398 



Profs. Liveing and Dewar. 



[Xov. 27 r 



cordingly stop to point out in a general manner the course of the 

 single theory : and in connexion with it, but more briefly, that of the 

 double theory ; and I then, in the second and third parts respec- 

 tively, consider in detail the two theories separately : first, that of the 

 single functions, and then that of the double functions. The para- 

 graphs of the memoir are numbered consecutively. 



The definition adopted for the theta-functions differs somevrhat 

 from that which is ordinarily used. 



V. " On the Spectra of Sodium and Potassium.'" By G. D. 

 LlVEING, M.A., F.R.S., Professor of Chemistry, and J. 

 Dewar, M.A., F.R.S.. Jacksonian Professor, University of 

 Cambridge. Received November 20, 1879. 



In the course of our observations on the reversal of the spectra of 

 metals, we have many times had occasion to observe the spectra of 

 sodium and potassium, and have noticed that they have been imper- 

 fectly described. M. Lecoq de Boisbaudran describes them more com- 

 pletely than anyone else : but as seen in the electric arc in one of the 

 crucibles described by us in connexion with the reversals, there are in 

 each spectrum several additional lines, which make the whole far more- 

 regular and symmetrical than they appear in his account. These 

 additional lines are seen in the arc given by a battery of 25 Grove's 

 cells as well as in that given by a dynamo-electric machine. They 

 show best in a long arc, and as the vapours conduct well it is easy to 

 draw out the arc of 25 cells to the length of an inch or more. We 

 have generally used carbonates of the metals, sometimes chlorides. 



In the case of sodium we have already noticed ("Proc. Boy. Soc," 

 vol. xxviii, p. 473) that the pair of lines next more refrangible than D- 

 (which we may for convenience call the third group) are accompanied 

 by a fainter pair on their more refrangible side. Lecoq de Boisbaudran 

 notices one only of these faint lines. By micrometer measurements of 

 their distances from their brighter companions, we have deduced the 

 wave-lengths 5673*6, 5668*6, for this pair. A line closely correspond- 

 ing to the latter of these lines is to be found in Kirchhoff 's map of 

 the Solar Spectrum (1165*2). 



The next pair of lines, or fourth group (5155, 5152), are sharply 

 defined, and have no other line close to them ; but the brignt green 

 pair, or fifth group (4983, 4982), are diffuse lines, usually seen as a 

 band but noted by Lockyer to be a double line, and have a third 

 line on their more refrangible side, of which we find the wave- 

 length to be 4980*5. We feel sure that there ought to be a fourth 

 line in this group, but have never been able to detect it. It is 

 possible that two of the four lines may overlap, and so appear as one ; 



