in Theory and Practice. 371 



box be placed perpendicular to the arm BO), we have 



Aft) 

 pN 



since /u, is so small ihat we can put cos/u.=:l. Hence the 

 spectrum is " normal " at 0. Further, in this case, 



ft) . 



N 

 /. since AC=psinj/, 



Thus, if one absolute wave-length is marked on AC, and the 

 instrument is in perfect adjustment, we can mark on the beam 

 AC a scale of wave-length? for each spectrum, and the abso- 

 lute wave-length of any line is known at once. It is im- 

 portant to notice that this scale on the beam is identical with 

 the scale on the photographic plate, and that all the spectra 

 are in focus at C at the same time, and stay in focus however 

 C moves along AC, it being rigidly fastened to B. These 

 facts alone would render a concave grating preferable to a 

 plane one ; but it has many other points of superiority. It 

 is the only spectroscope suitable for use in both the ultra- 

 violet and the infra-red. Much longer photographic plates 

 can be used than with any other instrument, since they can 

 easily be bent so that they are entirely in focus. Between 

 the slit and the camera-box no lens is interposed. Besides the 

 saving in light and cost, there are no corrections necessary for 

 spherical aberration, imperfections of lenses, right- and left- 

 handed quartz, &c. Further, the concave grating is astigmatic, 

 i. e. a point of light as the source is brought to focus, not in a 

 point, but in a line. The advantages of this fact are : — 



(1) A narrow spark at the slit is broadened out into a wide 

 spectrum. 



(2) Greater accuracy in compaiing metallic and solar lines, 

 as will appear later when the use of the instrument is described. 



(3) No " dust-lines," as they are brought to a different 

 focus. 



(4) A spectrum is obtained which is broad enough to stand 

 enlarging. 



Theory of Errors in Adjustment. 



The mounting of the slit, grating, and camera-box on the 



circumference of a circle of radius ^ passing tlirough the 



2B2 



