570 Stoney — Cause of Double Lines in Spectra. 



gradual, slow in comparison with the much more rapid motion of P in the dominant 

 orbit, which is going on at the same time. 



However complex the dominant orbit may be, it will be shown in Chapter IV. 

 that the motion of P in it is equivalent to the coexistence and superposition of a 

 number of " partials," each of which is a pendulous elliptic motion of P repre- 

 sented by — 



x=^a cos 6t, 



(1) 

 y = b sin 6i, ) 



a, b and 6 being constants which differ in the different partials. 6, which is the 

 angular velocity of the growing angle 6t, may also be called the stviftness of the elliptic 

 motion. It is the same as 277-w/;', where m is t\\e frequency of the elliptic revolutions 

 in a jot of time. The periodic time is, of course, j/m. The value of m must lie between 

 80 and 500, whenever the frequency of this elliptic motion is the same as that of any 

 undulation in the aether which can produce a line in the parts of the spectrum that 

 have been explored; and as in ordinary air each molecular joui-ney lasts oil the 

 average about 420 jots, there is time for a vast number — say from 35,000 to 

 210,000 — of the revolutions of the point P represented by equations (1) to take 

 place during one flight of the molecule. 



If the dominant orbit of P were the real orbit of P, each of its partials would 

 produce a single line in the spectrum. But it is not likely that the motion can go 

 on without its being affected by disturbing forces emanating from other parts of 

 the molecule, or from the fether in its neighbourhood ; and so many revolutions of 

 P take place during one of the flights of the molecule that there is abundant time 

 for the operation of these distm-bing forces. Now, the investigations that have 

 been made into the perturbations whicli occur within the solar system enable us to 

 predict at once what kinds of effects such disturbing forces would produce. They 

 are (1°) an apsidal motion of the elliptic partial in its own plane ; (2°) a processional 

 shifting of the line of nodes in which this plane intersects the " invariable plane"; 

 (3°) a periodic change in the inclination of these two planes ; (4°) a periodic change 

 of the ellipticity of the partial. All these may be regarded as perturbations of 

 relatively long period, but the conditions within the molecule may be such as to 

 occasion (5°) disturbances of shorter period affecting any one or more of the 

 foregoing, and producing an effect on them somewhat like that of nutation super- 

 imposed upon precession. We shall accordingly proceed to inquire how each of the 

 foregoing perturbations would manifest itself in the spectrum. 



The first problem of this inquiry only requires to be enunciated. It is — 



Problem I. — How will a simple elliptic motion of P in the molecules of the 

 gas, such as that represented by equations (1), manifest itself in the spectrum of the 

 gas? 



