178 Prof. W. Gibbs on the Measurement of Wave-lengths 



o 



successfully accomplished by Angstrom* ; but an attentive study 

 of his work, as well as of the elaborate researches of Van der 

 Willigenf and Ditscheiner J, will show that new measurements 

 will be far from superfluous. The imperfections even of the 

 best ruled glasses are so great that it may be reasonably doubted 

 whether the wave-lengths of very fine lines can be satisfactorily 

 measured directly. Methods of determining such wave-lengths, 

 depending upon the comparison of the refraction- and diffrac- 

 tion-spectra, have been given by myself § and by Thalen||. As 

 it seems at least desirable to multiply such methods, I will here 

 give first a discussion of the method of Stokes in its original 

 form, and afterwards a simplification of that method, which will 

 also have its uses. 



If Cauchy's formula for dispersion, 



b , c 



be reduced to its first two terms, and if we then eliminate the 

 constants a and b from three of the equations of the form 



b 



we shall obtain the three following equations, involving only 

 wave-lengths and indices of refraction : — 



K= fr*~ Wa) l , ..... (i) 





X- f^lhl (2) 



X* = ^ZZii (3) 



fog — ^i) 

 1 



fo3- w l)^+ (V^s)^ 



Of these equations (1) and (3) serve for extrapolation and (2) 

 for interpolation. To test the degree of accuracy attainable in 

 determining wave-lengths by these formulae, I have selected the 

 measurements made by Van der Willigenf. The indices of 

 refraction determined by the Dutch physicist are in fact the only 



* Recherches sur le Spectre Solaire. Berlin, 1869. 

 t Archives du Musee Teyler, vol. i. p. 1. 



X Sitzungsberichte der k, k. Akad. der Wissenschaften, vol. i. (1864). 

 § Silliman's American Journal, vol. xlvii. March 1869. 

 || Memoire sur la determination des longueurs d'onde des raies metalliques, 

 1868. 

 % Archives du Musee Teyler, vol. i. p. 70. 



