54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 68 



be of finite width, an intensity is observed which corresponds to the 

 sum of the intensities of the energy of the various wave-lengths 

 falHng on the observing device, a bolometer in the present case. A 

 correction must be determined for reducing the observed intensity 

 to the pure or monochromatic value. Such a correction for the case 

 where both the slit and the observing apparatus subtend the same 

 angular value in the spectrum has 'been determined by Runge." His 

 method of deriving the correction is not directly applicable to the 

 present case where the widths may be unequal and the following 

 modification in the derivation was suggested by Dr. Abbot and 

 worked out in cooperation with the writer in 1909. The resulting 

 equation was applied to all the observed energy curves of the present 

 research. 



Let ,v denote the position (deviation) in the spectrum under con- 

 sideration. At X, then, lies the middle of the slit image of the color 

 wliose wave-length may be A. This slit image will extend from the 



deviation x— — to x-\- ^ where a is the slit width expressed as its 



angular value in the spectrum. It is assumed here, with safety, that 

 the spectrum on each side of x is a minimum deviation spectrum, 

 although this it not strictly true. Each wave-length as it falls in 

 succession from the center of the slit upon the center of the bolometer 

 is kept automatically in minimum deviation but the image of the 

 whole spectrum formed at any time at the bolometer is not strictly 

 a minimum deviation spectrum. 



The amount of energy, which should appear in the deviation from 

 X to x-\-dx, is not condensed in the interval dx but spread over the 



interval from x — - to x-\- . Let the amount of this energy be 



adEx where dEx is the amount of energy flowing through unit slit 

 in unit time. Of this energy only the portion dEx • dx falls in the 

 interval between x and x + dx. However portions of the slit images 



belonging to the deviations x— to .r+ to each side, do fall 



22 



within the interval dx so that the total amount of energy falling in 



the interval between x and x + dx is equal to 



dx 



^..= e(.+ |)-h(.v-1)U.. 



Ueber die Differention Empirischen Fnnctione," Zeitschrift fiir Mathe- 

 matik und Physik, 42, 1897 ; see also Hyde, Astropliysical Journal, 35, p. 237, 

 1912. 



