23 MR. W. DODGSON ON A 



This process is repeated for each of the four middle 

 groups, the mean points of an end group being determined 

 with the paper and centre C in the same positions as for 

 the second group from that end. 



A nearer approximation to the true position of the mean 

 points may then be found by making use of those already 

 obtained, to find more correctly the radius of the circle 

 through the three groups, and repeating the process of 

 measuring and plotting. 



In one case an isolated point occurs ; this is taken as one 

 group, and the curve drawn through it. 



The curve consists of arcs of circles which pass through 

 the six mean points, with radii varying from 645 inches at 

 the upper end, to 6i| inches at the lower end, drawn by 

 means of the rod A A, having a drawing-pin fixed to it. 



The wave-lengths corresponding to the scale-readings of 

 the observed lines in the tAvo spectra were then found by 

 measurement from the curve to -roVo of an inch, by means 

 of a lens and a scale of hundredths of an inch. 



The above method of graphically drawing a curve may 

 be extended to the case where the points are nearly uni- 

 formly distributed, and not divided into groups naturally 

 as in the case of air-lines. 



Divide the points into any number of groups, about an 

 equal number in each group. Find the [mean points as 

 described, by aid of lens and vernier scale on the rod; 

 draw the curve through the points by the best practical 

 method. The number of groups taken will be guided by 

 judgment, and will depend on what the degree of the proposed 

 curve shall be. The greater the number of groups, the 

 greater will be the degree of the equation to a curve 

 passing through their mean points, and the greater pro- 

 bably will be the irregularities in the variation of the radius 

 of curvature. 



