L. Bell — Absolute Wave-length of Light 357 



Calibration of the Gratings. 



In my previous paper the need and method of determining 

 the errors of ruling in a grating were briefly noticed. It is 

 fitting here to enter somewhat more into detail. 



The grating space is never perfectly uniform throughout the 

 whole extent of the ruled surface. The variations may be in 

 general classed as regular and irregular. In the first class we 

 put variations in the grating space which are purely periodic 

 or purely linear. These produce respectively " ghosts," and 

 difference in focus of the spectra on opposite sides of the 

 normal. Either fault might be large enough to unfit the grat- 

 ing for wave length determination, and would be always unde- 

 sirable, but nevertheless would introduce no gross errors into 

 the result. Variations of the second class include the displace- 

 ment, omission or exaggeration of a line or lines, and what is 

 of great importance, a more or less sudden change in the grat- 

 ing space producing a section of the grating having a grating 

 space peculiar to itself. The former types of accidental error, 

 unless extensive are harmless, and are present in most gratings 

 usually showing as faint streaks in the ruling. It is with the 

 last mentioned error that we mainly have to do. 



Consider a grating the space of which is sensibly uniform 

 except throughout a certain portion. Let that portion have a 

 grating space distinctly larger or smaller than that of the re- 

 mainder of the grating. If the abnormal portion is a consid- 

 erable fractional part of the whole grating it will, in general, 

 produce false lines and injure or ruin the definition of the 

 grating. Such a grating we should nowadays throw aside as 

 useless, although many of the older gratings are thus affected. 

 Suppose however that the abnormal portion is confined to a 

 few hundred lines. Such a series of lines will have little bril- 

 liancy and less defining power and consequently will simply 

 diffuse a certain amount of light without either producing false 

 lines or, in general, injuring the definition. In short, when 

 the full aperture of the grating is used, the spectra produced 

 will be due only to the normal grating space, the abnormal 

 portion having little or no visible effect. If however we 

 attempt to evaluate the grating space by measuring the total 

 length of the ruled surface and dividing it by the number of 

 spaces therein contained, we shall obtain an incorrect result, 

 since this average grating space, including, as it does, the 

 abnormal portion, will be necessarily. different from the normal 

 grating space which produces the spectra observed. 



In general if n be the total number of spaces and s the 

 normal grating, space the length of the ruled surface will be 

 ns+A, where A is a quantity depending on the magnitude 



