L.Bell — Absolute Wave-length of Light. 359 



braic 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 por- 

 tions 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 i*esult. 

 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 de- 

 tect 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 em- 

 ployed was as follows. The stops of the comparator were set 

 as close together as practicable, limiting the run of the car- 

 riage to a distance which varied in different cases from 4 to 10 mm . 

 Then the grating to be examined was brought under the micro- 

 scope and micrometer readings were taken on the lines just 

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

 along about the length of the run and the process repeated till 

 the whole grating had been gone over. The variations in the 

 micrometer readings then gave the variations in the length of 

 n spaces in different parts of the grating. The only assumption 

 involved was that the variation in the different sections did not 



