Stoney — Cause of Double Lines in Spectra. 605 



a full symbolical representation of the resultant motion. If e,„ represents the 

 elliptic partial whose frequency is m, then the resultant motion may be concisely 

 represented by the symbolical equation 



Resultant motion = e^i + 6m2 + ^mz t &c., 



where the symbol t signifies " superposed upon." Now, of these several elliptic 

 components, we can obtain from the observations full details, except unfortunately 

 in at least two particulars. There is nothing in the spectrum which can reveal 

 to us the phases in which either they, or the apsidal motions by which they are 

 affected, are at any one instant of time : and these phases are essential to the com- 

 pleteness of the symbolical equation, which when written out in full would appear 

 as follows : — 



The position of the electron at the instant t 



is identical with 



the position of the point P at that instant in the pendulous elliptic 

 component whose frequency is wzi 



superposed upon 



its position at that instant in the pendulous elliptic component whose 



frequency is m^ 



superposed upon, 



&c., &c., &c. 



There are under the most favourable conditions at all events two unknown 

 constants in each term of the above symbolical equation, and under unfavour- 

 able conditions the number of unknown constants may be five — constants to the 

 value of which the appearances in the spectrum give us no clue. 



Under these circumstances the best course would appear to be to frame 

 hypotheses as to what the motion of the electron is, and to find whether we can 

 think of any motion which would have elliptic partials with the periodicities, 

 forms, relative amplitudes, and directions of motion which the observations 

 indicate, and which would retain their periodic times through a great range 

 of temperature. 



One naturally thinks first of the motion of an electron travelling without 

 friction along a prescribed path under the influence of a central attraction varying 

 directly as the distance. The curve to which it is trammelled being represented by 



the function F may evidently be such as to produce the observed series of lines ; 

 and if the dynamical conditions were such that F does not alter during the flight 

 of the molecule, k must diminish when energy is transferred to the surrounding 



