482 PROCEEDINGS OP THE AMERICAN ACADEMY 



can only be used by identifying the more prominent lines, with those 

 whose wave-length is known, and interpolating the remainder approx- 

 imately. If, as is often the case, these standard lines cannot be recog- 

 nized, the photograph becomes useless. To show the amount of dis- 

 tortion, suppose a spectrum to contain three similar double lines A, B, 

 and C, whose indices of refraction are 1.5, 1.6, and 1.7, and that we 

 use a 60° prism, the line B being in the position of minimum deviation. m 

 The deviations of the three lines will then be 48° 34', 53° 8', and 58° 

 11', and their dispersion 1.528, 1.667, 1.878; that is, A and will be 

 at distances of 4° 34' and 5° 3' from B instead of equidistant, and the 

 interval between the components of each line will be as 1.528 : 1.667 : 

 1.878 ; the distortion in this case amounting to about 20 per cent. 



If now the portion of the screen which receives the line C be 

 brought nearer the prism, the parts of this line will approach one an- 

 other, and since their distance apart is proportional to their distance 

 from the prism, the three lines will appear alike, if the screen is so in- 

 clined that the points where they are projected are at distances, 



as 



1.528 1.667 1.878 

 or as .654 : .600 : .532. 



A simple calculation shows that the screen must be slightly curved to 

 fulfil this condition, but if plane, the distortion will be only about one 

 and a half, instead of twenty per cent, the angle of inclination with the 

 ray B being about 37°. If an achromatic lens was used for the pro- 

 jection, all parts of the spectrum would not be in focus, but with a 

 single lens the focal distance of the violet is always less than that of 

 the red rays. If then we use such a lens, inclining the screen at the 

 same time corrects the distortion, and brings all parts into focus at 

 once. By placing the prism at a suitable distance from the lens, both 

 sources of error may be almost entirely eliminated. The oblique inci- 

 dence of the light on the sensitive surface would be an objection to this 

 method, but would be partly counterbalanced by the fact that the 

 length of the spectrum would be thereby increased more than one half. 

 Or, if preferred, the prism may be turned, so that, applying the cor- 

 rection for distortion as above, the screen shall be more nearly perpen- 

 dicular to the light. 



In conclusion, this spectrum would possess the following advantages 



