ACCORDING TO THE UNDULATORY THEORY. 485 



When this ex23ression, which represents the intensity of the resulting 



2b 

 wave of light, is differentiated in relation to -y- , it is clear that A becomes 



2b 

 a maximum or minimum, if sin 2 tt — =0; that is, A becomes a maxi- 



\ 



mum when -— is = 0, 1 , 2, 3, 4, etc., and it becomes a minimum when 

 A. 



2b 



\ 2» 2' 2' 2' 2' °^'^' 



The result of an indefinite quantity of wave-systems of light be- 

 comes also a maximum or minimum, under precisely the same circum- 

 stances as the result of only two such systems. To make apparent the 

 hypothesis which I have advanced, I have constructed in fig. 1 , Plate VI., 

 the equation (6) in such manner that the values of the intensity A, 



which represent the different values of — , are taken as ordinates, 



and the logarithms — as abscissae. As the difference of the loga- 

 rithms of two numbers depends on the relation of those numbers, and 

 not on their absolute magnitude, the difference between two points of 

 the axis of the abscissae, which represent two lengths of undulation, 

 standing in a given relation to one another, must be independent of the 



representative substituted value of — , and consequently must be of 



^qual magnitude along the whole curve. 



In order to examine the phaenomena of absorption which are exhi- 

 bited in a spectrum whose extreme lengths of undulation (red and 

 violet) are to one another as 1-58: 1, I described a spectrum (fig. 2) 

 whose length, log. TSS, and whose divisions, red, yellow, green, &c., 

 take in the lengths 



I outermost red i limit b etween red and yell ow o.„ 



*^S' limit between red and yellow 8' limit between yellow and green' 



If I now at first suppose the distance b between the reflecting sur- 

 faces to be very small, for example equal to ^\j of the length of the wave 



of the red light, the value — - which represents that of the red light 

 2b 



light originating in this case become a (1 — r)-, a (1 — r)- »'-, a {\-r)"r'*; a 

 {\ — r)'r'^, &c., and the final results are 



A = 



J 



1 _ 2r'2cos 2 r — -I- f' 



which according to tliis differs from the one before obtained only in this parti- 

 cular, that the magnitude r of the denominator is changed into r'. It thence fol- 

 lows that all the conclusions which may be drawn from one of the formula?, may 

 al«o be drawn from the other. 



2l2 



