L. Bell—Absolute Wave-length of Light. 179 
The difference in the above resylts is by no means large com- 
pared with the results obtained from different gratings by other 
investigators, but it certainly is enormously great compared 
with the experimental errors alone. 
As nearly as can be judged these ought not in either grating 
to exceed one part in two hundred thousand, while the above 
discrepancy is about one part in thirty-five thousand. 
Its cause must be sought in the individual peculiarities of 
the gratings, rather than in the method of using them. 
All gratings are subject to irregularities of ruling, and the 
effects of these is various, according to the nature and magni- 
tude’ of the defects. Linear or periodic errors in ruling, unless 
very small, will make themselves apparent by changing the 
focus of the spectra or producing ghosts, respectively ; and if . 
such errors are large, render the grating totally unfit for exact 
measurement. Accidental errors, such as a flaw or break in the 
ruling, are also serious, but are easily detected and may be 
approximately corrected, as was done by Angstrém in the case 
of one of his gratings. Any marked and extensive irregulari- 
ties of spacing will produce bad definition or false lines, and in 
most cases both. If, then, a grating on microscopical examina- 
tions is free from flaws and on the spectrometer gives sharply 
defined spectra, alike in focus and free from ghosts, it is safe to 
conclude that it is tolerably free from the errors above men- 
tioned, but unfortunately there is one fault that does not at 
once become visible, while it introduces a very serious error in 
the measurements. This is a rather sudden change in the grat- 
ing space through a portion of the grating, usually at one end. 
Such an error is usually due to abnormal running of the screw 
when the dividing engine is first started, and may in this case 
be avoided by letting the engine run for some time before 
beginning to rule. Thus Grating I, ruled with this precaution, 
is nearly free from this error. Sometimes, however, it is the 
terminal or an intermediate portion of the grating that is thus 
affected in which case the error may be due to a change of tem- 
perature or to a fault in the screw. If an error of this kind is 
extensive, it will produce the effect of two contiguous gratings 
of different grating space, injuring the definition and widening 
or reduplicatiug the lines. When, however, the abnormal spac- 
ing is confined to a few hundred lines it produces no visible 
effect when the whole grating is used, but simply diffuses a 
small portion of the light and increases or decreases the average 
grating space. For it is evident that such a portion of the 
grating must possess little brilliancy and less resolving power, 
and the more its spacing differs from that of the rest of the 
grating, the less chance of visible effect and the greater error 
mtroduced. Such a fault is compatible with the sharpest 
