April 28, 1892] 



NATURE 



607 



Double Orange. 



The abnormality in a Maltese orange described in Nature 

 of April 7 (p. 534) would appear of common occurrence in the 

 Queensland or South Australian fruit. A friend assures me that 

 in a case recently received from Australia, 80 per cent, of 

 the contents showed small oranges, more or less perfect, either 

 embedded in the pulp or in the rind. The quality of the fruit 

 I observed was in no way affected. It would, however, be 

 interesting to obtain further testimony. Although the small 

 oranges may not affect the commercial value of the fruit, their 

 presence must be undesirable in the groves where perfection is 

 sought. Gerald B. Francis. 



Katrine, Surbiton. 



T' 



ON THE LINE SPECTRA OF THE ELEMENTS, 



HE distribution of the lines in the spectra of the 

 elements is by no means so irregular as it might seem 

 at first sight. Since Lecoq de Boisbaudran, in 1869, dis- 

 covered the general plan in the spectra of the alkali 

 metals, a number of interesting facts have been brought 

 to light, which will probably one of these days find their 

 mechanical explanation, and will then greatly advance our 

 knowledge of the molecules. 



Mechanical explanations of some of the facts have 

 been attempted already. Lecoq de Boisbaudran explains 

 the fact that the rays of the alkali metals are, on the whole, 

 less refrangible the greater the atomic weight, by observing 

 that the oscillations of a body suspended in a given 

 elastic medium will become less frequent when the mass 

 of the body is increased. This explanation, however, 

 seems to me to remain rather vague and unsatisfactory 

 as long as it does not lead to any numerical results that 

 agree with the observations. Taken literally, it makes 

 the oscillation-frequency inversely proportional to the 

 square root of the atomic weight, which is far from being 

 the case. 



A second well-established fact has received different 

 explanations by Julius ^ and by Johnstone Stoney.- It has 

 long been observed by Hartley that in the spectrum of 

 several elements a number of doublets or triplets of lines 

 appear, the oscillation-frequencies in each doublet or 

 triplet differing by the same amount. Recent measure- 

 ments by Prof. Kayser and myself have confirmed this 

 observation. Julius believes that this phenomenon is 

 due to a cause analogous to the combination tones in the 

 theory of sound. 



If two rays, with oscillation-frequencies a, 8, combine 

 with other rays, p, q, r, s, to oscillation-frequencies 



p + » 



'/ + 

 ? I- 



the same difference a - ^ will occur several times. That 

 the doublets under consideration are in many cases re- 

 markably strong is accounted for by the fact that the 

 intensity of the combination tone is proportional to the 

 product of the intensities of the primary tones, so that it 

 must become very strong when the amplitude of the 

 primary tones is sufficiently increased. 



Johnstone Stoney gives a different explanation of the 

 doublets. He supposes that the path of the molecule 

 from which light emanates is an ellipse, which by dis- 

 turbing forces is gradually changed, and he shows that 

 on this supposition, instead of one ray, two rays or more 

 would originate, and the oscillation-frequencies of these 

 rays would differ by an amount depending on the rate of 

 change of the ellipse. If now, instead of the ellipse, the 

 path of the molecule is any other curve, it can be con- 

 sidered as consisting of a number of superposed ellipses, 

 all of which change in the same way on account of the 

 disturbing forces. To each of the ellipses a doublet of 

 lines corresponds, and the oscillation-frequencies of each 



' Julius, Annates dc P Ecole Polytcchnique de Del/t, tome v. (1889). 

 ^ Stoney, Trans, of the Roy. Dublin Soc., voL iv. (1891). 



NO. TT74, VOL. 45] 



doublet differ by the same amount. In this explanation 

 I do not understand the decomposition of the arbitrary 

 curve in a series of superposed ellipses. For the move- 

 ment is supposed not to be periodical, and Fourier's 

 theorem then would not apply, at least the periods of the 

 superposed ellipses would not be definite, as long as there 

 are no data except the arbitrary curve itself. 



Besides, both Johnstone Stoney and Julius only try to 

 explain one of a number of regularities that have been 

 observed in the spectra of the elements. A plausible 

 suggestion about the movement of the molecules ought 

 to explain more than one of the observed phenomena. I 

 think it may be useful to point out the other regularities 

 that have been observed in the distribution of lines, and 

 for which as yet no mechanical explanation has been 

 attempted. 



(i) The doublets and triplets existing in the spectrum 

 of an element can be arranged in series which show an 

 appearance of great regularity. These series seem to be 

 analogous to the over-tones of a vibrating body. But 

 they possess a remarkable peculiarity, which, as far as I 

 know, is without analogy in the theory of sound. The 

 difference of two consecutive oscillation-frequencies de- 

 creases as these increase, and there seems to exist a 

 finite limit to the oscillation-frequencies of a series. If « 

 represents integer numbers, the oscillation-frequencies of 

 a series may with great accuracy be represented by the 

 formula — 



A - B«-2 - C«-*, 



where A, B, C are positive constants. B has nearly the 

 same value for all the series of the different spectra. A 

 is the limit towards which the oscillation-frequency tends, 

 when n increases. 



(2) For elements that are chemically related, the series 

 are distinctly homologous, both in appearance of the 

 lines and in the values of A, B, C, and with increasing 

 atomic weight shift towards the less refrangible end of 

 the spectrum. Homologous series have been observed in 

 the following groups of elements : — 



Lithium, sodium, potassium, rubidium, caesium ; 



Copper, silver ; 



Magnesium, calcium, strontium ; 



Zinc, cadmium, mercury ; 

 Aluminium, indium, thallium. 



In the first two and in the last group the series consist 

 of doublets,^ while in the remaining two groups they con- 

 sist of triplets. Thus we may say that the spectrum 

 shows a relationship between the elements similar to 

 that between their chemical properties. It is interesting 

 to note that magnesium forms a group with calcium and 

 strontium, and appears more nearly related to them than 

 to zinc, cadmium, and mercury. 



(3) The doublets and triplets in each group broaden as 

 the atomic weight increases. In the first group the 

 difference of oscillation-frequencies is nearly proportional 

 to the square of the atomic weight. The constant differ- 

 ence of the oscillation-frequencies in the doublets and 

 triplets may also be noted in the values of A, B, C. For 

 a series of doublets or triplets we have two or three 

 different values of A, but only one value of B and one 

 value of C. 



(4) In each of the spectra of sodium, potassium, rubi- 

 dium, and caesium, a series of doublets has been observed, 

 in which the oscillation-frequencies do not differ by a 

 constant amount, the difference diminishing inversely 

 proportional to «<. For these series A and B have only 

 one value each. The least refrangible doublet of the 

 series has the same difference of oscillation-frequencies 

 as the doublets in the other series of the same element. 

 In the spectrum of lithium there is a homologous series of 

 single lines. All the lines of these series have the same 



' Lithium has here to be excepted, whose lines are all single. 



