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



in which n and z are the running coordinates, P, a, and b 

 being determined by the condition that the parabola shall pass 

 through three given points, suppose 



n x z^ n 2 z 2 , n B z B . 



We easily find that this condition is fulfilled if 



Mo— n x 



P = 



n 9 — n. 



2a = F 



n 2 — ni 



+ n ± + n 2 , 



(6) 



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

 be represented by an ellipse, the derived curve would have 

 the equation 



(a + nf = Y(b-z), (7) 



in which, as before, P, a, and l> can be determined so as to 

 make the curve pass through three given points.] 



The hyperbola, of which equation (5) is the derived curve, 

 is of course 



(a-n) 2 =F.(b+f); (5a) 



and the ellipse corresponding to equation (7) is 



(a+n)*=F(b-f), (7a) 



in which n and y are the running coordinates. 

 These are equivalent to 



and 



(.-.^(fti^), .... (55) 

 (a W = p(5-^), • • • • < W > 



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

 we use 1000 times the values on page 508. 



Application to Series P. 



Series P appears to be best represented by regarding the 

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

 solar spectrum — as corresponding to m = 2. The values of 

 m for the other lines will then be as in the following Table: — 



