THE STRUCTURE OF THE SERIES OF LINE- AND BAND-SPECTRA. Oval 
the principal series we find that here also the denominator 15 plays an important part. 
Thus, considering the first components, the values of ¢ are for Li: 0°199, for Na: 
0°548, for K: 0°805, for Rb: 1°083, and for Cs: 1°328, hence very nearly 53, 7%, 13, 
“i8and 22. Except Li, the values of c and » form an arithmetic progression. For we 
notice that » is represented by the fractions— 3, s45, o%, 33%, 3%, the numerators of 
which are obtained from those of the quantities ¢ by subtracting 4. Such regularities 
eannot be accidental, although we must confess that at present it is impossible to 
assign a meaning to them. Nor are they confined to the group of elements here 
considered. Thus we may easily convince ourselves that, for instance, the four series 
of Oxygen mentioned before are represented by the equations : 
1. Triplet: (ve —v) =[4°95404 — 10][m? — (4)°] yo = 23212'5 
2. Triplet : = [4:95750 — 10][(m — 2)? - (4&)"] 23207°3 
1. Pair: = [4-96523 — 10][(m — 8)? + (48)'] 21201°7 
2. Pair: = [4°95587 — 10][m? - (,2,)°] 21212-7 
Similar conditions we find in three of the six Helium-series, viz., 
Ist P.S. : [vo —v] =[4'95884 - 10][(m— 3s)? +(,%)7] v2 = 38466°8 
Ist S.S. : = [4:95913 — 10][m?— (2,)°] 29931°6 
3d S.S. : = [4:95930 — 10][m? — (25)"] 27182°4 
whereas in the other three series the fractions contain the denominator 2 x 15, viz., 
2nd P.S. : [ve -v]  =[4:96161 — 10][m? + (.5)°] v2 = 320369 
Ond 8.8. : = [4:96066 — 10][(m — 28,)* - (s5)"] 29229-2 
4th S.S.: =[4-95943 - 10][(m — 4, )* - (s55)"] 27181-4 
The series of the three elements Mg, Ca and Sr, on the other hand, appear to be 
well represented by fractions with the denominator 14. 1 have found the following 
numerical equations : 
Mg st S$.S.: [ve—v] =[4:95105 - 10](m+-5,)(m — 58) va = 39781 
2nd 8.8. : =[4-94696 — 10](m+12)(m —-%) 39779 
Ca 1st SS: =[4-95797 - 10](m+18)(m - 3%) 34067 
Qnd 8.8. : = [4-94622 — 10](m + 24)(m — +4) 34005 
Sr 1st S.S.: = [4-93097 — 10](m+28)(m—42 31636 
2nd 8.8. : = [4:92352 - 10](m+32)(m— 31079 
All these regularities seem to me interesting enough to be mentioned in this dis- 
cussion, although [ admit that without a theoretical foundation they are perhaps of but 
little importance. Nevertheless the mere fact that the RypBeRG-THIELE equation is 
capable of showing so many interesting links between the series of different chemical 
elements, of which we see no traces in other formule, speaks highly in its favour, 
especially if considered in conjunction with the no longer doubtful property of this 
formula, that it satisfies the observations much better than other empirical equations 
hitherto proposed. But the chief importance of the RyppeRG-THIELE formula seems to 
me to lie in some other properties which we are now to discuss. 
