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



amount to an entire space, an hypothesis quite secure in gra- 

 tings with spaces as large as those employed. It was thus pos- 

 sible to determine qnite accurately the variations in the grating 

 space throughout the whole grating. 



It should be noted that since these variations may be of 

 almost any kind and magnitude the errors produced by them 

 will not in general be eliminated by combining the results ob- 

 tained from several gratings. It may happen that the gratings 

 used by one experimenter will have errors that will counter- 

 balance each other, while those used by another will all have 

 errors of the same sign. For instance, by the merest accident 

 the gratings used by the writer gave nearly identical results 

 corrected and uncorrected, while those used by Peirce uniformly 

 required a reduction in the resulting wave-length. The num- 

 ber of gratings used by a given investigator is however so small 

 that the errors will very seldom be eliminated, while no com- 

 bination of the results obtained from different orders of the 

 same grating can produce any useful effect whatever. 



Each of the gratings used in this research was examined 

 minutely by the above methods and in each was found an ab- 

 normal portion of one sort or another. Of eight gratings which 

 I have calibrated all have shown a similar error and of more 

 than twenty which I have examined in the spectrometer only 

 one (grating III) failed to show an abnormal section at one end. 

 Since this is the commonest form of the error in question, it is 

 but natural to inquire why it cannot be avoided by covering 

 the defective end. . The reason is simple enough. By stopping 

 out the defective portion the grating is reduced to an incom- 

 mensurable length which enormously increases the difficulty of 

 measuring it. A grating which is in length some convenient 

 submultiple of a meter is easy to measure with a comparatively 

 high degree of exactness, but one which is, say, twenty seven 

 millimeters long, is exceedingly difficult to measure accurately 

 since it involves a long micrometer run or the errors of sub- 

 division down to single millimeters. It is therefore better to 

 use the full aperture of the grating and find A by calibration. 



In calibrating the gratings used, I divided I and II, which 

 were thirty millimeters long, into six sections of 5 mm , and the 

 large gratings III and IY into centimeters. Each grating was 

 carefully gone over five times and the mean result taken. The 

 following corrections were found. 



The actual variations found in each grating are given below, 

 the figures given being the difference of n lines from the dis- 

 tance between the stops, the lines being taken in the consecu- 

 tive sections of the gratings. 



