NO. 8 WATER-VAPOR TRANSPARENCY — FOWLE 65 



this deviation plus that scattered to other deviations. The sum, 

 excluding the " step " value and therefore equal to the amount scat- 

 tered and lost from the corresponding wave-length, is expressed at 

 the foot of the column of zero deviation. It amounts to about 3 per 

 cent of the intensity observed at the deviation to which the energy 

 belongs. This correction of 3 per cent, in accordance with one of 

 the assumptions, is independent of the wave-length and therefore 

 ■does not alter the shape of the energy curve. 



-^ P E{d + x)S{x)dx 



Consider next the horizontal lines. The numbers added in this 

 direction, including the " step " value, give the values of the term 

 containing the second integral. When added, excluding the " step " 

 value, they give the amount of light scattered into the region indi- 

 cated by the " step " value of the line from the regions whose devia- 

 tions are indicated at the tops of the columns of the individual terms 

 of the sum. Remembering that the first-integral term does not 

 affect the shape of the desired energy curve since it may be put in 

 the form of a constant factor multiplying the observed energy of 

 each deviation, the values connected with the second integral are 

 those in which interest will at present center. 



In the set of sums in the right-hand group of columns, will be 

 found in the first column the sums taken horizontally from the 2d 

 to the 8th columns inclusive. These values give the energy scat- 

 tered from the wave-lengths between the deviations —4 and +2 cm. 

 (i. e., wave-lengths transmissible by quartz) into the corresponding 

 deviations of the horizontal lines. These values therefore should 

 be, and are, proportional to the field energy obtained by the insertion 

 of the quartz plate. The next column gives the sums of the numbers 

 taken horizontally completely across, but omitting the " step " values. 

 They represent the total field energy due to scattering from all wave- 

 lengths. The next column gives the division of the second of these 

 sums by the first, or is the ratio by which the total field light exceeds 

 that contributed from the region for which quartz is transparent. 

 The last column includes the factor 1.18 to correct for the reflection 

 from the quartz surfaces. 



It is evident then from inspection of the last two columns that the 

 deflection obtained on the insertion of quartz has to be increased not 

 only by 18 per cent for losses by reflection from the quartz surfaces 

 but also by an added amount of from 2 to 11 per cent in order to 

 obtain the total energy scattered from all spectrum regions into that 



