the Spectrum of Sodium. 



513 



If we regard this particular line as the first term of the 

 series, it will be found that the primary curve belonging to 

 the series closely approximates to an hyperbola. If we regard 

 that line as the second term, the curve approximates, but not 

 so closely, to an ellipse. We shall therefore adopt here the 

 former supposition. The values of m will then be as in the 

 following Table :— 



m. 



m- 



X— +/C 



(which is nearly the same 

 as ri), by observation. 



1 

 2 



3 

 4 

 5 

 6 



7 

 8 



1000-0 

 2500 

 1111' 

 62-5 

 40-0 

 27T 

 20-40816 

 15-625 



-176-2686 

 + 87-5500 

 +162 3935 

 + 194-1200 

 +210-5142 

 +220-0515 

 +226-1441 

 +230-2185 



The coordinates in the Table are coordinates of the derived 

 curve. It is approximately a parabola in the position of fig. 3. 

 Taking equation (5) as its equation, the constants are to be 

 determined by the condition that the parabola shall pass 

 through three of the observed points, suppose through 



^=1000, * 3 = 111-1', z 6 =27'7 r , 



^=-176-2686, ^=162-3935, ^=2200515. 



Using these values in equations (6), we find 



log P = 2-526,3843, 



a=434-0587, 



6 = 108-514, 



and computing the values of x, i. e. n, for the other terms, we 

 get:— 



