210 II. Crew — Period of Rotation of the Sun. 



I attempted to detect any heating effect by observing atmos- 

 pheric lines, and, failing to discover any motion when the 

 image was rapidly shifted from one jaw of the slit- plate to the 

 other, I conclude that this effect would be negligible in meas- 

 uring the displacement. But this is not true, because, in the 

 latter case, the sun has more time to heat the plate. 



When we consider that, if the whole differences between the 

 two results were due to the heating of the slit-plate, the dis- 

 placement of an atmospheric line on the micrometer would be 

 only - x ^ of the distance between D : , and D 2 , it will not be sur- 

 prising that it was not detected by direct observation of the 

 motion. 



Without knowing what displacement of the slit by heat 

 would be required to harmonize the two results, I computed 

 the amount of this error as follows : Of two thermometers, 

 placed one on either side of the slit, that in the sun's 

 image indicated at the end of one minute (the average time 

 of a complete reading), an excess of 10° C. over the other. 



If the angle of incidence be denoted by i, the angle of dif- 

 fraction by r, the order of the spectrum by n, the wave-length 

 by X, and the grating space by e, then 



n\ 

 sm i + sin r = — = constant. 

 e 



, cos i ,. 



. • . dr = di 



cos r 



where di is the angular displacement of the slit and dr is the 

 resulting angular displacement at the micrometer. When the 

 eastern limb of the sun was on the slit the displacement was 

 always in a direction opposite to that when the western limb 

 was observed, so that these effects were added. Not only so, 

 but since the increment di is negative when the grating is 

 "right/' dr will be positive and the reading of the micrometer 

 will be too large. If now the grating be turned " left," di 

 will be positive, and hence the micrometer reading too small. 



There were 20 revolutions of the micrometer to the centi- 

 meter, and the ratio of the focal length of the telescope to the 

 collimator was 1*08 ; so that if we call the micrometer error 

 dm and the linear displacement of the slit ds, then 



cos % 



dm = — 20 X 1'08 X ds micrometer revolutions. 



cos r 



The condensing lens had a clear aperture of 8 cm with a focal 

 length of 135 em , thus giving an image of l*25 cm diameter. 

 The jaws of the slit-plate were of blackened brass, were a 

 little wider than the sun's image, and expanded toward the 

 slit. If we assume that the expansion took place throughout 

 that part covered by the image, then for 10° C. : 



