50 Proceedings of the Royal Irish Academy. 



multiples with small factoi-s of aliquot parts of the normal interval with 

 small denoniinatoi-s. Hence the gi'eat«r number of those lines may be 

 mentioned in support of the Kunge rule. The lines, A = 2888*93 and 

 X = 4oOS"27, seem in this respect doubtful. Fortunately the relations 

 between the inten'als in these two cases are evident, and make the choice of 

 factoi-s definite. These simple relationships and the facts that 1"13 and •251 

 can be represented by rational fractions of a, that the denominators of these 

 have ali-eady occurred, that in X = -ilSS'Sl the adoption of the aliquot part 



~ was thoroughly justified by the possibility of the accurate measurement 

 lo 



of the separations and the close agreement between observed and calculated 



values, and that here again the delations are very small, all show that these 



lines are not exceptions to the Eunge iiile. 



It is needless to examine these for e^'idence in favour of or against the 



Eitz law. Owing to the absolute fi-eedom in the choice of the values of the 



symbols in this rule, and the few values for components which have to 



be satisfied, it is at once evident that the obtaining of perfect agreement is 



very easy, and the law cannot be considered to have been tested by such 



examples. 



Tli^ follovAruf eighty-niiiie liiies have each four components. 



[Table Y, pp. 51, 52, 53.] 



With such a small number of components the difficulty of choosing the 

 niunbers under A is very great. If one takes into account the possible error, 

 the intervals might in many eases be classed as multiples of different aliquot 

 parts. The various aids to the proper selection have already been mentioned. 



One group of thi-ee lines has the same separations : 2733'34, 3071'69, 

 o791'35. These three lines possess aU the characteiistics necessary in a 

 series. They show the same Zeeman Effect, diminish in intensity in the 

 order from red to \dolet, and the difference between the fi-equencies ' of 

 consecutive membei-s decreases with diminishing wave-length. Four lines 

 are necessary to establish a series. With the aid of three the constants in 

 the series formula are fixed : and the f oiuth Hue serves for the necessary test. 

 Using the above three Hues constants were calculated ; but the tests gave 

 values to which no observed line in the spectrum gave a close enough 

 correspondence. Although the required fourth line would by the rule of 

 diminishing intensities Iw comparatively weak, still one woiild expect it to be 

 visible. Any Hues on the red side which might belong to the series appear 

 according to the calculations to lie bevond the limits of the observed 



