202 Mr. G. Higgs. On the Geometrical Construction 



Now, from the equation to the parabola y 2 = px, the formu 

 X = V+ ia derived, where Y = the wave-length in 1/10 10 m. 



units of a point in the spectrum coinciding with the vertex of the 

 curve ; p, the latus rectum ; n, any number of units, reckoning from 

 the origin ; c, a constant. 



In practice a representation more suitable for lantern projection 

 being desirable, two units are taken on y for each line of the series ; 





the equation then becomes \ = V -{ j- , where L = 4p t and c 



has twice its former value. 



The computed places in the tables are derived from the equation in 

 the latter form ; the maximum want of agreement between these and 

 the observed positions not exceeding (for a and B) 0'015 tenth- 

 metre. 



In the case of A the agreement is not quite so close, the maximum 

 difference being about 0'05 tenth-metre. 



It might be supposed that the greater difference arose from uncer- 

 tainties of observation, caused by the greater haziness and breadth of 

 the lines composing the A group ; but it so happens that each com- 

 ponent is in itself so much of a double as to show a bright rift in the 

 centre, which facilitates the centralisation in some degree. 



The differences referred to are attributable to the fact that the 

 curve for any series in A, B, or a is not rigorously parabolic, but one 

 which cuts the parabola in three points, similar to the curve of sines, 

 cutting a straight line and terminating in the same phase as at the 

 origin. This difference is so extremely minute in B (and in a still 

 less) that it would require a representation more than 10 feet 

 square, or a good sized lantern screen, to show two separate tracings 

 at a point of maximum divergence, assuming the tracings to have but 

 a breadth of l/100th of an inch. 



Following the stronger doublets in the fluting or train of A on the 

 less refrangible side, is a secondary train of thinner, sharply denned, 

 doublets, which, with a solar altitude of about 10, may be traced on 

 the photographic prints to about the 12th position. This series, which 

 was not previously known to exist, conforms to the same formula, and 

 in the table of wave-lengths is denominated the " Secondary Train of 

 A." This secondary train follows in the wake of the right component 

 of the primary series. In the head, however, similar secondary 

 groups follow in the wake of both right and left components, over- 

 lapping and interlacing each other in such a manner that their 

 resolution into series can only be arrived at by deductive processes ; 

 the difficulty is increased by the fact that a large number of positions 

 are occupied by the dense lines of the main band. 



These two series will be referred to as " Sub-groups " in the head 



