214 



Scientific Proceedings, Royal Dublin Society. 



Application to Series S. 



This is the most interesting of the series so far as the present 

 inquiry is concerned, because it is the series to which belongs the 

 outlying double line which has been supposed to be a satellite of 

 one of the terms of Series D. 



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 a 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 7n will then be as in the following Table : — 



The co-ordinates in the Table are co-ordinates 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 deter- 

 mined by the condition that the parabola shall pass through three of 

 the observed points, suppose through — 



%,= 1000-0 

 i»i = - 176-2686 



S3 =111-1' 



x^ = 162-3935 



ze = 27-r 

 xe = 220-0515. 



Using these values in equations (6), we find 



log P = 2-526,3843 

 a = 434-0587 

 b = 108-514, 



