112 DR L. BECKER ON THE SOLAR SPECTRUM. 



From these tables it appears that the spectrum has been observed on 79 occasions 

 near the horizon, yielding a total of 17,782 observations. Since the work has been done 

 in 44 h 54 m , each line required on the average 9 seconds. There are 32 sunrises and 47 

 sunsets, the former with 45 per cent, of the observed lines. The observations of the sun 

 at medium altitudes amount to 8325, which have been determined in 29 h 7 m , thus allow- 

 ing about 13 seconds for each line, or half as much again as in low sun. While the slit 

 was as narrow in high sun as it could be made, it had to be opened more or less if the 

 sun approached the horizon. Yet there are several series, especially in the less refrangible 

 part of the spectrum, which have been obtained with a narrow slit down to the horizon. 



5. The Reductions. 



The lines were read off from the strips to one-thousandth of a revolution of the record- 

 ing wheel, by using a paper scale pasted on a piece of wood. One revolution covered 

 19f in. The marks made by the projecting nail on the recording wheel served as zero 

 points for each revolution. With the exception of the observations obtained in 1887, 

 this trying work was done twice over by James M'Pherson, the attendant at Dun Echt 

 Observatory. From these records the wave-lengths are easily computed when the correc- 

 tion of the zero point has been determined from the standard lines. 



Let C be the angle between the collimator and the viewing telescope, and x the angle 

 between the collimator and the normal to the grating, positive on the side of the viewer, 

 and let a be the distance in millimetres between the lines of the grating. Then we have 

 for the spectrum of the nth order 



± — = sin (C — x) — sin x . 

 a 



The positive sign has to be chosen if the directly reflected beam of light falls between 

 the collimator and the viewer or beyond the collimator, and the negative sign if it lies 

 on the other side of the viewing telescope. In the first position the less refrangible part 

 of the spectrum precedes the more refrangible rays when the grating is turned by the 

 recording apparatus. Let x x correspond to this position (I) of the grating, and x 2 to the 

 other (II), and let the dispersions be Ai and A 2 as defined by 



then we have 



A _ n 1 _ n 



1 a cos(C— a^) a cosa; 2 



and since « 2 >a^ , we have, disregarding the sign, 



A!>A 2 .* 



* Compare Hasselbero, Untersuchungen iiber das Absorptionsspectrum des Jodgases. St Petersburg, 1889. 



A dC 





1 n 1 



n 1 



coscc 2 ' 2 a cos(C— x 2 )~ 



a cosccj 



