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U n s y m m e t r ic a l C o m p o n e n t s i n t h e S t a r k J E ]e ct.

943

I t i s v e r y u n f o r t u n a t e t h a t ti m e d i d n o t p e r m i t o f f u r t h e r

e x p e r i m e n t s w i t h a w i d e r v a r i e t y o f e l e m e n t s a n d w i t h

d e v i c e s f o r t h e d e t e c t i o n o f r a d ia t i o n o f o t h e r k i n ds . T h e

i m p o r t a n c e o f a c o m p l e t e i n v e s t i g a t i o n a r is e s f r o m t h e f a c t

t h a t t h e t r a c i n g o f t h e s u b s e q u e n t h is t o r y o f th e a to m i c

n u c l e u s w h i c h h a s b e e n d i s r u p t e d b y th e c o ll is io n o f a n

~ - p a r t i cl e i s, a t p r e s e n t , o n e o f o u r f e w p a t h s t o a k n o w l e d g e

o f th e f o r c e s w i t h i n t h e n u c l e u s .

I n c o n cl u si o n, I w i s h t o t h a n k S i r E r n e s t R u t h e r f o r d f o r

g i v i n g m e t h i s v e r y i n t e r e s t i n g p r o b l e m ; a n d M r . B i e l e r f o r

h i s a s s i s t ance du r ing obse rva t ions .

Cavendish Lab oratory,

Cam bridge, 1921.

C . O n t h e A p p e a r a n c e o f U n s y m m e t ri c a l C o m p o n e n t s i n t he

S t a r k ~ f f e c t . B y A . lV[. ]~/[OSHARRAFA,B . S e . •

§ 1 . P r e l i m i n a r y .

H E t h e o r y o f s p e c t r a l li n es w h i c h h a s h i t h e r to p r o v e d

m o s t s u c c e s s f u l i n i n t e r p r e t i n g t h e r e s u l t s o f e x p e r i -

m e n t is b a s e d u p o n c e r t a i n a s s u m p t i o n s o f a q u a n t u m t y p e

i n t r o d u c e d b y B o h r t , S o m m e r fe l d $ , a n d o th e rs . S u c h

a s s u m p t i o n s a r e o n l y j u s t if i a b le in s o f a r a s t h e y g i v e

sa ti s [' ac to ry in te rp r e ta t ion s o f co r re la ted ph enom ena . The

e f fec t o f an e lec t r i c f ie ld upon spec t ra l l ine s em i t t ed by

s t~bstances su bje c te d to the f ie ld was f i rs t inv es t ig a ted

by J . S t a r k § in 9 3; a n d a n a p p r o x i m a t e t h e o r y w a s

f u r n i s h e d b y K . S c h w a r z s c h i l d [] a n d b y P . E p s t e i n ¶ i n d e -

p e n d e n t l y in 1 9 1 6 : t h e t w o t h e o r ie s a r e s i m i l a r a n d g i v e

s a t i s f a c t o r y e x p i a n a t io n s o f t h e p h e n o m e n o n a s i n v e s t ig a t e d

b y S t a r k . N o w , a c c o r d i n g t o th e ir t h e o r~ l , t h e c o m p o ~ e n t s

i n t o w h i c h a n y g i v e n s p e c t r a l l i n e i s s p l t u p a r e s . g m m e t r i c a l l y

d i s t r ib u ted abou t t he or ig ina l p os i t i on o /' t he l i ne . I n t h e

* Com municated by D r. J. W . Nicholson, F.R .S.

t See e . g . N . Bohr~ Con stitution o f A tom s and )Ioleeules, Phil.

M ag. Ju ly 1913.

I See Arno ld Sommerfeld~ Atom bau und Spektrallinien,' II. A uf.

(192l):

§ Berliner 8itz~ngsber.~ November 1913; Ann. d. Phys. x]iii, p. 983

(1914).

'.l K. Sehw arzschild, Z u r Q uanten theorie, JBerliner Sitzungsber.,

April 1916.

¶ P. S. Epstein, Zu r Theorio des Starkoffektes, Ann. d. Phys. 1.

p. 489 0916).

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9 4 4 M r . A . M . ~ o s h a r r a f a o n t h e A p p e a r a n c e o f

p r e s e n t p a p e r a c l o s er a p p r o x i m a t i o n is w o r k e d o u t , a n d i t

i s f oun d Esee § 4 ] t ha t f o r s t r on ge r f ie l ds t han t hose used by

S t a r k t h i s s y m m e t r y n o l o n g e r fo l lo w s f r o m t h e t h e o r y : o u

the o the r hand , a pa i r o f com po nen t s wh ich , f o r f ie lds com-

p a r a b l e w i t h th o s e t h a t S t a r k u s e d * , a p p e a r s y m m e t r i c a l l y

s i t ua t ed , w ou ld fo r s t r on ge r f ie lds be d isp l aced

i n t h e s a m e

direct ion

so t ha t the sy m m et ry i s des t roy ed , W e , natu r.~ ll y ,

a l so f i nd t ha t t he r e l a ti on be tw een t he s t r en g th o f t he f ie ld

and t he d i sp l acem en t s o f t he l ine s i s no l ong e r r ep re se n t ed

g r a p h i c a l l y b y s t r a ig h t l in e s , b u t b y p a r a b o li c c u r v e s w h o s e

curv a tu r e s chan ge s i gn wi th t he d i sp l acem en t s (i. e . d i sp l ace -

m e n t s o f o p p o s i te s i g n s c o r r e s p o n d t o p a r a b o l a s o f o p p o s i t e

c u r v a t u r e s ) .

I t a p p e a r s t o t h e p r e s e n t w r i te r t h a t a n e x p e r i m e n t a l

i nve s t i ga t i on o f t he S t a rk e f f ec t f o r fi el ds s t r onge r t han

t h o s e th a t h a v e a l r e a d y b e e n e m p l o y e d b y S t a r k i s h i g h l y

d e s i ra b l e a s a f u r t h e r t e s t o f t h e f u n d a m e n t a l h y p o t h e s e s o f

t h e q u a n t u m t h e o r y o f s p e c t r a : i f s u c h a n in v e s t i g a ti o n r e s u l t

i n t he ve r i f ica t i on o f t he p r ed i c t i ons a l r ea dy r e f e r r ed t o , t hen

t h i s w i l l a d d t o o u r f a i t h i n t h e f o u n d a t i o n s o f t h e q u a n t u m

t h e o r y o f s p e c t ra l l i n e s : w h e r e a s a n e g a t i v e e x p e r i m e n t a l

r e su l t wo t~ ld , un l e s s t he ana lys i s he r e p r e sen t ed be a t fau l t ,

l e ad us t o a r econs ide ra t i on o f ou r a s sumpt ions , and pe rhaps

to ce r t a i n mod i f i ca t i ons t he r eo f .

§ 2 . _Previous W or k.

T h e e q u a t io n s r e s t r i c t in g t h e m o t i o n o f a n e l e ct ro n m o v i n g

un de r t he i n f l uence o f an a t t r ac t i on t ow ards a nuc l eus a s w e l l

a s a fi x e d f o r c e F c a n b e w r i t te n i n t h e f o r m

w here I t i s P l a nc k s qua n tum of ac t i on , n l ~2 n~ a r e who le

num ber s , m~ i s t he mass o f t he e l ec t ron , and f l (~ : ) f 20 / ) a r e

g i v e n b y

f~ (f) = 2 ( e E + B ) + 2 W ~ - e F E 4 - ~ ;,

m ; ° I

f ~ ( . ~ ) - 2 ( e E - f l) 4- 2 W n + e F ~ 4 - - v -~ ,j

* Fo r the H lines, e. g. Stark used a field of abou t 28,500 volt × cm. -1

(= 9 5 c.o.s..electrostatie un its). W e find that a field of about 10 times

this streng th w ould give quite m easurab le effects.

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U n s y m m e t r i c a l C o m p o n e n t s in , t il e S t a r k E f f e c t. 945

H e r e ( - - e ) is t h e c h a r g e o n t h e e le c t r o n , E t h a t o n t h e

n u c l e u s , a n d a , / 3 , W a r e c o n s ta n t s a r i s i n g f r o m t h e i n t e -

g r a t i o n o f t h e J a c o b i a n D i f f e re n t i al E q u a t i o n *. W r e p r e s e n t s

t h e e n e r g y o f t h e e le c t r o n . T h e c o o r d i n a t e s $ a n d • a r e

p a r a b o l i c c o o r d i n a t e s i n a c c o r d a n c e w i t h t h e e q u a t i o n

~ + i ~ = - ~ ~ + i , ) ~ , . . . . . 3 )

w h e r e x , y , z a re C a r t e s i a n c o o r d i n a t e s a t t h e n u c l e u s , 0 m

being chosen par a l le l to the ex terna l f i e ld

F . T h e l i m i t s o f

i n t e g r a t i o n f o r t h e t w o f ir st i n t e g r a l s i n ( 1 ) a r e th e m a x i m a

a n d m i n i m a o f ~: a n d ~/ r e s p e c t i v e l y . N o w t h e s e t w o

i n t e g r a l s a r e b o t h o f t h e s a m e f o r m ; s o t h a t w e c a n w r i t e :

j o I * +

V r ~ D r dr---- 2n h, . (4)

t h u s d e n o t i n g t h e t w o c a s e s f o r ~: a n d ~/ b y t h e s u ff ix e s 1

a n d 2 r e s p e c t i v e l y w e h a v e

- i : d q ,

,=2mow, ~ , = . , o ( e E + ) , C , = \2~ / Sa)

D I = - - m o e F ;

/ n 3 h \ 2 l

A ~ = 2m 0 W , B , = m o ( e E - - # ) , C , = - - [ ~ ) , ~ (5 b)

D~ = moeF .

N o w S o m m e r f e l d t w o r k s o u t t h e v t il ue o f t h e c o n t o u r

i n t e g r a l o n t h e l e f t - h a n d s i d e. T h e v a l u e h e g i v e s is

f

B ~ D k - A ( 3 B ~ - c )

0 )

F r o m (4 ) a n d (6 ) w e c a n w r i t e ,

D ( 7 )

- - -

B o t h S o m m e r f e ld a n d E p s t e i n h a v e o b t a i n e d t h e v a l u e

o f W / w h i c h E p s t e i n d e n o te s b y ( - - A ) q b y s l i g h t l y d i ff e re n t

m e t h o d s t o t h e f ir s t o r d e r i n F [ E p s t e i n s ( - - E ) ] . W e

s h a l l p r o c ee d t o a s e c o n d a p p r o x i m a t i o n .

* Fo r a fuller treatm ent of this sectmn, see Epstein s p ap er al eady

referred to, also Som merfeld's Atom bau u.s.w.' II . Auf. p. 542, and p. 482.

Jaeobi's method of integrating the Ham iltonian transformed equations is

also given by Ap pell, ' Mdcanqque rationelle,' ii. p. 400 (Pa ris, 19 04 )..

f ' Atombau u.s.w .' Zusatz vii. p. 482, under f.; we, however, w rite

~/0 for his ( - ~ /O).

P h i l . M a g .

S . 6 . Vo l . 43 . No . 257 .

M a y

192 2. 3 P

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9 4 6 M r , A . M . M o s h a r r a f a o n

the Appearance o f

§ 3. C alcu lations .for C omparatively L ar ge _Fields.

W e s h al l t r e a t t h e t e r m i n D i n e q u a t i o n (7 ) a s a c o r r e c t i v e

o

t e rm . L e t /~ , ~ + A ~ = / ~ r, f ~ r + ' B = ~ ' , e tc ., d e n o te t h e

s u c c e ss iv e a p p r o x i m a t i o n s t o t h e v a l u e o f / ~ ; s im i l a rl y f o r

A , B , a n d W . W e s e e t h a t t o t h e f ir s t o r d e r o f s m a l l

q u a n t i t i e s

1

B ~ -- - [ B I + A B i ] ~ = [ B , + m o A B ] ~ f r o m ( 5 a )

_ : B ? . 2 , n o B , ~ B , . . . . . . . 8 a )

a n d s i m i l a r l y

1

B , f l- - B 2 2 - - 2 m o B 2 A ~ f r o m ( 5 b ). ( 8 b )

o

N o w t h e e q u a t i o n s f o r d e t e r m i n i n g A f~ c o u l d e a s i ly b e

s o lv e d , b u t a s w e a r e a s s u m i n g E p s t e i n ' s w o r k ~ e s h a ll

m e r e l y g i v e h e r e t h e v a l u e o b t a i n e d o n s o l v i n g h i s e q u a t i o n s

( 61 ) * . W e h a v e

o ~ . F . h 4 ( n l + n 2 _ t _ n s )

a B = . . . . .

9 )

64mo2eE27r~

w h e r e

N - - ( 6n2~+ 6n :ns + n~ J)

(2n l 4- us )

+ (6n l~+6nln2+ns~) (2n~+ns ) ,

( 1 0 )

s o t h a t w e h a v e f r o m (8 ) a n d (9 )

1 o o h 4(n l + n 2 + n s ) N 1

B 1 2 = B 1 ~ + 2 m o B i x 6 -~ m o _ , . ( l l a )

s i m i l a r l y

1

B . ~ = B 2 ~ - - 2 m oB ~ x

0

a ls o , B ~ is o b t a i n e d f r o m ( 7) o n n e g l e c t i n g t h e t e r m i n D ,

t h u s :

h 4 • (n l + n , + n~ ) . N

64rno~eE~Tr4 . F ; (1 1 b)

* Ann.

d. Phy s. 1. 1). 508 (19 16) ; our ~ eorrespond s to Epstein's

(e~f l ) .

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U n s y m m e t r ic a l C o m p o n en ts i n t h e S t a r k E f f e c t . 947

F r o m ( 1 1 ) a n d ( 1 2 ) w e h a v e

3 2m o eE 'T P ( ~ / C + ~ i ) F

( 13 )

S u b s t i t u t in g t h is v a l u e fo r B ~ i n t h e t e rm i n v o l v i n g D o n

t h e r i g h t -h a n d s i d e o f ( 7 ) , w e h a v e

_ _ q r ; ~

-I-

F

32moeE ~

v A 7P

o r , s u b s t i t u t i n g t h e v a l u e s o f ] ) f r o m (5 ) , w e h a v e

~r-]F2

(14)

_ 1 2 ~ E ~ . ~ A 3 / 2 ;

w r i t in g the tw o equa t ions em bodied in (14=) in fu l l and

a d d i n g , w e o b t a in

m o e E = ~ / ~ _ ~ J -1

r e e f 3 n ~ - - n 2 I ~\

4A

\2 7r~ - ~

3h4(n, + n, +

n~)N

[ ~ / C + n , + n , ) h i ]

F , ( 15 )

128Aa'27r4E~ L ~ J

W e p ro c e e d t o s o l v e fo r A b y p u t t i n g

A = - - ( K + L F + M F ~ ) . . . . . (1 6 )

W e h a v e

V X i ¢ - £ i ~

= s K F

a n d

a n d 1 i

1 4 M K L 2 _ \

a p p ro x i m a t e l y , l

,,

( 17 )

3 P 2

j

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9 4 8 M r . A . ~ '[ . M o s h a r r a f a

o n t he A p p e a r a n c e o f

T h u s , s u b s t i t u t i n g i n ( 1 5 ) a n d p u t t i n g

~ / - ~ = n a h i

2,n. J

w e h a v e , o n e q u a t i n g t h e c o e ff ic ie n ts o f p o w e r s o [ F ,

K = ¢ 4~r2(m °eE)' . . . . . (1 8 )

( n l + n 2 + n z ) ~ h 2 '

3 h 2

L = 4 - ~ - E ( n 2 - n t ) ( n x + n ~ . + n a ) , •

( 1 9 )

L ~ 3 m o e h L

M = 4 K 2 ~.K 3 /2 n 2 - n 0

3 1,4 n l + n ~ + n 3 ) ~ 2 0 )

6 4 r r 4 E .~K . . . .

O n s u b s t i t u t i n g f r o m (1 8) a n d ( 1 9 ) i n ( 2 0 ), w e f i n a l l y

o b t a i n

M = - 27h~ (nl + n2 4- na) 3

256~r~E4mo2e2 N ' , . . . . (2 1 )

w he~o N = ( ~ + ~ + n 3 ) ( ~ - . 0 ~ + Z ~ . . (2~)

W e t h u s f i n a l l y h a v e t h e f u l l e x p r e s s i o n f o r th e e n e r g y :

27r2m0e~E2 3 F h 2 .

W = - (n . + n~ + n3) '2h 0 8 ~ E ( n , - n ~ ) (n a + n~ + n , )

+ 27h (n~ + n 2 -6 n3) 3

N FL

( 2 3 )

512 7r6 E4 m o3 e :~

T h u s i [ A W r e p r e s e n t t h e c h a n g e i n W d u e to t h e i n t r o -

d u c t i o n o f t h e e x t e r n a l f ie ld F , w e h a v e

3 F h 2

27h6 (nz + n~ + n.~)3~ , - z

_ , V . . ( 2 4)

T h u s A v [ t h e c o r r e s p o n d i n g c h a n g e i n f r e q u e n c y ] i s

g i v e n , a c c o r d i n g t o B o h r ' s a s s u m p t i o n

h a y = A W ~ - - A W . ,

w h e r e W , . d e n o t e s t h e

e n e r g y

f o r m o t i o n in a p a t h [ c h a -

r a c t e r iz e d b y t h e q u a n t u m n u m b e r s m l m 2 m ~ ] f r o m w h i c h

t h e e l e o tr o n s t a r t s t o m o v e t o w a r d s t h e n - p a t h , b y t h e

f o r m u l a

3 h F

a ~ - 8 .~ ,,o E ~ ~ - ~ , ) n t + ~ +

~ )

- , ~ - m 0 m ~ + ~ + m ~) }

27hSF'~

+ 512~r~E4moae~ -- (n~ + n~ + n3) 3N '(n )

+ ( .,~ + . ~ + m~)N (m) } , (~ 5)

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Un sy mme t r i c a l Co mp o n e n t s i n t h e S ta rk . E f f e c t . 9'49

w h e r o ~ q r ( m ) a n d N t ( n ) a r e i d e n t i c a l f u n c t i o n s o f 'in a n d n

r e s p e c t i v e l y .

§ 4 . A p p l i c a t io n to t h e H~ l i n e .

W e p r o c e e d t o a p p l y e q u a t i o n (2 5) t o s p e c i f ic l in e s o f t h e

e l e m e n t s . L e t u s t a k e a s a n e x a m p l e t h e H ~ l in e o f t h e

B a l m e r S e ri es . H e r e n l q - n 2 + n 3 = 2 , m z - l - m 2 + m 3 ~ 3 ,

v = 4 5 7 1 x 1014, k = ' 6 5 6 2 8 × 1 0 - 4 ; l e t u s a ls o w r i t e (25)

i n t h e f o r m

A v = ( P ~ - Q 1 ) × K f l ? + ( Q 2 - P 2 ) K 2 F 2 ; (2 6)

t h e n

P1 = n ~ - - nl) (nl + n2 + n 3 ) , Q , = m 2 - - , n l m ~ + m : + m 3 ) ,

3 h

K t = 87r%~o]~' [

P ~ = ( ~ + ~ + n ~ ) ' ( . ~ - ~ ,1 )~ + ( 1 + .0 +

~ ) ~ , , ) ,

q ~ = ( ~ + ~ + m ) ' ( m ~ - , n l ) ~ + (m ~ + . , ~ + , , ~ ) 3 ~ ( , n ) .

2 7 h 5

K 2 -

5127r~E ~o~ ~, J

T h e n w r i t i n g d o w n i n a t a b u l a r f o r m th e p o ss ib l e v a l u e s

o f n i n o n 3 a n d m l m : m a , w o h a y % o n a v a i l i , g o u rs e lv e s o f

S o m m e r f e l d ' s A u s w a h l p r i n z i p f o r t h e d e f i n i ti o n o f t he

p l a n s o f p o l a r i z a t i o n a n d t h e r e s t r i c ti o n s o n t h e p o ss ib l e

c o m b i n a ti o n s o f t he q u a n t u m n u m b e r s :

( 2 7 )

TABLE A.

I

I I .

I I L

V.

g I .

2 0 0 0 128

1 1 0 2 144

1 0 1 --2 144

0 1 1 0 19 2

0 2 0 4 64

0 0 2 4 6 4

% . ~ . ~1. Q~. Q,.

a. 3

b. 2

e. 2

d. 1

e. 1

f . 1

y. 0

h. 0

i. 0

j . 0

0 0 0 1458

1 0 3 2025

0 1 -- 3 2025

1 1 0 2106

2 0 6 1458

0 2 -- 6 1458

2 1 3 2025

1 2 --3 2025

3 0 9 729

0 3 --9 7 29

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95

M r. A . h i . M osha r , a f a

on the Appearance o~

TABLE B

F i r s t G r o u p .

m ~ n a = O

; p - c o m p o n e n t .

(I. b) ......

(I1. d) ......

I I . e )

......

( I I . f ) . . . . . .

(IV.g ) ......

(IV. # .......

(V. g) .... .. k

(v. h) ......

(v. i). . . . . .

(v.j ) . . . . . .

P1-Q1.

- - 3

+ 2

- - 4

+ 8

- - 3

- 9

+ 1

+ 7

- 5

+13

Q 2 - - ~ 2

1 8 9 7

1962

1314

1314

I:)1 - - [~1.

(I. c) ... ... + 3

(I II . d) .., -- 2

I

(I II .f ) . .. + 4

n I . e ) . . . . . . - 8

I

1 8 9 7

1962

1314

1314

1833

537

1951

1951

665

665

(IV.h ) ... + 3

(i v. j) .. + 9

(v i. a) ...i - 1

(V i.g) ... - 7

(V i. g) -,.i + 5

(VI. i) ... [ -- 13

1833

537

1951

1951

665

665

S e c o n d G ro u

P 1 - - Q 1 °

I . a ) . . . . . . o

I . e ) . . . . . . - - 6

(i i. b) ...... - 1

(i i. c) ...... + 5

(i i. g) ..... - 1

(i i. h) ...... + 5

(I I. i) ...... - 7

(I I. j ) . . .. . . +11

(IV . e) ...... -- 6

(V. e) ... ... - 2

(v . f) . .. .. . +~o

(V.d) ...... + 4

(IV. d) ...... o

TABLE C.

). ma-- n := +1 ; n -co mpone n t .

q 2 - - P 2

1330

1330

1881

1881

1881

589

589

1266

1394

1394

2042

1914

P 1 Q 1 •

(i. d) ...... 0

(I .f ) .. . . .. + 6

( I l L e) ... + 1

( II i . b) . . . . 5

(I II . h) ... + 1

( I I I . g ) . . . . 5

(I II . j ) . .. + 7

(II I. i) . .. -u

(I V. f) ... + 6

(v i. f) ... + 2

(VI.e) ... I 0

v t . ~) .. - 4

1978

1330

188l

1881

1881

]88i

589

589

1266

1394

1394

2042

T h e a r r a n g e m e n t o f t h e t a b l e s i s v e ry s i m p l e . I n

T a b l e A w e p u t d o w n a l l t h e p o s s i b l e v a l u e s fo r t h e n ' s a n d

th~ m ' s separ a t e ly fo r t he l ine H~. Then in Tab le s B and C

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9/10

Uns lmmetrlcal Components in the Stark Effect . 9 5 1

w e c h o o s e s u c h c o m b i n a t i o n s a s g i v e r i s e t o ms--na--'.-O

o r m 3 - - n 3 = ___1 r e s p e c t i v e l y . T h e g r o u p i n T a b l e A c o r r e -

s p o n d s to l in e s w h e r e t h e p l a n e or p o l a r i z a t i o n i s p e r p e n -

d i c u l a r t o t h e i m p r e s s e d f i el d F [ i . e . t h e e l e c t r ic f o r c e

p a r a l l e l t o F ] , a n d t h a t o f' T a b l e B t o l in e s w h e r e t h e l i g h t

i s p o l a r i z e d i n a p l a n e p a r a l l e l t o F f t. e . t h e e l e c t r i c f o r c e

p e r p e n d i c u l a r t o F ] .

W e o b se rv e t h a t w h e r e as ( P 1 - Q ~ ) h a s a n e g a t i v e v al ue

n u m e r i c a l l y e q u a l t o e v e r y o n e o f it s p o s s ib l e p o s i t i v e v a l u e s ,

( Q 2 - 1 ~ 2 )

on the other hand has an invariable positive sign

a n d a roughlg constant order of magnitude, vlz. 108.

I f w e a v a i l o u r s e l v e s o f th e m o s t r e c e n t v a l u e s ~ f o r t h e

c o n s t a n t s i n v o l v e d i n t h e f o r m u l a ( 2 5 ) , v i z .

h : 6 5 4 7 × 1 0 -~7, e -- -- 4 7 7 4× 1 0 - l° , e _ 5 . 3 0 1 × 1 0 1 7 ,

m

a n d if w e p u t E : e f o r h y d r o g e n , w e h a v e

K ~ = 5 7 8 4 × 1 0 s. K ~ ----7 6 77 x 1 0 ; ( 2 8 )

s o t h a t ( 2 6 ) c a n n o w b e w r i t t e n

A v = 5 ' 7 8 4 × 1 0 S x Z × F + 7 6 7 7 × R z × 1 0 4 x F ~, (2 9 )

R - - Q 2 - P~

w h e re z - ( P ~ - Q 1 ) , ~ - 1 00 0 '

o r o n t h e sc a le o f w a v e - le n g tl ~ s , s in c e A v = - - ~ d X,

- -A% --- - '8304 × 10 -~° x F x Z + 1 102 × 10 -~4 × R zF 2. (30 )

H e r e i t m u s t b e r e m e m b e r e d t h a t F i s m e a s u r e d i n a b so l ut e

c .G . s, e l e c t r o s t a t i c u n i t s . I n ( 3 0 ) w e o b s e r v e t h a t Z is a

w h o l e n u m b e r , p o s i t iv e o r n e g a t i v e , b e t w e e n 0 a n d 1 3 a n d

t h a t R z v a r i e s f r o m a b o u t ½ t o a b o u t 2 .

I [ w e a s s m n e a v a l u e f o r F :- -- 10s [ = 3 0 0 , 0 0 0 v o lt × e m . - l ~ ,

t h e n i f X~ b e w r i t t e n f o r X × 1 0 s [ i. e . i f w e m e a s u r e X ', t h e

w a v e - l e n g t h , i n / ~ n g s t r S m u n it s~ w e w r i t e :

- - A k ' ---- 8 3 0 4 Z + 1 1 0 2 × R~ . . . . . (3 1 )

W e t h u s s ee t h a t f o r s m a l l v a l u es o f Z , t h e s e c o n d t e r m

o n t h e r i g h t - h a n d s i d e o f ( 3 1 ) i s q u i t e a p p r e c i a b l e c o m p a r e d

w i t h t h e f i r st t e r m [ e. g . f o r Z ~ - 1 t h e r a t i o i s a b o u t ¼ ] ; and

* These are quoted from 1~. A. M illikan's ~ T h e Ele ctron , ' Th e

University of Chicago Press, Th ird Impression 1918, pp. 238 and 251.

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9 5 2

Un symm etrical Co mpo nents in the Sta rk Effect.

since this term has an invariable va lu e/ or equa l an d opposite

values o f Z it/ollo w s that the symm etry o f the lines is destroyed.

A l s o t h e p a r a b o l i c r e la t i o n b e t w e e n A r a n d F [ o r ~ a n d F ]

is f u r n is h e d b y ( 2 9 ) a n d ( 3 0 ) r e s p e c t i v e l y . W e g i v e h e r e a

t a b l e o [ t h e d i s p l a c e m e n t s o f t h e n i n e l in 'e s o b s e r v e d b y

S t a r k f o r a h y p o t h e t i c a l f ie ld o f 3 0 0 , 0 0 0 v o l t x c m . - 1 a s

p r e d i c te d b y o u r t h e o r y .

p o

m p o n o n t . n - c or n p o n e n L.

Z . .. .. . + 2 L

- 2

1~ .., 1 962 1 962

, 1 1 4 . 4

AX ...1--18 8 -

÷ 3 I - - 3

1 833 [ 1 833

26 9 I+ 22'9

+ 4

1 314

-34 7

- 4

1 314

+31 '8

0

i

I I

+ 1

1'881

-10 3

--1

1 881

+6 4

T h e n - c o m p o n e n t l i n e w h i c h o c c u p i e s t h e o r i g i n a l p o s i t i o n

o f t h e H ~ l in e i s s e en t o s p l it i n t o t h r e e c o m p o n e n t s - - t w o o f

w h i c h a r e , h o w e v e r , v e r y d o s e t o g e t h e r - - f o r h i g h e r f ie ld s .

T h e p o si ti o n o f t h e s e l in e s m a y , h o w e v e r , b e a p p r e c i a b l y

a f fe c t e d b y h i g h e r t e r m s in e q u a t i o n ( 30 ) t h a n t h e l a s t

t e r m w e h a v e l a k e n a c c o u n t o f ( i. e . t e r m s i n F 3 e t c . ) . I t i s

t o b e o b s e r v e d t h a t t h e f u n c t i o n s o f th e q u a n t u m n u m b e r s

i n v o l v e d s e e m to b e c o m e m o r e an d m o r e i m p o r t a n t i n d e t e r -

m i n i n g t h e o r d e r o f m a g n i t u d e o f t h e r e s p e c t iv e t e r m s a s w e

p r o c e e d t o c o n s i d e r h i g h e r p o w e r s o f F . H o w e v e r , t h e

a b o v e c a l c u la t io n s o u g h t to f u r n i s h a f a i r l y a c c u r a t e t h e o r y

f o r fi e ld s o f t h e m a g n i t u d e w e h a v e c o n s i d e r e d ; a n d , in o u r

o p i n io n , i t w o u l d b e h i g h l y d e s i r ab l e t o m a k e e x a c t m e a s u r e -

m e r it s f o r s u c h f ie ld s . W h e t h e r t h e a b o v e p r e d i c t i o n s w i l l

o r w i l l n o t b e v e r i f i e d , r e m a i n s t o b e s e e n .

I n c o n c lu s io n , I w i s h t o e x p r e ss m y t h a n k s t o P r o f . J . W .

N i c h o l s o n f o r u s e f u l s u g g e s t i o n s .

King's College, London,

5Iay 1921.