Stoney — Cause of Double Lines in Spectra. 591 



and (^s) or equations (^5) and {e^) will determine q and r, and the determinations 

 in wMchever way made are identical. Hence k, p, q, and r become known, and 

 equations {d) enable us from them to determine a, b, a and /3. 



Hence, the form (a, b), the phase (a + e), and the position (/3, y, a), of the 

 elliptic motion, can be determined in terms of u, v, M, iV, and e, of equations (^4) ; 

 and thus, through them, the elliptic motion is completely determined in terms of 

 the coefficients A, A', B, B', C, C and 6, of one of the vertical columns of equa- 

 tions («2)- We accordingly arrive at the conclusion that — 



Theorem B. — Any motion of a point in space may be regarded as the 

 coexistence and superposition of one definite set of partials which are 

 the pendulous elliptic motions determined as above from the several 

 vertical columns of equations {a^). 



These partials will, in general, lie in different planes, and be in different phases. 

 The periodic time of each will be the periodic time of that vertical column of equa- 

 tions (^2) from which it is derived. Seven constants are associated with each 

 partial — of these, a, b, and 6 give the ellipse and the swiftness of motion in it, 7 and 

 CO give the jDosition of its plane, /3 gives its position in that plane, and finally {a+ e) 

 gives the position in the ellipse at which P was at the instant ^ = 0. 



Before proceeding further it may be well to refer again to an objection that 

 is likely to be felt. It may at first sight seem very improbable that within a 

 molecule there can be parts of it moving so freely as to describe definite orbits that 

 suffer steady perturbation. But we must remember, as was pointed out on p. 564, 

 that in dealing with the internal motions of molecules we have reached a stage 

 where there is no longer ani/ degradation of motions such as that effected by 

 friction or viscosity — in fact where the motions, whatever they are that occur in a 

 molecule during its flights, are performed without loss of energy other than that 

 communicated to the aether — with no loss ivhatever arising from the dynamical relations 

 of the parts of the molecule to one another. 



The only alternative hypothesis is that the molecules are rigid. Here we 

 might have a rotation, and if the three principal moments of gyration were unequal 

 we should have the instantaneous axis describing an elliptic cone, and so supplying 

 the condition for double lines. But, nevertheless, the hypothesis is inadmissible, 

 as it would necessitate a constancy in the rotation which is inconsistent with the 

 varying brightness of the spectrum at different temperatures, and which indeed 

 independently of this could not survive the collisions that are going on, as is 

 evident from dynamical considerations. We may therefore adhere with confidence 

 to the hypothesis made in this Memoir, that there are relative motions going on 

 within the molecules which are unimpeded except by the aether. 



