366 Mr. Louis Bell on the Absolute 



the form of the quantity A before mentioned, are very nearly 

 as follows : — 



Grating. A. 



I -0-10 



II +0-40 



III -2-00 



IV +0-45 



It should be distinctly understood that the corrections 

 deduced from the calibration are necessarily only approximate. 

 A very minute examination of a grating on the spectrometer 

 is impossible, since a small section of the ruled surface has 

 not sufficient resolving power to give measurable spectra. 

 On the other hand, while calibration gives the variations of 

 the grating-space with a high degree of exactness, it obviously 

 cannot definitely decide how far these variations are integrated 

 in the spectrum measured. Consequently, while calibration 

 will in every case give a valuable approximation, it must 

 necessarily leave residual errors. 



In these experiments the gratings were always measured 

 parallel to the terminations of the lines. Consequently the 

 length of each grating as found directly must be multiplied 

 by cos (90°— a), where a is the angle made by an individual 

 line with the line formed by the locus of the terminations. 

 In the case of gratings I., II., III., this angle was found by 

 measuring a test-plate as described in my previous paper, and 

 was found to be within a very few seconds of 89° 56'. 



Grating IV., ruled on the new engine, was tested by 

 measuring the sides and diagonals of the ruled surface, and 

 gave an almost exactly identical value of a. No correction, 

 therefore, need be introduced for this cause, since cos (90°— a) 

 does not differ sensibly from unity. 



Final Result for Absolute Wave-length. 

 Only one equation needs to be added to those already given 

 for S a 2 . This is the one for the third 5-centim. space, neces- 

 sary to determine the absolute length of the first 15 centim. 

 5-centim., (3) and (4) were compared, and the following 

 relation was found between them : (4) = (3) + O'M. The 

 relation found in 1885 was (4) = (3) + I'M. Consequently 

 (3) has not sensibly shortened, and nearly the whole change 

 found in S a 2 has taken place in the last five centimetres. 

 Writing now the absolute lengths of 



DiihS^ and 15-cm. S a 2 , 

 Dm^ 8 ^ 100-00666 millim. at 20°. 

 15-cm. S a 2 = 150-00897 „ at 20°. 



