Light by Cnsym metrical Atoms and Molecules. 401 



some specified type of atoms. The method of calculation will 

 depend upon whether we suppose that the electrons in the 

 undisturbed atom are describing circular orbits, or whether 

 they are in equilibrium under a complex type of force. We 

 shall begin with the first supposition, and consider the effect 

 produced by a small disturbing force X cos qt acting parallel 

 to x in the plane of the orbit, the orbit being described under 

 the action of a central force equal to prl (r 2 + d 2 ) 11 ; where 

 r is the distance from a point in the plane of the orbit, 

 and d a constant. If d vanishes, we have the law of the 

 inverse square; it is convenient, however, to take the more 

 general law, for we shall require it when we consider 

 molecules where there is more than one centre of positive 

 electricity. 



The orbits we shall consider are those which are approxi- 

 mately circular. Consider first the undisturbed orbits. The 

 circular orbit is represented by 



x = a cos (nt + e), y = a sin (nt ■+- e) , 



where 2 2 J9 » 



yu, = n 2 (a 2 + d 2 )K 



If the orbit is not circular, but only approximately so, and 

 if ;- = a + f, where f is a small quantity, we can easily show 

 that 





where 



D 2 = a 2 -f a 2 ; 



if jt? 2 = 4 — 3a 2 /D' 2 , we see that we may write 



r — a — ae cos \p(nt + e) — a)}, 



where e is small. 



The values of x and y for an orbit of this type are repre- 

 sented if 



<j>=nt+€, -f = (p-l)(nt + e)-G), x = (p 4- l)(n* + e) — o> 



by the expressions 



x = a cos <f) — ki ae cos ty + k 2 ae cos %, 



y = a sin <j> + k x ae sin yfr + k 2 ae sin ^, 



where 



,11,11 



Following the methods of the Planetary Theory, we shall 



