NO. 8 WATER-VAPOR TRANSPARENCY FOWLE 63 



The integrals of the second and third terms will be seen to both 



E(6) 

 contain the term S(.v) rrrn \ d-^' which is not desired but which 



■C- ( C'o ) 



fortunately occurs in the two integrals with opposite sign. In other 

 words, the function used for the scattered energy includes the energy 

 which should be observed at i9 = o and which is not to be considered 

 as scattered energy. This energy is accounted for in E{6) . 

 Accordingly the following expression is obtained : 



or transposing, 

 E{6) =E,(^) + 1^^ [_^ S{x)dx- j^^-j^^ 1^^ E{d + x)Six)dx. 



All the functions on the right-hand side of the second equation 

 are known except E{6). For this may be substituted a first approxi- 

 mation to it obtained by subtracting from the observed lamp deflec- 

 tions the amount of scattered energy indicated by the quartz plate, 

 suitably corrected, as already described, for the reflections from the 

 surface of the plate. The resulting values, which call Ea{0) will be 

 found at their greatest to difi'er by only about i per cent where they 

 are of importance in deriving the additional scattered energy. Hence 

 Ea{9) will be a sufficiently close approximation for use in the second 

 and third terms. 



Table i6 shows the process used to evaluate this expression for the 

 total field light. The numbers in the first column and the first line 

 indicate the prismatic deviations {6) measured in centimeters on the 

 plate (i cm. = 4' of deviation in the spectrum, zero of deviation at 

 1.8 /x). Each other number is a measure of the energy under the 

 curve S{d) summed for a difference of deviation extending from 

 — 0.5 to +0.5 from the indicated deviation. It represents that por- 

 tion of energy scattered from the deviation at the top of the column 

 into that indicated in the first column. 



Ea{e) 



Consider first the numl^ers surrounded by the rectangles and ap- 

 pearing like a flight of steps. These represent Ea{d), the first 

 approximation to the true amount of energy in the spectrum of the 

 lamp for the corresponding deviations indicated in the first line or 

 column. They represent also the terms common to both integrals. 



