Wave-length of Light. 369 



wave-lengths given by Miiller and Kempf. The probable 

 error of their wave-lengths is in general not less than one 

 part in two hundred thousand. That the value assigned by 

 them to the absolute wave-length is as near the truth as it 

 probably is, is not due to lack of faults in the gratings. Their 

 results for the line D x were as follows : — 



Grating. 



W.L. 



"2151" . . 



. . 5896-46 



" 5001 " . . 



. . 5896-14 



" 8001 " . . 



. . 5895-97 



" 8001 L " . . 



. . 5896-33 



A discussion of these errors as exemplified in the paper 

 under consideration would take up too much space to be in- 

 serted here, but one or two points are worthy of notice. 

 When a grating gives different results in the different orders, 

 it is evident that there are in it serious errors of ruling, and 

 the maximum amount of the variation will give a rough 

 estimate of their size as compared with those of other gratings. 

 Applying this test, the four gratings rank as follows : — 

 " 5001," " 8001 L," " 2151," " 8001," where the first, which 

 gave for the w.l. 5896" 14, had no sensible variation in the 

 different orders, and the last, which gave 5895*97, varied in 

 the most erratic fashion. It by no means follows, however, 

 that because a grating gives identical results in the various 

 orders, it is therefore free from errors of ruling. Witness 

 grating III. of this paper, in which the error was of a kind 

 which could not be detected at all in the spectrometer. Yet 

 it was large enough to give, if neglected, 5896 - 28 for the 

 wave-length of !){*. Speaking of errors in gratings, a case 

 in point is the work of Peirce. On account of the reasons 

 heretofore noted, Peirce's standards of length are somewhat 

 uncertain in value, so that from this cause no definite cor- 

 rection can be as yet applied to his wave-length. Three of his 

 gratings, however, I have calibrated, and each of them showed 

 an error tending to diminish the wave-length. If the mean 

 result obtained from these had been assumed to be correct, it 

 would have been equivalent to the introduction of a constant 

 error. Peirce's preliminary result is for this reason too large 

 by more than one part in a hundred thousand ; how much 

 more, it is impossible to say without knowing the results 



* The results given by the gratings used by the author, neglecting the 

 correction A, would be as follows : — 



I. 5896-20; II. 5896-14; III. 5896-28; IV. 5896-12. 

 Curiously enough the mean would be practically unchanged. 



