the Emission-Spectrum of a Black Body, 219 



for . c d6 _ n 



X= 5T d\-°> 



d 2 (f) 5CV 5 



dX 2 ~ X 1 ' 



72JL 



-=^ is negative, therefore the value corresponds to a maximum. 

 Let this value he called \ m . The corresponding value of <£ is 



in 



As both <f) and d<f>/d\ vanish for \=oo, the curve is an 

 asymptote to the \-axis. 



Further, d 2 (f>/d\ 2 = for the roots of the equation 



3OX 2 2 -12c\0 + c 2 = O; 

 therefore for 



x=x m (i ±v A). 



log -^ 



For these two points the curve has points of inflexion. If we 

 put X = \ m (1 + e) , then 



__c _5_ 



_ G^ Wi+ 6 )9 _ Ci i+6 . 

 therefore 



If we put — e for e, then 



rm 



In this case the absolute total of the series is greater and 

 therefore <f>/<f> m less than when e is positive. So far as e< 1, 

 the ordinates at an equal distance from the maximum are less 

 on the side of small wave-lengths. 



In an earlier work* I showed that the energy curves of 

 black bodies at different temperatures cannot cut one another. 



From this it may be deduced that the curve must fall away 

 slower toward the side of the long waves than the curve 



const. 



But this is in reality the case with our curve : d<j) x /d\ is in 

 absolute magnitude always less than 5C/X 6 , and only reaches 



* Wied. Ann. lii. p. 159 (1894). 



S2 



