562 HEXRY A. EOWLAXD 



comparison of these values shows little or no systematic variation in the 

 different plates exceeding ^ division of Angstrom. Plates 16, 17, 18, 

 and 5, 6, 8, all give the region 3900 as derived from 5200 and 5850, and 

 thus give a test of the relative accuracy of these latter regions. It is 

 seen that the two results of the region 3900 differ by about -015 division 

 of Angstrom. Were the wave-lengths of the region 5170 to 5270 to be 

 increased by -020 the discrepancy would cease. The amount of this 

 quantity seems rather large to be accounted for by any displacement of 

 the spectra on the plates, but still this may be the cause. Again, it is 

 possible that different gratings may give this difference of wave-length 

 from the cause I have mentioned above. This cause, as I have shown, 

 exists in the same degree in plane gratings as in concave. I have not 

 attempted to correct it in this case, but have simply taken the mean of 

 the two values for the region 3900, and so distributed the error. This 

 is the greatest discrepancy I have found in the results except in the 

 extreme red. 



Thus the region 3100 to 3200, a portion for which Plate 20 is to be 

 relied upon, gives the wave-length of the ultra violet -01 division of 

 Angstrom higher from the region 4200 than from 6300. As the dis- 

 crepancies in this region before the invention of the concave grating were 

 often a whole division of Angstrom, I have regarded this result as satis- 

 factory. Indeed, until we are able to make all sorts of corrections due 

 to the change in the index of refraction of the air with the Barometer 

 and thermometer, it seems to me useless to attempt further accuracy. 



With the advent of photographic plates into the table, especially the 

 longer ones required for metallic spectra, it becomes necessary to cor- 

 rect them for the departure from the normal spectrum due to the use 

 of long plates. The plates in the box are bent to the arc of a circle of 

 radius r. When afterwards straightened we measure the distance by a 

 linear dividing engine. Hence, what we measure is the arc with radius r. 

 Let and ft be the angles of incidence and diffraction from the grating. 

 We have then to express ft in terms of d. Let X be the wave-length, 

 and n and N the number of lines on the grating to 1 mm. and the order 

 of the spectrum respectively. Then 



A = T7 (sin a + sin /? ) ; 



nN 



%r <5 / 



sin j3 = - Tr sin cos [r + p ~ 

 H A \ 



In these formula? a is the angle to the centre of the photographic 

 plate, and ft and d are also measured from the centre, f is the angle 



