Wave-length of Light. 361 



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

 be well 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 grating for wave-length determination, and would 

 always be undesirable, but nevertheless would introduce no 

 gross errors into the result. Variations of the second class 

 include the displacement, omission or exaggeration of a line 

 or lines, and, what is of great importance, a more or less 

 sudden change in the grating-space producing a section of 

 the grating having a grating-space peculiar to itself. 'The 

 former types of accidental error, unless extensive, are harm- 

 less, 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 spacing 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 

 remainder of the grating. If the abnormal portion is a con- 

 siderable 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 now throw aside 

 as useless, although many of the older gratings are thus 

 affected. Suppose, however, that the abnormal portion is con- 

 fined to a few hundred lines. Such a series of lines will have 

 little brilliancy and less definiug-power, and consequently will 

 simply diffuse a certain amount of light without either pro- 

 ducing 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 measur- 

 ing 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 



