NO. 8 WATER-VAPOR TRANSPARENCY FOWLE 55 



The intensity of the spectrum at x may be defined as the energy over 

 an indefinitely small interval dx divided by dx. That of the impure 

 spectrum at x is therefore 



{.(..^ )-£(..- 1)} 



dE 

 That of the pure spectrum is , /' • a as a becomes infinitely small. 



However, only the relative intensity from one part of the spectrum to 

 another is required and not necessarily the absolute infinitely small 

 intensity which the abstract pure spectrum would have. 



In measures with the bolometer not even the intensities in this 

 impure spectrum are obtained directly but rather the sum of the 

 intensities in it over the region covered by the bolometer. If the 

 middle of the bolometer is at the deviation x and its width is b, then 

 it receives in a unit time the amount of energy 



F(.v. = |j{£(.,- + .+ «)-£(.■• + .- ^)}... 



2 



The observed intensity in the spectrum is proportional to this F{x). 

 A development of -, f , which is proportional to the intensity in the 

 pure spectrum, in terms of F{x) is desired. 



dF 

 If f{x) is taken to denote -rr , then by Taylor's theorem 



CIA' 



E{x + v+^^)=Eix)+f{x)[v+ l)+ij'(.-^')(c'+iy+- ■ ' • 

 so that 



fl E (.V + .+ t) rf. = £(.v)ft+/(.r) f, +/'(.v) 3»|; + ''' + . . . . 



i 



Making a similar development for the second term of the expression 

 for F{x) and subtracting, there results 



F(.r)=2{/W|';-+/"(.r)?'^^«*'+... 



Let b = an, a being the slit width and n the ratio of the width of the 

 bolometer to that of the slit, then 



F(^) =2 ['^<';/(.v) + ""'^"^ f'M 



+ '??!l3±i_0'?!+3!5*) /iv(_v) + 1^ 



