the Spectrum of Sodium. 



509 



be prepared for what we shall learn further on, viz. that this 

 pair of lines is due to a negative value of n. 



Before, however, we can draw the diagram for any of the 

 series of lines, we are confronted at the outset with a difficulty. 

 We have to settle what three points the curve is to pass 

 through. This depends on what the number m is for the 

 least refrangible line. It is 3 in the case of the hydrogen 

 series, but there seems no reason to conclude with Kayser 

 and Runge that it is 3 in other cases. A preliminary diagram 

 was made on millimetric paper to help in determining this 

 point. Each supposition as to the value of m in the least 

 refrangible line furnishes a distinct set of points corresponding 

 to the observed values of n for the terms of the series. It 

 was easy to draw curves through the several sets plotted 

 down in this way, and that set was preferred which most 

 nearly agrees with the supposition that an ellipse or hyperbola 

 takes the place of the parabola of the hydrogen series ; or 

 rather (since it was 



diagram of the derived 

 curves that was em- 

 ployed) that a parabola 

 with its axis vertical 

 takes the place of the 

 straight line of the 

 hydrogen series. This 

 may be seen by inspec- 

 tion in some cases. In 

 others it cannot be so 

 determined, and it was 

 necessary to have re- 

 course to the calculation 

 by which a parabola is 

 passed through three 

 of the points, and by 

 which the deviations of 

 the other points from 

 the parabola are com- 

 puted. The case in 

 which these deviations 

 selected. 



Fig-. 3. 



proved to be smallest is the one finally 



If the curve furnished by the relation between n and y is 

 an hyperbola, the derived curve (representing the relation 

 between n and z) is the part above the axis of n of a parabola 

 such as that represented in fig. 3, its equation being 



(a->i) 2 = F(b + z), . . 

 Phil. Mag. S. 5. Vol. 33. No. 205. June 1892. 



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2M 



