Wave-length of Light. 365 



and the large gratings III. and IV. into centimetres. Each 

 grating was carefully gone over five times and the mean 

 result taken. The following corrections were found. 



The actual variations found in each grating are given below, 

 the figures given being the difference of n lines from the distance 

 between the stops, the lines being taken in the consecutive 

 sections of the gratings. 



Grating I. 

 Sections 1 2 3 4 5 6 



Eesiduals 0*78 0-98 0-81 1-03 0-86 1-24 



Grating II. 

 Sections 1 2 3 4 5 6 



Eesiduals 2*07 1-93 1-52 1-68 1-31 0-45 



Grating III. 

 Sections 1 23456789 10 



Eesiduals.. 2*80 2-85 1-77 2-77 2-70 2-77 2-67 2-64 2-73 2-77 



Grating IV. 

 Sections 1 23456789 10 



Eesiduals.. 0*31 0-28 0-35 0-43 0-40 0-43 0-31 0-35 0-28 0-82 



The calibration of III. is worth describing in detail. Cen- 

 timetre 3 was evidently too long. I therefore measured the 

 centimetres from 15 to 25 millim. and from 25 to 35 millim. 

 The former was quite normal, but the latter showed an increase 

 almost identical with that of the whole third centimetre. I 

 then examined the grating in a strong light and detected at 

 27 millim. from the end a faint line, such as usually indicates 

 a few wavering lines, caused perhaps by dust under the 

 diamond point. Placing, however, this line under the micro- 

 scope, a band of perhaps twenty lines appeared with spacing 

 noticeably wider than usual. Here was a very serious flaw 

 in a grating to all appearance absolutely perfect. A most 

 critical examination in the spectrometer of course failed to 

 detect it, but it was both detected and located with unerring- 

 certainty by the process of calibration. Micrometrical 

 measurements on this group showed an excess of about 2*5 

 over an equal number of spaces elsewhere on the grating. 

 This quantity, of course, had to be taken account of in 

 connexion with the previous calibration. 



The deduction of the necessary corrections from the data 

 given by calibration requires no little care and judgment, and 

 can be properly done only in connexion with a detailed study 

 of the spectra given by various portions of the gratings con- 

 cerned. For the four gratings used by the author, these 

 corrections, applied directly to the lengths of the gratings in 



