DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 401 



but they depend to a larger extent than (l) and (4) on the exactness of the limit. 

 This inexactness is, however, in general more than compensated by the largeness of 

 the quantities dealt with. Collateral relations also are capable of giving very exact 

 values, but always subject to uncertainty as to the actuality of the relations indicated 

 by the numerical coincidences. This is less apparent in the F series of tlir high 

 melting-point elements in Group III., where the relations are largely M.-ililishr<l by 

 analogy between the different elements involved. No. (5) is affected by the exactness 

 of the limit, and is only useful when the separation is taken between the first two 

 orders and it is a considerable multiple of A, as, for instance, 117A in Al. 



For the special purpose of obtaining as exact a value as possible of the ratio A/ir 3 it 

 will be better to exclude from consideration Na, Ga, He, Sc, 0, S, and Se. Na is 

 excluded on account of the uncertainty as to whether F. and P.'s interferometer 

 measures of the P (2) lines are to be taken as giving the value of v for the S and 

 D series, in which a somewhat larger value is indicated by observers using ordinary 

 methods. Ga is omitted on account of its poor spectroscopic data. He because its v, 

 although very accurately determined, is so small that slight errors are very large 

 proportionate ones. because v is small and the observations not so exact, and 

 Sc, S, and Se because their spectra have not been sufficiently discussed. There 

 remain 17 elements for consideration. In the following the case of each element is 

 considered first, with estimates of its possible error. Then using these possible errors 

 as probable errors, the most probable value of ^ is deduced by least squares. The 

 ratio S/w 2 is denoted by q. 



K. The observations determining v are very bad. The v adopted gives A = 

 D 12 (2) = 261A and gives A = 2932'27-130--364 W == 39'097-003, and is 

 about 1. The value of q from this is 361'944 '11. This is adopted with probable 



error = '1. 



Rb. The only source is from v , since there is no light from the 

 satellites are doubtful. The value in Table I. is 36r40'5G. 

 taken = 'GG. 



Cs. Table I. gives 361 74 "33. D n (2) is so close to 17A that 

 to adopt it. The observations seem to show that should 1* 

 denominator is subject also to an observation error of 228. 



the consequent value of q is 362'24 "30, but this value of ( makes the former 

 much less. The relation may be a coincidence, as it ought to be ne* 

 therefore be safer to take the first adopted value, 36174': 



Cu and Ag as in Table L, viz., 36r84f8, 361'81'2. 



Mg With =2,d v = -06, W == 24'362-002, ,, + * gives q = 



The actual first D line has been seen to be uncertain, and in any case A 2 u 

 that the actual multiple cannot be obtained. There is an order di: 

 between m = 2 and 3, but the observation errors, and those Jue to f, give A v 

 less exactness than from , + ,. Value therefore adopted, 3 



VOL. CCXIII. A. 



