﻿Temperature on the Spectra of Incandescent Gases. 201 



spectra of incandescent opaque bodies could not make a conti- 

 nuous impression on our sensorium, unless the discontinuity of 

 the physiological function were such that a maximum value in 

 the one function were always compensated by a minimum in the 

 other. But since the assumption of such a relation between 

 the incandescent body and our sensorium would evidently be 

 absurd, from the continuity of the spectra of incandescent opaque 

 bodies the continuity of the function J follows, as well as that of 

 the physiological function of the intensity of the sensation in 

 its dependence on the wave-length. 



That the function J, for a constant value of \, does not change 

 discontinuously with the temperature, but much rather increases 

 continuously therewith, may be inferred from the circumstance 

 that, as far as observations have hitherto gone, the spectrum of 

 an incandescent opaque body becomes continuously brighter in 

 all its parts with increasing temperature, even though the quick- 

 ness of this increase may be very different for different values 

 of \. From this it follows that, for those values of the tempe- 

 rature for which E possesses strongly prominent maxima or 

 minima, A must also have such maxima or minima, and that, 

 in general, the alterations undergone by E through changes of 

 temperature must be accompanied by alterations of A in the same 

 direction. Now, since, according to the observations hithei % to made, 

 the values of E for all values of \ have been found to increase with 

 rising temperature, the values of A also must be supposed in general 

 greater with a high than with a lower temperature. 



Hence results an important consequence in relation to the 

 conversion of a discontinuous spectrum into a continuous one, 

 at various temperatures, by increase of the density of the in- 

 candescent gas ; for if we consider the ratio of intensity of two 

 adjacent parts of the spectrum, where for the values of X and 

 X y (which differ but little from each other) the values of the 



two functions ~ and -^ can differ but little, and hence their 



Ax A x , 



ratio may be taken as equal to unity, then according to the 

 earlier part of this memoir the expression for this ratio is 



Ea* l-(l-Ax)". 



Ex,, 1-(1-Ax>' 



Here, the greater Ax and A A , the quicker the value of = r ^~ 



E\ /0 - 



converges toward unity as the value of a increases; and the 

 consequence of this will be, first the widening of the line in ques- 

 tion, and finally the continuity of the whole spectrum. 



In the example above adduced we put Ax =0*1 00, and 

 Ax, =0*005; and for these values the ratio of intensity of the 



