4T'_' Scientific Intelligence. 



between their roots and the observed frequencies of spectral lines, 

 or because they have been based on hypotheses and assumptions 

 which are apparently inadmissible. The present paper by E. T. 

 Whittakkr is, on the whole, free from these objections. 



The author begins by recapitulating the experimental evidence 

 which has led most spectroscopists to believe that band spectra 

 are due to vibrations of the molecules and not of smaller con- 

 stituents of the radiating matter. Attention is then called to the 

 fact that many properties of chemical substances are of the 

 "additive" kind. From this fact it may be inferred that atoms 

 retain in large degree their individuality when they are com- 

 bined with one another to form molecules, so that a molecule is 

 to be regarded not as a complete rearrangement of the electrons 

 or other elements of which its atoms are composed, but rather as 

 a system in which the atoms exist with comparatively little altera- 

 tion in their internal structure, but with mutual connections such 

 as may be expressed by additional terms or other modifications 

 in the dynamical equations. Therefore Whittaker builds up his 

 model from two constituent systems representing the two atoms 

 of a diatomic molecule. For mathematical simplicity he also 

 supposes the atoms to be alike, so that the molecule represented 

 is that of a chemical element. 



This dynamical model is next investigated according to the 

 well-established laws and processes of analytical mechanics, with 

 the result that a final equation is obtained which expresses the 

 frequencies of the possible vibrations of the diatomic system 

 explicitly in terms of suitable parameters, etc. This formula 

 presents a certain peculiarity, in that the frequency of vibration 

 occurs in it linearly, whereas in the equation for determining the 

 free periods of dynamical systems in general the frequency 

 enters by its square. In the course of the analysis the permissible 

 types of connection between the atoms in the molecule are 

 arranged in three classes, each of which is discussed at some 

 length. Whittaker shows that the gyroscopic type of connection 

 is the one which accords best of all with many of the chemical 

 and physical properties of atoms and molecules. Thus, all of the 

 assumptions underlying the mathematical analysis are very 

 plausible and are consistent with experience. 



When certain terms of the final formula are omitted, an equa- 

 tion results which is precisely of the same form as the empirical 

 formula for band spectra as discovered by Deslandres. Since the 

 laws of Deslandres, as embodied in his formula, are generally 

 looked upon only as first approximations to a more general law of 

 nature, Whittaker points out that the retention of the terms of 

 his equation will suffice to satisfy the more general case. Finally, 

 it is shown that a special set of legitimate assumptions leads to 

 Balmer's empirical formula for the series spectrum of hydrogen. — 

 Proc. Roy. Soc, vol. lxxxv, 262. h. s. u. 



