Wave-length of Light. 363 



of the results from different orders of spectra can possibly 

 eliminate the class of errors we are discussing, since the 

 algebraic sign of the error will be the same for all orders, and 

 it will be in every case a nearly constant fraction of the wave- 

 length. 



The problem before the experimenter is then the following: 

 To detect the existence and position of any abnormal portion 

 of the grating in use, to separate as far as possible such 

 portions as produce a visible effect from those which do not, 

 and thus finally to determine the proper value to be assigned 

 to the quantity A. 



The- investigation is somewhat simplified by the fact that, 

 for the most part, abnormal spacing occurs at an end of the 

 ruled surface, generally at the end where the ruling was 

 begun, since, when the engine is started, it is likely to run for 

 some little time before it settles down to a uniform state. 

 Then, too, one is able to disregard the slight and gradual 

 variations in the grating-space which appear in every grating, 

 since their effects will in general be integrated in the spectrum 

 produced. 



It only remains, therefore, to study those larger and more 

 sudden changes which can produce a sensible error in the 

 result. It is evident that the process of examination indicated 

 above will serve to detect the more extensive faults, together 

 with any errors of figure in the surface, but an abnormal 

 portion, consisting of only a few hundred lines, will not have 

 resolving power enough to produce a marked effect. Making 

 then a slit in a card just wide enough to expose a sufficient 

 number of lines to give tolerable definition, one can examine 

 the grating, section by section, and still further discriminate 

 between the normal and abnormal spacing, errors of figure 

 being included as before. But as the number of abnormal 

 spaces decreases, a point will be reached when this method 

 breaks down completely; and since the error in the resulting 

 wave-length may be as large in this case as when the fault is 

 more extended, another method must be sought. So far as I 

 know, the only method which will detect and evaluate all 

 these errors is that which I have called calibration, measuring 

 the relative lengths of n grating-spaces taken successively 

 along the ruled surface. The process employed was as 

 follows: The stops of the comparator were set as close to- 

 gether as practicable, limiting the run of the carriage to a 

 distance which varied in different cases from 4 to 10 millim. 

 Then the grating to be examined was brought under the 

 microscope, and micrometer-readings were taken on the lines 

 just within the run of the carriage; the grating was then 



