392 



NA TURE 



[February 22, 1906 



region " (p. 269). The ethnographical and zoological 

 references in the book show high expert knowledge, 

 but it may be noticed, perhaps with surprise, that on 

 pp. 297 and 298 he accepts the theory of the marine 

 origin of the fauna of Lake Tanganyika. 



The illustrations in the book are numerous and 

 excellent, and it is illustrated by two fine maps by 



has more fully developed an idea that he was first led 

 to enunciate in 18S8, after the publication of Lord 

 Kelvin's Baltimore lectures on molecular dvnamics. 

 Prof, von Lindemann's method consists, not in 

 deriving an empirical relationship between the wave- 

 lengths or frequencies of the spectral lines, but in 

 investigating mathematically the possible waves which 





Fig. 2.— In Ihe Libyan Desert. From " The Nile Unest.' 



Bartholomew, showing the orographic features, and 

 the characteristics of the surface and vegetation in 

 north-eastern Africa. J. YV. G. 



THE FORM OF THE ATOMS IN RELATION 

 TO THEIR SPECTRA. 



SINCE Balmer's important discovery in 1885 that 

 it is possible to calculate the wave-lengths of the 

 first nine lines of the hydrogen spectrum by means 

 of a simple formula, the existence of series of lilies, 

 obeying simple mathematical laws, has been estab- 

 lished in the case of the spectra of several other 

 elements, notably by the researches of Rydberg and 

 of Kayser and Runge. Among the various attempts 

 that have bei/i made to account for these series . 

 lines, and, in general, for the different spectra, the 

 most promising seems to be that of Prof. F. von 

 Lindemann, of Munich, who in some recent papers ' 



1 "Zur Theorie tier Spectrallinien," Sitznngsber. Math. phys. Class,;, 

 der Kgl. Bayer. Akad., 1901. xxxi., 441 ; 190?. xxxiii., ij \ a leciure, 

 printed in the SUddeutsche Monatshefte for September. 190s, 1 I whit h a 

 translation is published in the Monist for January of this year, contains a 

 popular summary of the earlier work and an outline of results not yet 

 published in detail. 



a hypothetical atom tan send out into the luminiferous 

 ether. 



His assumptions are the simplest possible. His 

 atom consists of a certain amount of elastic isotropic 

 matter of definite shape. The mathematical theory 

 of the different kinds of vibrations of which such a 

 body is capable is well understood, but the actual 

 working out for any special case is difficult because 

 it depends on functions which have to be discovered 

 for each shape, and are, generally speaking, new to 

 mathematicians. 'Ihe wave-lengths of each kind of 

 vibration sent out into the ether appear always as 

 roots of a transcendental equation involving those 

 functions. Such an equation has an infinite number 

 of roots, each when real corresponding to a definite 

 line. One equation thus corresponds with a " series 

 of lines. The theory gives for one body a number 

 of such equations, and therefore a number of such 

 "series" of lines, which together form the whole 

 spectrum. This agrees with observed facts. 



Prof, von Lindemann investigates, in the first paper 

 quoted, the case of a spherical atom, filled throughout 

 with matter of a definite density and elasticity. In 

 (his case, which is comparatively a simple one, the 



NO. 1895, YOL - 73] 



