188 RADIATIOlSr IN" THE SOLAE 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 we 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 vary, and Professor Langley, who has devoted years 

 of work to the subject, has recently obtained evidence indicating 

 quite considerable variation. 



We may, hoAvever, assume that we are not very far from the true 

 value if we say that the stream of radiation from the sun falling 

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

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

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



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

 earth is 46,000 times the area of the sun's surface. The energy from 

 1 cm- of the sun thus passes through 4(5,000 cm'- at the surface of the 

 earth. It is therefore 46,000 nndtiplied by one twenty-fourth calories, 

 or 1,020 calory-seconds. But from the tal)le already given a black sur- 

 face at 6,250° absolute, say 6,000° C, gives 1,930 calories per second, 

 or the temperature of the sun's radiating surface is 6,000°, if he is a 

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

 is made in taking him to be one. 



Let us now take another illustration of the fourth power law. 



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

 in full sunlight at the distance of the earth. Let it be 1 cm- in cross 

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

 second. 



It will soon warm up to sucli a temperature that it giA^es out just as 

 nuich as it receives, and since it is so small heat will rapidly flow 

 through it from side to side, so that it will all be very nearly at the 

 same temperature. A s})here 1 cnr' in cross section has area 4 cm-, 

 so that it must l)e giving out fi'oni ench sciuare centimeter of its 

 surface T,V = '^•t)! 04 calory each second. Kroui the tal)le above it will 

 be seen that this corres])onds very nearly indeed to a temperature of 

 300° absolute or 27° C\, say 80° F. 



It is to be noted that this only ap])lies to a little round body. A 

 flat ])late facing the sun would be about 60' C\ hotter, while if it were 

 edgewise to the sun it uiight be very uuich coldiM-. 



Let us now see what would be the teuqxM'ature of the small black 

 sphere at othei- distances from the sun. It is ejisily seen that inas- 

 nuich as the heat received, and therefoiv that given out, varies 

 inversely as the s(|uare of the distance, the tem|)ei-ature, by the fourth 

 power laAV, will \arv invei-sdy as the s(|uai'c root of the distance. 



Here is a table of temperatures of sn)all black spheivs due to solar 

 radiation : 



