14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 92 



Moreover since a^ + b- — 2ab= (a — b)-, the error increases with the 

 difference between the coefficients. 



" Now, in the general case, if we suppose the original radiation L 

 to be composed before absorption, of any number of parts Ai, A2, 

 A3, + . . . . having respectively the coefficients of absorption a^, Oo, 

 Cg, + . . . . the true value of L is given by a series of fractions 

 which may be written in the form 



^- 2Aa^ —^ 



whereas the value of the original energv by the customary formula 

 would be 



2(Aa)- 



L 



2Aa- 



so that, all the quantities being positive, by a known theorem, 



L>La, and for the same values of Ai,A2, A3, this inequahty is 



greater, the greater the difference in the values of the coefficients 

 (ii, CI2, as, ... . 



" But this is stating in other words that the true values, found by 

 observing separate coefficients of transmission, are always greater than 

 those found when we do not distinguish between the radiations of 

 which the light (or heat) of the star or sun is composed, and also that 

 the amount by which the true values are greater, increases with the 

 difiference between the coefficients. 



" We have stated above that the usual hypothesis makes the coef- 

 ficient of transmission a constant. It will be seen from the above 

 table, however, that it varies from one stratum to the next; that it 

 is least when obtained by observations near the zenith; and that it 

 increases progressively as tvc approach the horison." 



"RESEARCHES ON SOLAR HEAT AND ITS ABSORPTION BY THE 



EARTH'S ATMOSPHERE. A REPORT OF THE MOUNT 



WHITNEY EXPEDITION." 



" If the observation of the amount of heat the sun sends the earth 

 is among the most important and difficult in astronomical physics, 

 it may also be termed the fundamental problem of meteorology, nearly 

 all whose phenomena would become predictable, if we knew both the 

 original quantity and kind of this heat ; how it affects the constituents 

 of the atmosphere on its passage earthward ; how much of it reaches 

 the soil; how, through the aid of the atmosphere, it maintains the 



