ACCORDING TO THE UNDULATORY THEORY. 485 
When this expression, which represents the intensity of the resulting 
i eae BiB | 
wave of light, is differentiated in relation to {> it is clear that A becomes 
. Sa wd abe Db wes : $ 
a maximum or minimum, if sin 2 7 = =0; that is, A becomes a maxi- 
26 
mum when eis is = 0, 1, 2, 3, 4, ete., and it becomes a minimum when 
26 belie 
TH bLELLD be. 
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 vy 5 are taken as ordinates, 
a 
and the logarithms oa as abscissa. 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 abscissee, which represent two lengths of undulation, 
standing in a given relation to one another, must be independent of the 
representative substituted value of x and consequently must be of 
gequal magnitude along the whole curve. 
In order to examine the phenomena 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. 1°55, and whose divisions, red, yellow, green, &c., 
take in the lengths 
outermost red limit between red and yellow 
log. limit between red and yellow log. limit between yellow and green’ &e. 
If I now at first suppose the distance 6 between the reflecting sur- 
faces to be very small, for example equal to 3, of the length of the wave 
of the red light, the value ES which represents that of the red light 
light originating in this case become a (1—1)*, a (1—r)? 7/7, a (l—r)?r!4; @ 
(1—r)?r'®, &c., and the final results are 
r ya a(l—r)? 
26 
Ji 2 tat rit 
a 
which according to this differs from the one before obtained only in this parti- 
cular, that the magnitude r of the denominator is changed intor’. It thence fol- 
lows that all the conclusions which may be drawn from one of the formulz, may 
also be drawn from the other. 
? 
212 
