252 Mr. Louis Bell on the Absolute 



measurement that its use is preferable to the other interference 

 methods, which involve usually the exact determination of a 

 single very small linear quantity. The ingenious attempt of 

 M. de Lepinay* to avoid this difficulty is interesting theoreti- 

 cally, but practically it involves a quantity even more uncer- 

 tain than the average standard of length (the relation between 

 the kilogramme and the metre), to say nothing of the experi- 

 mental difficulties of the method. The angular measurements 

 of nearly all the later investigators have been quite good 

 enough to furnish very exact values of wave-length ; but in 

 every case it has been the measurement of the grating-space 

 that has produced the manifold errors and discrepancies in the 

 results. It has been the aim of the present research to inves- 

 tigate this fruitful source of errors, and, as far as possible, to 

 avoid the difficulties springing from it. 



In a previous paper f I briefly discussed the advantages of 

 transmission- and reflexion-gratings. It only remains to add 

 that further experience has convinced me that, not only are 

 speculum-metal gratings far superior in brilliancy and sharp- 

 ness of definition, but that it is possible, contrary to what one 

 might suppose from their large coefficient of expansion, to 

 rule them with almost perfect uniformity over a length as 

 great as a decimetre. This large size, too, gives a great ad- 

 vantage in determining the grating-space ; apart from the fact 

 that speculum-metal has a coefficient of expansion not widely 

 different from that of any one of the materials usually employed 

 for standards of length, and that its temperature can be ob- 

 tained with comparative ease. 



Methods and Instruments. 



The plane-grating can be used for wave-length measure- 

 ment in a variety of ways, according to the preference of the 

 investigator or the arrangement of the spectrometer. Five 

 tolerably distinct methods may be enumerated. The general 

 relation between the wave-length and the angles of incidence 

 and diffraction is 



\=s(smi-£ sin(</> — i*)) r ; 



where X is the wave-length, s the grating- space, i and cf> the 

 angles of incidence and diffraction respectively, and n the 

 order of the spectrum observed. Making i=0 6 , this at once 



* Joum. Phys. [2] v. p. 411. 



t Am. Joum. Sci. [8] xxxiii. p. 167; Phil. Mag. [5] xxiii. p. 260. 



