ACCORDING TO THE UNDULATORY THEORY. 501 



When c is given it is easy to determine the difference 5 between the 

 lengths of undulation for two minima lying close to one another, 

 namely y and y — S. 



If we then suppose ^_£_^ = i y and ^^^ = i (7 " ^)> 



we have »i' = — + i and 5 = — Z — (13) 



For another length of undulation y' we obtain in the same manner 



c+y' 

 and consequently 



S : S' = -L 



c + V c + y' 



if c is rather considerable, — v — becomes very nearly equal to — — — ,, 



and we then have also very nearly S : S' = y"^ : y''^ . . . . (14) 

 By means of which formula the comparison of the observed with the 

 calculated phsenomena may be effected. 



The locality in which I have hitherto performed my experiments has 

 not allowed me to make an exact calculation of the fixed lines present 

 in the solar spectrum, although this is the surest way to determine the 

 relation between the refrangibility and the wave-length, because we can 

 then make use of the exact calculations of Frauenhofer. I have there- 

 fore only been able to decide as to the colour corresponding with the 

 length of the undulation by the eye. The calculations then which I 

 have hitherto made can only be considered as approximations ; I shall not 

 therefore produce them here. Notwithstanding, they have completely 

 convinced me that the phsenomena of absorption and those Avhich must 

 follow from the hypothesis laid down by me are identical. An example 

 of this may, however, be worthy of mention, although the calculation 

 must only be considered as an approximation. In the spectrum of iodic 

 gas, fifteen stripes occupied 9' 30" from the orange-coloured to the red ; 

 ten stripes between the yellow and green occupied 5' 30" ; I therefore 

 suppose that the distance between two neighbouring stripes, at the limit 

 between the red and orange, amounts to 38", and at the limit between 

 the yellow and green [to 31". If we now insert in the formula (14), 

 instead of y and y', the two corresponding wave-lengths (0*0000246 

 and 0*0000219 English inch, according to Herschel's table), we have 



: a' = 38 : 30*6. 



As to the rest, it is self-evident that by the undulation-length of a colour 



1 mean the length of undulation im t/ie absorbing medium. Since in the 

 examples mentioned the lengtlis of undulation were taken as they were 

 calculated in the air, and moreover the squares of the lengths of undu- 



2m 2 



