336 



SCIENCE 



[N. S. Vol. XXXIX. No. 1001 



"solar constant of radiation" is the num- 

 ber of calories per square centimeter per 

 minute which would be produced by the 

 complete absorption of the solar radiation 

 in free space at the earth's mean solar 

 distance. 



Preparatory researches of great interest 

 were made in the eighteenth century by 

 Bouguer, Lambert, DeSaussure and Leslie. 

 Determinations of the solar constant of 

 radiation, however, may be said to have 

 begun about eighty years ago with the 

 investigations of Sir John Herschel, Prin- 

 cipal Forbes and Pouillet. The problem 

 comprises two parts: first, to measure the 

 intensity of the solar radiation at the 

 earth's surface; second, to estimate the loss 

 it has suffered in passing through the 

 atmosphere. It will be convenient to con- 

 sider the atmospheric influence briefly be- 

 fore taking up the methods of measuring 

 the solar radiation, and then to return to 

 a more thorough discussion of the atmos- 

 pheric transmission. 



ATMOSPHERIC TBANSMISSION 



The determination of the transmission 

 of the atmosphere rests primarily upon 

 the hypothesis of Bouguer, first put for- 

 ward in the year 1729 and elaborated in 

 Bouguer 's posthumous work published in 

 the year 1760. The late Dr. Langley has 

 placed this matter in so very clear a light 

 in his paper on the "Amount of the Atmos- 

 pheric Absorption"^ that I can not do 

 better than to quote from his statement. 



If a beam of sunlight enters through, a crevice 

 in a dark room the light is partly interrupted by 

 the particles of dust or mist in the air, the apart- 

 ment is visibly iUuminated by the light laterally 

 reflected or diffused from them, and the direct 

 beam, having lost something by this process, is not 

 so bright after it has crossed the room, as before. 

 In common language, the direct light, to an ob- 



2 American Journal of Science, Third Series, 

 Vol. 28, September, 1884. 



server in the path of the beam, has been partly 

 ' ' a;bsorbed, ' ' and the problem is, to determine in 

 what degree. If a certain portion of the light 

 (suppose one fifth) were thus scattered, the beam 

 after it crossed the room would be but four-fifths 

 as bright as when it entered it; and, if we were 

 to trace the now diminished beam through a sec- 

 ond apartment altogether like the other, it seems 

 at first reasonable to suppose that the same pro- 

 portion (i. e., four fifths of the remainder) would 

 be transmitted there also, and that the light would 

 be the same kind of light as before, and only di- 

 minished in amount (in the proportion 4/5 X 4/5). 

 The assumption originally made by Bouguer and 

 followed by Herschel and Pouillet, was that it was 

 in this manner that our solar heat was absorbed 

 by our atmosphere, and that by assuming such a 

 simple progression the original heat could be cal- 

 culated. 



If Ao be the intensity of the original 

 beam before entering the transparent 

 medium whose transmission is to be inves- 

 tigated, then after the passage through the 

 first stratum of unit thickness let us sup- 

 pose a fraction of the original represented 

 by p has passed through, so that what was 

 Af, becomes Af,p. Then since a second 

 stratum identical with the first in consti- 

 tution and thickness must, according to 

 Bougnier's assumption, have an identical 

 effect, the ray which was A^ will emerge 

 from the second stratum A^p^, and so on. 

 The fraction p transmitted by the unit of 

 thickness is the common ratio of a geo- 

 metric progression, so that after passing 

 through a thickness m of the medium, the 

 intensity of the light which was formerly 

 J-o will become ^oP*"- 



As the height to which the atmosphere 

 extends in appreciable density is very 

 small compared with the radius of the 

 earth, the thickness of the layer traversed 

 by a solar beam of a zenith distance not 

 exceeding 70° is approximately propor- 

 tional to the secant of the zenith distance 

 of the sun at the time of observation. If 

 we regard unit thickness as that corre- 

 sponding to barometric pressure of 760 



