in the Atmospheres of certain Fixed Steers. 



201 



Let mi and 1113 be the micrometer readings on any two known lines, 

 ,, n> ■> ,, „ for an intermediate un- 



known line, 



„ Xi and A 3 the corresponding wave-lengths of the known lines, 

 then to find X 2 corresponding to m- 2 we have 



( [A a - A ] - [A, - A ] ) [A 3 ] = [A 2 - A ] (1), 



7/(3 — Till 



where the square brackets denote the logs of the included quantities. 



That the second differences of AX/ As for successive values of A, are 

 not strictly constant for the whole length of our spectrum is shown by 

 the -different values of el and A Q obtained above. 



If we assume A a constant =3718 and interpolate the wave-lengths 

 of A 2 and a 3 , by means of our formula (1) we obtain 



Known. ' Computed. Known — Computed. 



A, ;. 4425-52 4425-36 +0-16 



A 3 4282-54 4282-72 -0-18 



The differences " known - computed " considerably exceed the prob- 

 able errors due to the observations and the small inaccuracies of the 

 determinations of the fundamental wave-lengths, thus showing that 

 errors have been introduced by neglect of the small variations in the 

 second differences of the successive values of A Xj As. 



It is however very easy to take account of these variations by com- 

 puting an auxiliary table for different values of A with the argument 

 X h Thus, on the assumption that A varies proportionally to X 1 we 

 have : — 



Mg. 



A. A . 



4100 3732 



4200 3727 



4300 3722 



4400 3717 



4500 3712 



4600 3707 



Taking X from this table with the argument ' approximate wave- 

 length of the line, whose definitive wave-length is required,' we find 

 the intermediate wave-lengths accurately represented.* 



As well known iron lines are found within 30 or 40 tenth-metres of 

 all the unknown lines, it is always sufficient for the purpose of inter- 



* I find that the wave-lengths of solar lines as measured by Campbell (' A. P. 

 Journal.' October, 1898) are also very beautifully represented throughout by this 

 simple method of interpolation. 



