DR L. BECKER ON THE SOLAR SPECTRUM. 113 



From the constant of the grating a= # 0017592 mm. and C= 25°, we find for the second 

 spectrum if X = 5500 A.U. 



a; t =-6 -2; a; 2 = 31°-2; Ai = 116A 2 - 



Suppose the rays from the edges of the slit enclose the angle 25 before diffraction, and let 

 the angles be 2<j x and 2<r 2 after diffraction. Then 



cr l _d(G—x l ) _ cos x t _ <r 2 _ d(G — x 2 ) _ cos x 2 

 s dx x coscc 2 ' s dx 2 cosa? x 



<r 1 >s><r 2 - 



This shows that the angular value of the slit remains unaltered if the collimator serves 

 also as viewing telescope. Further, we see that the angular value of the slit in spectrum 

 I, which gives the greater dispersion, has increased. The separation of close lines 

 depends both on the dispersion and on the apparent size of the slit ; we must therefore 



compare — and 



4i _j A 2 



'i 



Ai_ nil A 2 __ W 1 



therefore 



a-! a s cosa^ <x 2 as coscc 2 



A_i/ A_ 2 



which means that although the dispersion Ai is greater on side I than on side II, the 

 separating power is less in the first position. 

 In the special case for X= 5500 A.U., it is 



42 = i-i6^- 1 . 

 <r 2 0"i 



In this investigation one important point has not been taken into consideration at all, 

 viz., the intensity of the light. It would require special experiments to find the intensity 

 of the diffracted rays for the several positions of the grating with regard to the direction 

 of the incident light. But we may compute the direct loss of light incurred by our 

 spectroscope. The breadth of the ruled surface of the grating allows the same amount 

 of light to be received from the collimator in both second spectra. After diffraction the 

 horizontal diameter of the beam of light becomes 



, cos a?, . . , 7 cos x, . . 



d,= -4 m. and <L = l 4 m., 



1 cosa^ l cos% 



or for X = 5500 A.U., 



d x = 3-44 in. ; d 2 = 4"65 in. 



The aperture of the viewing telescope being 4 in., the second position of the grating 

 entails a loss of light of about 15 per cent, 



