508 Dr. G. J. Stoney's Analysis of 



curve, viz. x = k(l— 4=z), 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 num- 

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

 fractions 1, 1/2, 1/3, &c, and for z the squares of these, viz. 

 1, '25, -l f , '0625, -04, •027 / , -02040816, -015625, -012345679, 

 •01, &c, or numbers proportional to them. 



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

 oscillation-frequency). It has hitherto been assumed that it 

 is only the positive values of n that need 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. Trans. B.D.S., vol. iv. p. 570), 



/27Ttt \ 



x = a cos ( —r— t), 

 W] / 



y=b$mi-j-tl 



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

 direction 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 (loc. cit.), the con- 

 stituents of which either occupy the same positions when 

 + n is changed into — n, or each simply exchanges 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 further on (p. 515) ; but in 

 either case the same two positions in the spectrum are occupied 

 by the constituents of the double line. There is, however, 

 one alteration 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 indicated in the case of that outlying- 

 pair of sodium-lines that have been supposed to be satellites. 

 While all other sodium-lines are more nebulous on the less 

 refrangible side, the constituents of this particular pair are 

 nebulous on the more refrangible side. We should therefore 



