Calculation of Series in Spectra. 



565 



where A is the limit of the series, N is Rydberg's constant 

 109G79*2 *, /j is Rydberg's parameter, and m takes integral 

 values. If n l and n 2 are the wave numbers of two successive 

 lines, 



»*-% = * { ( ~^ )2 - (m+ \ + lt y } ■ 



Then 



Let 



x denote the value of (m + yu.) for the first line. 



^_„ 1=N j^__^_}, 



or 





N 



n 2 — n Y 



This is a biquadratic equation, from which, on the supposition 

 that the two lines are successive members of a series, the 

 value of x or m + fju for the first line can be obtained. The 

 next member is then 



n s 



="*+ N ((^-(^2)*) 



which can be calculated at once and compared with 

 observation. Mr. Savidge's Table gives the solution of this 

 biquadratic for values of « = N/(y> 2 — ?h) ranging from 1*5 

 to 80, and it is suitable for direct interpolation. 



Table I. a = 1-3 to a = 4-0. 



a. 



X. 



i * 



1 *■ 







a. 



i 



1 .v. 



OL. 



X. 







1-32 



0-9957 



170 



11091 



2-20 



1-2360 



315 



1-4341 



1-34 



1-0021 



1-72 



1-1146 



225 



T2477 



3-20 



1-4434 



1-36 



1-0085 



1-74 



1-1200 



2-30 



1-2592 



325 



1-4526 



1-38 



1-0148 



1-76 



11254 



2-35 



1-2705 



330 



1-4617 



1-40 



1-0211 



1-78 



11308 



2-40 



1-2817 



3-35 



1-4707 



1-42 



1-0273 



1-80 



11362 



2-45 



1-2927 



3-40 



1-4796 | 



1-44 



1-0335 



1-82 



1-1415 '< 



2 50 



1-3036 



345 



1-4885 



146 



1-0396 



1-84 



1-1467 



2-55 



1-3144 



3-50 



1-4973 



1-48 



10156 



1-86 



1-1520 



260 



1-3250 



355 



1-5060 



1-50 



10516 



1-88 



1-1572 



2*65 



1 3355 



3-60 



1-5146 



1-52 



10576 



1-90 



11623 



2-70 



1-3459 



365 



1-5231 



1-64 



10635 



1-92 



1*1675 



275 



1-3561 



370 



1-5316 



i-fie 



1-0693 



1-94 



M726 



2-80 



1-3662 



3-75 



1-5400 



1-58 



10752 



1-96 



1-1776 



2-85 



1-3762 ! 



3-80 



1-5483 



160 



1-0809 I 



1-98 



1-1827 



290 



1-3861 : 



385 



1-5565 



162 



1-0866 



2-00 



1-1877 



2-95 



1-3959 | 



390 



1-5647 



1-64 



1-0923 



2 05 



1-2000 



300 



1-4056 



3-95 



1-5728 



1-66 



1-0979 i 



2-10 



1-2122 ! 



3-05 



1-4152 



4 00 



1-5809 



1-68 



l 



1-1035 1 



2-15 



12242 



310 



1-4247 ■ 







Curtis, Roy. Soc. Proc. vol. xc. p. 605 (1914). 



