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



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 impos- 

 sible, 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 valu- 

 able approximation, it must necessarily leave residual errors. 



In these experiments the gratings were always measured par- 

 allel 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 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 IY ruled on the new engine was tested by measur- 

 ing the sides and diagonals of the ruled surface and gave an al- 

 most 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 Wcwe-length. 



Only one equation needs to be added to those already given 

 for S%. This is the one for the third 5 om space, necessary to de- 

 termine the absolute length of the first 15 cm . 5 Cm , (3) and (4) 

 were compared and the following relation was found between 

 them : (4) = (3) + 0^-4. The relation found in 1885 was 

 (4) = (3) + l / "*l. Consequently (3) has not sensibly shortened and 

 nearly the whole change found in S% has taken place in the 

 last five centimeters. Writing now the absolute lengths of 



Dnij S\ and 15cm. S%, 



Dm, S% = 100-00666 mm at 20°. 

 15cm S%=1 50-00897 at 20°. 



Applying now the relations found for grating I in the fore- 

 going section, 



s = 0'002500226 mm 

 And since <p = 45° 1' 48"-24 



i. = 5896-18 



Similarly for grating II, 



s = 0-003519041 mm 

 q> = 42° 4' 59""28 

 * = 5896-23 



