210 



Scientific Proceedings, Royal Dublin Society. 



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 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 Eunge 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 hydro- 

 gen series ; or rather (since it 

 was a diagram of the derived 

 curves that was employed) that 

 a parabola with its axis ver- 

 tical takes the place of the 

 straight line of the hydrogen 

 series. This may be seen by 

 inspection in some cases. In 

 others it cannot be so deter- 

 mined, and it was necessary 

 to have recourse to the calcu- 

 lation by which a parabola is 

 passed through three of the 

 points, and by which the de- 

 viations of the other points 

 from the parabola are com- 

 puted. The case in which these deviations proved to be smallest 

 is the one finally selected. 



If the curve furnished by the relation between n and ^ is a 



Fig. 3. 



