188 RADIATION IN THE SOLAR SYSTEM. 



Simple as the experiment appears, the determination is beset with 

 difficulties, the chief being the estimation of the fraction of the 

 energy intercepted by the atmosphere, and Ave are still unable to 

 give a very definite value. Indeed, we can not yet say whether the 

 outflow of energy is constant or whether it varies. In all probability, 

 however, it does A^ary, and Professor Langley, who has devoted years 

 of work to the subject, has recently obtained evidence indicating 

 quite considerable variation. 



We may, however, assume that Ave are not very far from the true 

 A'alue if we say that the stream of radiation from the sun falling 

 perpendicularly on 1 cm- outside the earth's atmosphere Avill heat 

 1 gm. of water one twenty-fourth of a degree centigrade every 

 second, or will give one tAventy-fourth of a calory per second. 



NoAv, the area of a sphere round the sun at the distance of the 

 earth is 4(5,000 times the area of the sun's surface. The energy from 

 1 cm- of the sun thus passes through -t('),000 cm- at the surface of the 

 earth. It is therefore 4(),000 multiplied by one tAventy-fourth calories, 

 or 1,920 calory-seconds. But from the table already given a black sur- 

 face at (^SnO*^ absolute, say 6,000° C, giA^es 1,1)30 calories per second, 

 or the temperature of the vSun's radiating surface is 0,000°, if he is a 

 full radiator — and there is good reason to suppose that no great erroi- 

 is made in taking him to be one. 



Let us noAv take another illustration of the fourth poAver hnv. 



Imagine a little black body Avhich is a good conductor of heat placed 

 in full svndight at the distance of the earth. I^et it be 1 cm- in cross 

 section, so that it is receiving one tAventy- fourth of a calory per 

 second. 



It will soon Avarm up to such a temperature that it gives out just as 

 much as it receiA^es, and since it is so small heat will rapidly flow 

 through it from side to side, so that it Avill all be v^ery nearly at the 

 same temperatui-e. A sphei-e 1 cm- in cross section has area 4 cm", 

 so that it must l)e giving out from each square centimeter of its 

 surface ^V= ^-0104 calory each second. From the table above it Avill 

 l)e seen that this corresponds very nearly indeed to a temperature of 

 300° absolute or 27° C, say 80° F. 



It is to be noted that this only applies to a little round body. A 

 flat plate facing the sun Avould be about ()0° C. hotter, Avhile if it Avere 

 edgeAvise to the sun it might l)e very much colder. 



Let us noAv see what Avould be the temperature of the small black 

 sphere at other distances from the sun. It is easily seen that inas- 

 much as the heat received, and therefore that giA^en out, varies 

 inversely as the square of the distance, the temperature, by the fourth 

 IWAver laAV. Avill vary iuAersely as the squai'e root of the distance. 



Here is a table of tenii)eratures of small black spheres due to solar 

 radiation : 



