5'4 



NATURE 



[September 22, 1904 



hotter, while if it were edgewise to the sun it might be 

 very much colder. 



Let us now see what would be the temperature of the 

 small black sphere at other distances from the sun. It is 

 easily seen that, inasmuch as the heat received, and there- 

 fore that given out, varies inversely as the square of the 

 distance, the temperature, by the fourth power law, will 

 vary inverselv as the square root of the distance. 



Here is a table of temperatures of small black spheres due 

 to solar radiation : — 



; from Sun's centre 



3f million miles ... 

 23 million miles ... 

 At Mercury's distance , 

 At Venus's distance 

 At Earth's distance 

 At Mars's distance 

 At Neptune's distance . 



Temperalure Centigrade 



1200° C. Cast iron melts. 



327° Lead nearly mel(«. 

 210 Tin nearly mclls. 

 85° Alcohol boils freely. 

 27° Waini summer day. 

 - 30° Arctic cold. 

 -219" Nitrogen frozen. 



We see from this table that the temperature at the earth's 

 distance is remarkably near the average temperature of the 

 earth's surface, which is usually estimated as about i6° C. 

 or 60° F. This can hardly be regarded as a mere co- 

 incidence. The surface of the earth receives, we know, an 

 amount of heat from the inside almost infinitesimal com- 

 pared with that which it receives from the sun, and on the 

 sun, therefore, we depend for our temperature. The earth 

 acquires such a temperature, in fact, that it radiates out 

 what it receives from the sun. The earth is far too great 

 for the distribution of heat by conduction to play any serious 

 part in equalising the temperature of different regions. 

 But the rotation about its axis secures nearly uniform 

 temperature in a given latitude, and the movements of the 

 atmosphere tend to equalise temperatures in different lati- 

 tudes. Hence we should expect the earth to have, on the 

 average, nearly the temperature of the small black body 

 at the same distance, slightly less because it reflects some 

 of the solar radiation, and we find that it is, in fact, some 

 10° less. 



Prof. Wien was the first to point out that the tempera- 

 ture of the earth has nearly the value which we should 

 expect froin the fourth power law. 



Here is a table showing the average temperatures of the 

 surfaces of the first four planets on the supposition that they 

 are earth-like in all their conditions : — 



Table of Temperatures of Earlh-like Planets. 

 Mercury ... ... ... ... ... 196° C. 



Venus ... ... ... ... ... 79° ,, 



Earth ... ... ... ... ... 17° ,, 



Mars —38° ,, 



The most interesting case is that of Mars. He has, we 

 know, a day nearly the same in length as ours ; his 

 axis is inclined to the ecliptic only a little more than ours, 

 and he has some kind of atmosphere. It is exceedingly 

 difficult to suppose, then, that his average temperature 

 can differ much from —38° C. His atmosphere may be 

 less protective, so that his day temperature may be higher, 

 but then to compensate, his night temperature will be 

 lower. Even his highest equatorial temperature cannot 

 be much higher than the average. On certain suppositions 

 I find that it is still 20° below the freezing point, and until 

 some new conditions can be pointed out which enable 

 him to establish far higher temperatures than the earth 

 would have at the same distance, it is hard to believe that 

 he can have polar caps of frozen water melting to liquid 

 in his summer and filling rivers or canals. Unless he is 

 very different from the earth, his whole surface is below the 

 freezing point. 



Let us now turn from these temperature effects of radi- 

 ation to another class of effects, those due to pressure. 



More than thirty years ago Clerk Maxwell showed that 

 on his electromagnetic theory of light, light and all radi- 

 ation like light should press against any surface on which 

 it falls. There should also be a pressure back against any 

 surface from which radiation is reflected or from which It 

 is issuing as a source, the value In every case being equal 



NO. 182 1, VOL. 70] 



to the energy In a cubic centimetre of the stream. The 

 existence of this pressure was fully demonstrated indepen- 

 dently by Lebedew and by Nichols and Hull some years 

 ago in brilliant experiments in which they allowed a beam 

 of light to fall on a suspended disc In a vacuum. The disc 

 was repelled, and they measured the repulsion and found it 

 to be about that required by .Maxwell's theory. Nichols 

 and Hull have since repeated the experiment with greater 

 exactness, and there is now no doubt that the pressure exists 

 and that it has Maxwell's value. 



The radiation, then, poured out by the sun is not only 

 a stream of energ>'. It is also, as it were, a stream of 

 pressure pressing out the heavenly bodies on which it falls. 

 Since the stream thins out as it diverges, according- to the 

 inverse square of the distance, the pressure on a given 

 surface falls off according to the same law. We know the 

 energy in a cubic centimetre of sunlight at the distance of 

 the earth, since, moving with the velocity of light, it will 

 supply 1/24 calory per second. It is easy to calculate that 

 it will press with a force of 6xio-° degree on a square 

 centimetre, an amount so small that on the whole earth it 

 is but 70,000 tons, a mere trifle compared with the three 

 million billion tons with which the sun pulls the earth by 

 his gravitation. 



But now notice the remarkable effect of size on the re- 

 lation between the radiation pressure and the gravitative 

 pull. One is on the surface and proportional to the surface, 

 while the other penetrates the surface and pulls every grain 

 of matter throughout the whole volume. 



Suppose we could divide the earth up into eight equal 

 globes. Each would have half the diameter of the earth 

 and a quarter the surface. The eight would expose twice 

 the surface which the earth exposes, and the total radiation 

 pressure would be doubled, while the total gravitative pull 

 would be the saine as before. Now divide up each of the 

 eight Into eight more equal globes. Again the radiation 

 pressure would be doubled, while gravitation would be the 

 same. 



Continue the process, and it is evident that by successive 

 division we should at last arrive at globes so small and 

 with total surfaces so great that the pressure of the radi- 

 ation would balance the pull of gravitation. Mere 

 arithmetic shows that this balance would occur when the 

 earth was divided up into little spheres each 1/40,000 cm. 

 in diameter. 



In other words, a little speck 1/40,000 cm., say 1/100,000 

 of an inch in diameter, and of density equal to that of the 

 earth, would be neither attracted nor repelled by the sun. 



This balance would hold at all distances, since both 

 would vary in the same way with the distance. Our arith- 

 metic comes to this : that if the earth were spread out in 

 a thin spherical shell with radius about four times the 

 distance of Neptune, the repulsion of sunlight falling on it 

 would balance the inward pull by the sun, and it would have 

 no tendency to contract. 



With further division repulsion would exceed attraction, 

 and the particles would be driven away. But I must here 

 say that the law of repulsion does not hold down to such 

 fine division. The repulsion is somewhat less than we have 

 calculated owing to the diffraction of the light. 



.Some very suggestive speculations with regard to comets' 

 tails have arisen from these considerations, and to these 

 Prof. Boys directed the attention of Section A last year. 

 We may imagine that the nucleus of a comet consists of 

 small meteorites. When these come near the sun they are 

 heated and explosions occur, and fine dust is produced not 

 previously present. If the dust Is sufiiciently fine, radiation 

 may overpower gravitation and drive it away from the sun, 

 and we inay have a manifestation of this expelled dust in 

 the tall of the comet. 



I do not, however, want to dwell on this to-day, but to 

 look at the subject in another way. 



Let us again introduce our small black sphere, and let 

 us make it i sq. cm. in cross section, i'i3 cm. in diameter, 

 and of the density of the earth. The gravitation pull on it 

 is 42,000 times the radiation pressure. 



Now let us see the effect of size on the radiating body. 

 Let us halve the diameter of the sun. He would then have 

 one-eighth the mass and one-quarter the surface. Or, while 

 his \m]\ was reduced to one-eighth, his radiation push would 

 iinlv be reduced to one-quarter. The pull would now be 



