March 6, 1914] 



SCIENCE 



341 



sent the distribution of solar radiation out- 

 side the atmosphere, so as to leave no water 

 vapor bands in it at all. Had Langley 

 stopped with these steps accomplished, he 

 would have left us, as the result of the 

 Mount Whitney expedition, 2.060 calories, 

 the mean value as determined by high and 

 low sun observations at Lone Pine, or 

 2.220 calories, the mean value similarly 

 determined from observatio--':' "+ Mountain 

 Camp. But, by the train of reasoning 

 given on pages 142-144 of his report, he 

 convinced himself that the exponential 

 formula does not hold for the earth's 

 atmosphere, even for a strictly homogene- 

 ous ray. He therefore altered his results 

 by two different procedures, one of which 

 he states was of a kind to give too low a 

 value of the solar constant, and the other 

 too high. By this means he obtained the 

 values 2.630 and 3.505. The mean of these, 

 3.068, or in round numbers 3.0 calories per 

 sq. cm. per min., he adopted as the solar 

 constant. But in fact, both procedures 

 were calculated to give too high results, and 

 the most probable results of Langley 's ob- 

 servations lies below either of them, and is 

 in fact 2.22, or 2.06 calories, according as 

 the work at Lone Pine or Mountain Camp 

 is regarded as the better. In order to 

 recognize this, it is necessary to examine 

 the argument which led him to doubt the 

 accuracy of the exponential formula, as 

 applied to the transmission of homogene- 

 ous rays through the earth's atmosphere, 

 but first let us consider the basis of the 

 formula. 



"We have seen that Bouguer's formula 

 rests on the fundamental assumption that 

 the light is not changed in its nature in 

 passing from one layer to another, so that 

 equal layers take out equal fractions. This 

 is not the case except for homogeneous rays. 

 It is therefore necessary to divide the beam 

 up into parts, each containing rays of ap- 



proximately homogeneous transmissibility. 

 For this purpose it is necessary to observe 

 the spectrum of the sunlight by the aid of 

 the bolometer or other satisfactory delicate 

 heat-measuring instrument. Even so, it is 

 not possible to observe the transmission of 

 the atmosphere at every wave-length, so as 

 to determine the coefficients of transmis- 

 sion in the fine lines of absorption by water 

 vapor and oxygen which are introduced 

 by the earth's atmosphere. These lines are 

 mainly grouped in the great bands made 

 up of these fine lines which occur in the 

 red and infra-red spectrum, and for them 

 a special procedure must be adopted as was 

 introduced by Langley. In general, how- 

 ever, the bolometer suffices to give us atmos- 

 pheric transmission coefficients in sufficient 

 number to deal with the gradually chang- 

 ing transparency of the air for rays of 

 nearly adjacent wave-lengths. The proof 

 of the formula for atmospheric transmis- 

 sion for homogeneous rays follows : It will 

 be seen that the formula is one of extra- 

 polation solely, and is not applicable to 

 computations of the transparency at differ- 

 ent barometric pressures, unless it be the 

 fact (which is not usual) that the quality 

 of the air from the different stations to the 

 limit of the atmosphere is approximately 

 identical. This indeed may be the case 

 at very high elevations of 4,000 meters and 

 over, but is not the case for ordinary ob- 

 serving stations, so that in the use of the 

 formula of transmission it is generally 

 erroneous to introduce the barometric pres- 

 sure in the exponent as was done by 

 Pouillet. 



PEOOF OF POEMULA FOE TRANSMISSION 



Imagine the atmosphere to be made up of n 

 coneentrie layers so chosen in thickness as to pro- 

 duce separately equal barometric pressures, and 

 let the number n be so great that the transparency 

 of any single layer is sensibly uniform, although 

 the layers may differ from each other in trans- 



