TRANSACTIONS OF SECTION A. 611 



supposition that the motion of each electron is an orbit of some kind going on 

 ■within the molecules, it can be shown that the partials of the motion of the electron 

 •which causes the lines are elliptic partials, and that where an elliptic partial suffers 

 an apsidal perturbation, it divides into two circular sub-partials, giving rise to the 

 two constituents of a double line. We may infer from this that the sub-partials 

 correspondiug to the red constituents of the fourteen or more double lines of the 

 train of B are circular motions revolving one way, and that all the violet consti- 

 tuents of these double lines result from circular motions revolving the other way. 



In order to advance beyond this point it is necessary to make two further 

 hypotheses which probably are both true. Two hypotheses must here be ventured 

 upon because observations with the spectroscope give us no information as to the 

 phases of the elliptic partials or the planes in which they lie. One hypothesis that 

 recommends itself is that the circular sub-partials belonging to a connected series 

 of double lines, e.g., to the train of the great B group, lie in one plane. Another 

 hypothesis which we may venture to make, as a preliminary working hypothesis, is 

 that the amplitude of the motion of the electron has its maximum value at starting, 

 i.e., when that event has occurred at the close of a struggle between two molecules 

 which has set up the motion of the electron, which continues during the compara- 

 tive repose of the quiet, undisturbed journey in which the molecule is indulged 

 after its encounter. 



With these assumptions it is possible to synthesise all the motions causing the 

 red constituents of the double lines into one motion, which is, however, not circular, 

 but a slowly contracting spiral; and a similar resultant spiral motion turning the 

 opposite way is furnished bj' the sub-partials forming the violet constituents. 

 While these spirals are being traversed the radii or semi-amplitudes of the circular 

 motions of which they are composed, and which correspond to the individual line? 

 in the spectrum, may become shorter or longer owing to the escape of energy to 

 the aether, or absorption of energy from it ; so that the actual orbits are spirals which 

 maybe somewhat inside or somewhat outside those which result from the assump- 

 tion that the radii retain their length. These two spiral motions combine at each 

 instant into a .^single elliptic motion so elongated that it is nearly a linear vibration ; 

 and this elliptic motion continues to represent what occurs, if subjected to the f.ve 

 following perturbations : — 



1. A decrease of amplitude. 



2. A diminution of periodic time. 



3. A slow apsidal motion in a direction opposite to that in which the revolution 

 of the electron in the orbit takes place. 



4. A slight fluttering motion which may be represented by a very shallow wave 

 running rapidly round the ellipse. 



5. A further slight modification of the form of the ellipse which takes the form 

 of a secular perturbation. 



Accordingly we arrive at the conclusion that an elliptic motion undergoing these 

 perturbations is such a motion of an electron as would produce the entire series of 

 lines in the train of B. A similar motion would produce the train of A, of a, and 

 of each of the other similar groups, if such exist in the spectrum of oxygen. These 

 elliptic motions undergoing perturbations may be appropriately called mega-partials 

 in their relation to the actual orbit described in o.xygen by the electron that 

 produces all these trains of lines, since that orbit is the resultant which we should 

 get by superposing the motions in these few mega-partials. 



A similar treatment applied to ' the head ' of any of the oxygen groups shows 

 that it, too, arises from an elliptic motion subject to perturbations, the chief 

 differences being in the law connecting the falling-off of amplitude and the 

 periodic time ; that the quick, fluttering perturbation is absent ; and that the apsidal 

 motion takes place in the opposite direction. In oxygen the strength of the lines 

 of each sub-group fades out towards the red. When the fading is in this direction, 

 the periodic time decreases as the amplitude falls off. Whereas when, as in the 

 carbon spectrum, the lines fade out towards the violet, the periodic time becomes 

 longer as. the amplitude decreases. And, finally, if the lines present themselves, 



E R 2 



