DR L. BECKER ON THE SOLAR SPECTRUM. 123 



computed from the observed Greenwich mean time. Let t be the hour angle of the sun, 

 e the equation of time, I the longitude, and T the observed Greenwich mean time, then 



t = T-l-e. 



A table was prepared which gave the apparent zenith-distance with the two arguments, 

 hour angle t and the sun's declination. When the values of f had been interpolated from 

 these tables for every observed Greenwich mean time, they were entered as ordinates on 

 cross-lined paper, the abscissse being the current numbers of the lines to which they 

 belong. A curve was then drawn through the points and the number of the line read off, 

 for which the numerical value of /"was a whole number. Close to the horizon, however, 

 where f alters rapidly, it was necessary to secure more points of the curve by taking 

 f from the table with several intermediate values of the zenith-distance. 



7. The Probable Error of the Eesults. 



The complexity of the recording apparatus did not entitle us to expect any great 

 accuracy in observations which were at some distance from the standard lines. It is true 

 the working of the train of wheels had been examined under a high magnifying power of 

 a microscope, before the work was undertaken. But although the wheels appeared to 

 move regularly, when the fastest of the set was turned steadily, there was still the chance 

 of periodic errors being produced by the form of the teeth. 



It will be remembered that the bracket which carried the second wheel and the two 

 pinions could be pulled out of position to permit a quick motion of the grating. This 

 quick motion was used before every set of observations, in order to bring the required 

 region of the spectrum into the field of view. Therefore all the errors emanating from 

 irregularities of these wheels have the character of accidental errors. With the first 

 wheel, the endless screw, and the worm-wheel it was different. The grating had a fixed 

 position in relation to the worm-wheel, so that every line was observed almost in the 

 same position of these three parts. Yet the great number of standard lines acted 

 favourably. One revolution of the screw covered about 90 standard lines on an average, 

 thus rendering harmless all the periodic errors in the screw and the form of the teeth of 

 the worm-wheel. But the first wheel, which is on the same axis as the screw, turns 

 about a tooth and a half for the mean interval between the standard lines. Any irregu- 

 larities in the form of these teeth must lead to systematic error, which cannot be eliminated 

 by merely multiplying the observations. It was not until 1889 that the grating was 

 frequently altered in position with reference to the worm-wheel. Hence it was of import- 

 ance to observe the second spectrum on both sides of the normal of the grating. It is 

 true that, as already pointed out, the observations on one side preponderate, but those on 

 the other side are sufficiently numerous to test the magnitude of the errors arising from 

 the source under consideration. Moreover, the recording wheel worked in only one 

 direction, while the lines travelled in opposite directions through the field of view on the 



VOL. XXXVI. PART I. (NO. 6). X 



