May 30, 1895] 



NATURE 



10; 



observed in the spectrum of thallium. But, nevertheless, 

 I think any one will agree that their numerical relation 

 is no chance coincidence. Let us now make a drawing of 

 these doublets to the scale of l/X. Evidently the twelve first 

 lines will gi\e the same picture as the twelve second lines. 

 Let us therefore, to simplify matters, only plot down the 

 twelve first lines. At first glance this docs not show any 

 remarkable regularity ; but if we drop the fourth and 

 sixth line, we can arrange the rest in two series, as is 

 shown in Fig. i, both rows resembling the series of lines 

 in the spectrum of hydrogen, which are so accurately 

 represented by Balmer's formula. Recurring now to the 

 general list of lines observed in the spectrum of thallium, 

 we find that all five lines of the first series are accom- 

 panied on their more refrangible side by strong and easily 

 reversed lines, while the lines of the second series are 

 single. Thus not only does the symmetry of the drawing 

 justify the separation of the lines into two series, but their 



that only four liries out of sixty do not show any signs of 

 a system according to which they are grouped. 



I have given this detailed account of the arc spectrum 

 of thallium only as an e.xample ; for I might describe 

 many more spectra that show a similar regularity in the 

 distribution of many of their lines. Hut there is another 

 interesting point. The distribution of lines in the spectra 

 of chemically related elements shows evident signs of a 

 common plan. I will, for instance, describe the series of 

 triplets in the spectra of magnesium, calcium, and 

 strontium. > 



The most prominent lines in the visible spectrum of 

 magnesium are the thi-ee green lines 5184, 5173, 5168 

 10-" cm. forming the group 6 in the solar spectrum. In 

 the ultra-violet, at least ten repetitions of this group have 

 been observed, two more being doubtful on account of 

 their weakness and nebulosity. The differences of wave- 

 numbers have been found to be the same in all the groups, 



appearance teaches us the same. We may e.xpect to find 

 that a formula similar to that of Balmer connects the lines 

 of each of these two series. Indeed, for suitable values 

 of A, B, C the wave-numbers may be calculated from the 

 formula, 



A-B«- = -C«-> 



A and B having nearly the same values for both series, 

 and n assuming the values 4, 5, 6, 7, 8 for the first, and 

 3, 4, 5, 6, 7 for the second series. One may state the 

 formula thus : if the wave-numbers be plotted as ordinates 

 to the abscissie i 3-, I 4-', i 5-', &c., the points form a 

 parabola. If we now go on substituting for n the subse- 

 quent whole numbers, we find that all these calrulated 

 wave-lengths really exist in the spectrum. But they are 

 weaker and weaker for higher values of n. Prof Kayser 

 and I have been able to observe the wave-lengths calculated 

 by the formula of the first series for n = 9, 10, 11, 12, 13, 

 14, 15, 16, and by the formula of the second for « = 8, 9, 

 10, 1 1, 12, 13, 14, 15. We searched for the second members 

 corresponding to these lines, but could not detect them, 

 owing to our plates not being sensitive enough for wave- 

 lengths as small as 2100. However, they have nearly all 

 been observed by Cornu. If we accept Cornu's wave- 

 lengths, we now have two seriesof doublets of equal width 

 in the scale of wave-numljers, and a drawing of them shows 

 a remarkable symmetry (Fig. 2). The drawing comprises 

 47 out of 60 lines that constitute the arc spectrum of 

 thallium, including Cornu's observations. Of the thirteen 

 Imes left, five are the strong lines, mentioned abo\e, that 

 accompany the fi\e first lines of the first series on their 

 more refrangiljle side. The distance between each line 

 and Its companion grows smaller as we advance to smaller 

 wave-lengths, the last distance being not more than 0-45 

 10-8 cm. It seems probable that the next lines also have 

 their companions, which, however, so closely coincide with 

 them that it has not been possible to separate them. So 

 there are only eight lines left, the positions of which do not 

 enter into the general plan of the spectrum. Among these 

 eight lines there are two douljlets of the same difference 

 of wave-numbers as all the other doublets. Both widen 

 asymmetrically--one towards the more refrangible side, 

 the other to the less refrangible side. Thus we may say 



as may be seen from the following list. The wave-lengths 

 have not been reduced to vacuo, because all three lines of 

 one group are so near one another that they would all be 

 changed by nearly the same amount, so that the differences 

 of wave-numbers would practically remain the same. 



5183-84 

 5172-87 

 5't>7-55 



3838-44 

 3832 '46 

 3829-51 



333683 

 3332 '28 

 33300S 



3097-06 



3093 '14 

 3091-1S 



2942-21 

 2938-67 

 2936-99 



2848-53 

 2S46-91 



2781-53 

 2778-36 

 2776-80 



2736-84 

 2733'8o 

 273235 

 2698-44 



2695 "53 

 2693-97 



2672-90 

 2669-84 

 2668-26 



2649-30 

 2646-6! 

 2645-22 



I, 'A 

 19290-7 



'933' '6 

 i935i'5 

 26052-2 

 26092-9 

 261 13-0 



29968-6 

 30009-5 

 30029-3 



32288-7 

 32329-6 

 32350'i 



33988-1 

 34029 o 

 34048-5 



35105-8 

 35 '25 -8 



3595" '4 

 359925 

 36012-7 



365385 

 36579' I 

 365985 



37058-4 

 37098-5 

 37"9-9 

 37412-6 

 37455'4 

 37477 -6 



37745'8 

 37784-2 

 37804-0 



4I-I 



20-2 



40-6 

 19-4 



40-1 



21-4 



42-8 



22-2 

 38-4 



19-8 



In the sixth triplet, the first line has not been observed. 

 There is a very strong line 2852-22 not far from where the 



NO. 1335, VOL. 52] 



