Coincidences between the Lines of different Spectra. 3 



magnitude, and assumes the number of sources of error to be 

 practically infinite; as a result we should expect the curves 

 actually obtained to be steeper if anythiug than the theoretical 

 curve in the portion near the y-axis. 



It is obvious that the method can only be applied to spectra 

 which contain a considerable number of lines, and that 

 measurements of all the coincidences observed must be in- 

 cluded, otherwise the method will not give a correct result ; 

 it might under different circumstances cause us either to 

 underrate or overrate the probability in favour of the coinci- 

 dence. On the other hand, in dealing with the solar spectrum, 

 with the aid of Angstrom's map, it must be borne in mind 

 that the map is very incomplete, many lines being omitted ; 

 as a result we must not expect to find all the lines of any 

 substance in the map, even if these lines exist in the sun. 



We may illustrate the method by means of the curves 

 shown in figs. 1-5 (Plate I.). Fig. 1 is the Theoretical Curve 

 of Error; fig. 2 that actually obtained by comparing the values 

 of 21 lines in the arc-spectrum of iron, observed by Angstrom, 

 with their values obtained by Cornu ; fig. 3 is the curve ob- 

 tained on comparing KirchhofFs measurements of the spark- 

 spectrum of cerium (2? lmes) with those of Thalen. The 

 agreement in form between these curves is obvious, and, 

 considering the somewhat small number of lines included, 

 rather striking ; the greater steepness of the two latter curves 

 (owing to the finite number of sources of error) is also well 

 marked. Fig. 4 contains a comparison of the arc-spectra of iron 

 and nickel (19 lines) between wave-lengths 4850 and 5890; 

 and fig. 5 a comparison of those of iron and titanium (34 lines) 

 between the same limits. The divergence of these from fig. 1 

 is, as we should naturally expect, very marked ; so far as 

 any curves may be said to represent the results, the best 

 would be straight lines nearly parallel to the #-axis. 



Having given these instances as illustrations of the degree 

 of accuracy of the results to be obtained from the method, we 

 will proceed to examine its bearing on two problems of con- 

 siderable interest: (1) The existence of cerium in the sun; 

 (2) Professor Grunwald's recent investigations. 



Cerium in the Sun. 



The existence of cerium in the sun's reversing layer was 

 indicated as probable by Professors Liveing and Dewar* in 

 1882 ; and in the following year the same observersf pub- 



* Proc. Koy. Soc. xxxiii. p. 428, 1882 

 t Phil. Mag. [5] xvi. p. 401, 1883. 

 B2 



