Stone Y — Analysis of the Spectrum of Sodium. 211 



hyperbola, the derived curve (representing the relation between 

 n and z) is the part above the axis of w of a parabola such as that 

 represented in fig, 3, its equation being 



{a - nf = P {b + z) (5) 



in which n and z are the running co-ordinates, P, a, and b being 

 determined by the condition that the parabola shall pass through 

 three given points, suppose 



WiSx, ^2^25 W3S3. 



We easily find that this condition is fulfilled if 



Tl ^3 - ill 



2a = 

 b = 



(6) 



[Similarly, if the relation between n and y were such as to be re- 

 presented by an ellipse, the derived curve would have the equation 



{a + nf^P[b-z), (7) 



in which, as before, P, a and b can be determined so as to make 

 the curve pass through three given points]. 



The hyperbola of which equation (6) is the derived curve, is of 

 course [a - ny = P.{b + y''), {5a) 



and the ellipse corresponding to equation (7) is 



[a + ny = P{b- y') (7«) 



in which n and y are the running co-ordinates. 



These are equivalent to 



which give directly the relation between m and n, when for z we 

 use 1000 times the values on page 209. 



Application to Seuies P. 



Series P appears to be best represented by regarding the 

 least refrangible pair of the series — the great D lines of the solar 



SCIEN. PE.OC. R.U.S. VOL. VII. PART III. S 



