Structure of the Atom. 241 
The equations of motion of the pth corpuscle are 
Gry (dO,\"\ _—ive’ry ; 
222 TE ie as i +R, ; ° e (a) 


at 
PO, » dr de, | 
m( eS i “2)=9 es ary te) 
(os ve~ 
” iar = Ce ae Me Atlee Eee tae -(V) 
Retaining only the first powers of small quantities, we get 
dé . 
from these equations, if » is the value of when the motion 
dt 
1s steady, 
2 
| 
vera e 
— = maw" + —~ S, 



L* Aa? 
ot Pp 9 i ae Se e 
tae maw" = Pp (mo — FB ) +R, a 8. 
If pp, and @, vary as e'%, this equation may be written 
(A — mq?) pp + Arpp+1 t+ Aspprat... 
—2mawigdy + AByhy41 + aBohpiot+...=0, 
ar 4 pee psf F 
A= paStA’= 55 13(—= F +z +) 
S = a sin?= sin® — 
n n 
where 





Writing 1, 2, 3 for p we ue 
(A — mg*)p, + Apo + Asps... F An—1pa—2maaigd, + By, + aB.¢634+...=0 | 
(A—mg")p.+ Ayp3+ Aspst ......eee —2mawiqd, + 4B\$,+aB 6,4 ...=0 : 
(A—mq’)pn+ Aipit Aspst.......0. — 2mawigdn + aB,G,+ aBlg2+ ...=0 | 
By equation 8 we have 
2merg” of = a +...(C— mg’) dp—Cybp41— Cohpz2—-+ - =0. 
Writing 1, 2, 3 in succession for p we get 
2emeg" —B, 2 —B," wee = +(C—mg")b,—C,$2—- Cop3—...=0 | | 
C 
2umeoq = =p We + (C—mig ee Od, — C,4;—...=0 
a a "a igi 4 (B) 
| 2umeg —B," —B,@ 6 + (C—mgq?)g>— Cig, —Crdo—... =0 

