ATOM. 465 



The values of the periodic times of the different types of vibration are 

 given by the roots of a certain equation, the form of which depends on the 

 nature of the connections of the system. In certain exceptionally simple cases, 

 as, for instance, in that of a uniform string stretched between two fixed points, 

 the roots of the equation are connected by simple arithmetical relations, and 

 if the internal structure of a molecule had an analogous kind of simplicity, we 

 might expect to find in the spectrum of the molecule a series of bright lines, 

 whose wave-lengths are in simple arithmetical ratios. 



But if we suppose the molecule to be constituted according to some dif- 

 ferent type, as, for instance, if it is an elastic sphere, or if it consists of a 

 finite number of atoms kept in their places by attractive and repulsive forces, 

 the roots of the equation will not be connected with each other by any simple 

 relations, but each may be made to vary independently of the others by a 

 suitable change of the connections of the system. Hence, we have no right to 

 expect any definite numerical relations among the wave-lengths of the bright 

 lines of a gas. 



The bright lines of the spectrum of an incandescent gas are therefore due 

 to the harmonic vibrations of the molecules of the gas during their free paths. 

 The only effect of the motion of the centre of mass of the molecule is to 

 alter the time of vibration of the light as received by a stationary observer. 

 When the molecule is coming towards the observer, each successive impulse 

 will have a shorter distance to travel before it reaches his eye, and therefore 

 the impulses will appear to succeed each other more rapidly than if the mole- 

 cule were at rest, and the contrary will be the case if the molecule is receding 

 from the observer. The bright line corresponding to the vibration will there- 

 fore be shifted in the spectrum towards the blue end when the molecule is 

 approaching, and towards the red end when it is receding from the observer. 

 By observations of the displacement of certain lines in the spectrum, Dr Huggins 

 and others have measured the rate of approach or of recession of certain stars 

 with respect to the earth, and Mr Lockyer has determined the rate of motion 

 of tornadoes in the sun. But Lord Rayleigh has pointed out that according 

 to the dynamical theory of gases the molecules are moving hither and thither 

 with so great velocity that, however narrow and sharply-defined any bright line 

 due to a single molecule may be, the displacement of the line towards the 

 blue by the approaching molecules, and towards the red by the receding mole- 

 cules, will produce a certain amount of widening and blurring of the line in 



VOL. IL 59 



