February 22, 1906] 



NA TURE 



\Q 



calculation can be carried fairly far, but it is found 

 that the spectral lines so deduced obey a law of dis- 

 tribution simpler than any that has yet been found 

 by experiment to characterise any substance. Although 

 atoms are usually assumed for physical calculations 

 to be spherical, such a shape apparently is not really 

 possessed by the atom of any substance; but by using 

 the result established in this case, a simple relation- 

 ship is shown to be necessary between the wave-lengths 

 of the spectral lines of two similar elements and their 

 atomic weights. If these two elements are conceived 

 as being built up of the same material, having the 

 same form, density, and elasticity, and only their 

 size different, the wave-lengths of corresponding 

 spectral lines of the two elements are shown to be 

 proportional to the cube roots of their atomic weights ; 

 given the lines of one of the elements, those of the 

 second element can be calculated from the equation 



s/W 



V w 7 ' 



where A and A.' are the corresponding wave-lengths, 

 W and W the atomic weights of the two elements. 

 rhe elements of the following groups are found to 

 obey this rule with a greater or less degree of 

 approximation : — 



(1) Zinc, cadmium, and mercurv. 



(2) Magnesium, calcium, barium, and strontium. 



(3) Silver, copper, and gold. 



As an illustration, the following series of lines of 

 magnesium and calcium may be given. The 

 arrangement and wave-lengths are those adopted by 

 Kayser and Runge. 



From the similarity of their spectra, the elements 

 in each of the foregoing groups appear to be similarly 

 constructed, and the probability of this is strengthened 

 by the analogy of their chemical properties. On the 

 other hand, chemical analogy does not necessarily 

 imply similarity of form in the elements, as is shown 

 in the case of the alkali metals (lithium, sodium, 

 potassium, rubidium, cassium) ; these elements, in 

 spite of their close chemical similarity, do not exhibit 

 the simple relationship connecting wave-length and 

 atomic weight found in the groups already named. 

 Either these elements may be considered as built up 

 of different kinds of matter, or if of the same material 

 as possessing different shapes. 



Assuming that matter is uniform, the shape of the 

 atom may be varied, and instead of the simple sphere 

 the case of an elongated ellipsoid of rotation, formed 

 by revolving an ellipse round its major axis, may be 

 considered. The mathematical theory shows that the 

 spectral lines of such a luminous ellipsoid depend on 



NO. 1895, VOL. 73] 



three numbers, and that therefore these lines will be 

 capable of arrangement in groups according to three 

 principles. These numbers are obtained as the roots 

 of certain transcendental equations, and are to be 

 calculated from the lengths of the axes of the ellipsoid, 

 its density and elasticity, a calculation, however, which 

 on account of its difficulty is hardly practicable. The 

 first of the three numbers determines a group of 

 corresponding lines, a so-called series; the different 

 possible values of the number determine a certain 

 sequence of such series. The second number deter- 

 mines in each series a subordinate group of lines, and 

 the third number a single definite line in each sub- 

 group. The manner in which this third number 

 enters into the calculation shows, moreover, that the 

 frequencies of the single lines in the subgroups will 

 exhibit among themselves constant differences, differ- 

 ences, that is, depending solely on the nature of the 

 given ellipsoid. A type of distribution of the spectral 

 lines is thus afforded bv the theory which corresponds 

 with the well known law of distribution established 

 by Rydberg and bv Kayser and Runge in the case 

 of the alkali metals. The atoms of these metals 

 (Li, Na, K, Cs, Rb) may therefore be considered as 

 elongated ellipsoids of rotation, the axial lengths 

 being fullv defined in the case of each element, and 

 different in the different elements. 



A flattened ellipsoid of rotation, the so-called 

 spheroid, is by calculation found also to give rise to 

 groups, series, and subgroups, but the law of constant 

 differences is not so generally applicable. The roots 

 of the transcendental equations are, in this case, 

 partly imaginary, so that several groups consist of 

 a single strong line, others of a limited number of 

 lines. Such a grouping is actually found in the i ase 

 of the metals gold, silver, and copper. Hydrogen is 

 also of this type, its atom probably consisting of a 

 thin, round plate, which is to be considered as the 

 limiting case of a flattened ellipsoid. 



In the more general type of ellipsoid, that with 

 three unequal axes, the wave-lengths of the spectral 

 lines also depend on three numbers, defined by certain 

 equations, but in this case the lines cannot be 

 arranged in series and groups, but range over the 

 whole spectrum. Only when the form of the ellipsoid 

 approximates to that of an ellipsoid of rotation will 

 a few series arise. Such a distribution appears to 

 obtain in the spectra of the alkaline earths (barium, 

 strontium, calcium, and magnesium), that is, with 

 elements lying intermediate in chemical behaviour 

 between the alkalies and ordinary metals ; the form 

 here approaches that of the elongated ellipsoid of 

 rotation. With zinc, cadmium, and mercury, the 

 form approximates to the flattened type of the rotation 

 ellipsoid. 



Perhaps the most striking consequence of the theory 

 is that which follows from an alteration in the shape 

 of one of the simple ellipsoids of rotation. Such a 

 solid can be imagined as being gradually strained 

 in such a way that it passes into the more general 

 ellipsoid with unequal axes. During such deform- 

 ation the spectral lines will gradually and continu- 

 ously change, and the mathematical theory predicates 

 that out of each single line eight others can arise. 

 It appears, indeed, that the Zeemann effect, or the 

 resolution of a single line into two or more other 

 lines under the influence of a magnetic field, is ex- 

 plicable on this hypothesis. It may be observed that 

 the normal triplet which should result according to 

 Zeemann 's simple theory does not, as a matter of fact, 

 occur by any means frequently, the arrangement oi 

 the resolved lines having been shown by recent work 

 to be of a more complex character than was originally 

 supposed. Such a complexity finds a simple explan- 

 ation in Prof, von Lindemann's theory of strain. 



