies. Thus two bodies of the 
temperature and density of the sun, and about 4o metres 
in diameter, would neither attract nor repel each other. 
Two bodies of the temperature and density of the earth 
would neither attract nor repel each other if a little more 
than 2 cm., or just under an inch, in diameter. 
Suppose, then, a swarm of scattered meteorites 1 inch 
in diameter and of the earth’s density approaching the 
sun. Out in space their gravitation pull would be greater 
than their mutual radiation push, and there would be a 
slight tendency to draw together. -When they came within 
100 million miles of the sun radiation would about balance 
gravitation, and they would no longer tend to draw 
together. As they moved still nearer repulsion would exceed 
gravitation, and there would be a tendency—slight, no 
doubt—to scatter. 
It appears possible that this effect should be taken into 
account in the motion of Saturn’s rings if these consist 
of small particles. Let us suppose that Saturn is still 
giving off heat of his own in sensible quantity, and, merely 
for illustration, let us say that his temperature is about 
that of boiling mercury, 600° absolute. Imagine one of 
a thinly scattered cloud of particles near the division of 
the rings. At such a distance from the sun the particle 
will be receiving nearly all its heat from the planet, which 
will occupy about one-sixteenth of its sky. If the planet 
filled the whole sky the particle would be at 600°, and 
give out corresponding radiation. But filling only one- 
sixteenth of the sky it gives to the particle, and the 
particle gives out again, only one-sixteenth of the 600° 
radiation. It is therefore at ¢/1/16, or half the tempera- 
ture, 300° absolute, the temperature of the earth. Particles 
in the ring, then, about 1 inch in diameter would neither 
attract nor repel each other, and each would circle round 
the planet as if the rest were absent. 
Passing on from these mutual actions, let us see how 
radiation pressure will affect a spherical absorbing particle 
moving round the sun. We have already seen that the 
direct pressure of sunlight acts as a virtual reduction of 
the sun’s pull, and a small particle will not require so 
great a velocity to keep it in a given orbit as a large 
body will. A particle 1/1000 inch in diameter, at the 
distance of the earth from the sun, and of the earth’s 
density, will move so much more slowly than the earth 
that its year will be nearly two days longer than ours. 
In the second place we have the Doppler emission effect. 
The particle crowds forward on its own waves emitted 
in the direction of motion, and draws away from those 
it sends out behind. There is an increased pressure in 
front, a reduced pressure behind, and a net force always 
opposing the motion. This force is a very small fraction 
' = velocity of particle 
of the direct sun push, in fact only }X—— us 
velocity of light 
of that push. 
But, unlike that force, it is always acting against the 
motion, always dissipating the energy. The result is that 
the particle, losing some of its energy, falls in a little 
towards the sun, and moves actually faster in a smaller 
orbit. The particle we are considering would fall in about 
800 miles from the distance of the earth in the first year. 
Next year it would be hotter, the effect would be ‘greater, 
and it would move in further. I think it would reach the 
sun in much less than 100,000 years. As the effect works 
out to be inversely as the radius, a particle an inch in 
diameter would reach the sun in much less than a hundred 
million years. 
There is another Doppler emission éffect which must 
be mentioned. If the whole solar system is drifting along 
