Stoney — Analysis of the Spectrum of Sodium. 209 



its derived curve, viz. x = k [1- 4z), simplifies into fig. 2, in which, 

 as before, the horizontal lines represent the oscillation-frequencies 

 of the successive hydrogen rays. 



Hence the problem to be solved is reduced to the easier problem 

 of passing a parabola with its axis vertical through three given 

 points. 



For m we are to put in succession the positive whole numbers 

 1, 2, 3, 4, &c. ; that is for y we are to use the harmonic fractions 

 1, 1/2, 1/3, &c., and for s the squares of these, viz. 1, '25, '1', '0625, 

 •04, -027', -02040816, -015625, -012345679, -01, &c., or numbers 

 proportional to them. 



Some of these values may assign negative values to n (the oscil- 

 lation-frequency). It has hitherto been assumed that it is only the 

 positive values of n that need to be attended to ; that in fact the 

 negative values do not correspond to lines in the spectrum. This 

 seems to be a mistake : for the elliptic partial from which a line 

 arises being (see Stoney on double lines, Sc. Tr. E.D.S., Yol. lY., 

 p. 570), 



/2 TT « \ 



X = a cos — -. — t , 

 \ Ji J 



y = h sm[^ —T- ty 



the effect of changing the sign of n is simply to reverse the direc- 

 tion in which the electron travels round the ellipse. If the ellipse 

 maintains a fixed position, this partial produces a single line in the 

 spectrum, the position of which is the same whether n is positive 

 or negative. If the ellipse is subjected to an apsidal shift during 

 the flight of the molecule, the partial produces a double line in the 

 spectrum {Joe. cit.), the constituents of which either occupy the 

 same positions when + n is changed into - n, or each simply ex- 

 changes place with the other. Which of these will happen depends 

 on the direction of the apsidal motion, and on this we shall have 

 something more to say farther on (last paragraph on p. 216) ; but in 

 either case the same two positions in the spectrum are occupied by 

 the constituents of the double line. There is, however, one altera- 

 tion the lines must undergo when n changes sign, viz. that what 

 was before the more refrangible side of each line now becomes its 

 less refrangible side. Now, this accords with what we find to be 



