Post on 13-Mar-2020
-shy - ---shy
i--+
-- I --shy
--
-- ---
n (tfr) Lll-rzshy
~ shy1T
-
1fT 2-(J ~a v-)d7rshyR~~~fl~~l2 ~J~ -- -~ _~ u
n1 -
b I ~~m_2 L ~
I
uJ)1s - L vgt-12- = rmiddotH~i- 1shy
--(0() t+ a+Om s ~ T=- fa Cf k-
G 1+) -3 6 II 6 -IltOw
ar~--5 = ~ )(13~((o )((t) lt=-I-gt7--x-IO~ s-shy 11Yro-2 lt-
- -
- 1)7 ~Zs
=(f)_pound- aA _~ L -0 C -
shy~nt5 Le-) - __al -e trJM sCIj 13 11 sCu)I
--
~ ~ - - -shy
~t11 s [~ J--- 677 -pJ-~ ==shy~ -- -
-- - - -
I
__________ i
- ---------shy --shy
_---i---~--~-_-=-= -----shy
11 L tYL__ -15 _amp- (e-V-) J ----~ shy __1 ( 0 1-1 - 13b _ _ 2 _---- ---I shy
- t1middot= _
_ middot~middotfmiddot ~--~--_ -=-j~-- -3middotlt gu middot 0 0 _ _~l~
Imiddot L I 1 -+7shy L 2 _L 1 _ -ILL
2 I 0 1 2 I 0 I LL ~-1 -_LlL
1 - 11shy111-- -( _~~C4 ltpound01[-1gt of~i~ -n__~o_
-r11-- I-I --_ __0 - I ___ _ E - b rZ z- e~V- __
1=~l=~~~ _-middotFi lr~ _ I bullbull _ IJod_TJmiddotT ~_J~ - f l Ihlt w _ - V cJYl I
bull ~ ~~_ 1_middotmiddot v ___~-_ i~__idLfJr --= _Itgt--l 2_ - ~j_ ---==--R-=j~1~Ct~~~0~y- -=
I
-r bull ~pL~-(teltp[C~~J~)
~ LI egt-F [- II middot 1 ~ hI CrloVk) J
- - shy - -~ - shy - - - - -
-j~ ~ -~~~le-~ b-~- ~----
_ _ _rLfuLCamp-_f1 5 _ _ 1 ~ L) _ _ ~ _i
r-t----- -~plusmnrd~-tI cgt 1 ol7-_tf~J-----II----+_ _
_ _ _ _ q~----_------~---I ----__--E-----+--~----
-middot- -~1-- H- I------------------~------- - - - - - - lt- -=-----EfQl-l11-- - --1---- --shy- middot----- t1--- -shy c pound
----- 1+-1- - --- --- - ---- - - - 1-- - - - - shy
~
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
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---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
--
-- ---
n (tfr) Lll-rzshy
~ shy1T
-
1fT 2-(J ~a v-)d7rshyR~~~fl~~l2 ~J~ -- -~ _~ u
n1 -
b I ~~m_2 L ~
I
uJ)1s - L vgt-12- = rmiddotH~i- 1shy
--(0() t+ a+Om s ~ T=- fa Cf k-
G 1+) -3 6 II 6 -IltOw
ar~--5 = ~ )(13~((o )((t) lt=-I-gt7--x-IO~ s-shy 11Yro-2 lt-
- -
- 1)7 ~Zs
=(f)_pound- aA _~ L -0 C -
shy~nt5 Le-) - __al -e trJM sCIj 13 11 sCu)I
--
~ ~ - - -shy
~t11 s [~ J--- 677 -pJ-~ ==shy~ -- -
-- - - -
I
__________ i
- ---------shy --shy
_---i---~--~-_-=-= -----shy
11 L tYL__ -15 _amp- (e-V-) J ----~ shy __1 ( 0 1-1 - 13b _ _ 2 _---- ---I shy
- t1middot= _
_ middot~middotfmiddot ~--~--_ -=-j~-- -3middotlt gu middot 0 0 _ _~l~
Imiddot L I 1 -+7shy L 2 _L 1 _ -ILL
2 I 0 1 2 I 0 I LL ~-1 -_LlL
1 - 11shy111-- -( _~~C4 ltpound01[-1gt of~i~ -n__~o_
-r11-- I-I --_ __0 - I ___ _ E - b rZ z- e~V- __
1=~l=~~~ _-middotFi lr~ _ I bullbull _ IJod_TJmiddotT ~_J~ - f l Ihlt w _ - V cJYl I
bull ~ ~~_ 1_middotmiddot v ___~-_ i~__idLfJr --= _Itgt--l 2_ - ~j_ ---==--R-=j~1~Ct~~~0~y- -=
I
-r bull ~pL~-(teltp[C~~J~)
~ LI egt-F [- II middot 1 ~ hI CrloVk) J
- - shy - -~ - shy - - - - -
-j~ ~ -~~~le-~ b-~- ~----
_ _ _rLfuLCamp-_f1 5 _ _ 1 ~ L) _ _ ~ _i
r-t----- -~plusmnrd~-tI cgt 1 ol7-_tf~J-----II----+_ _
_ _ _ _ q~----_------~---I ----__--E-----+--~----
-middot- -~1-- H- I------------------~------- - - - - - - lt- -=-----EfQl-l11-- - --1---- --shy- middot----- t1--- -shy c pound
----- 1+-1- - --- --- - ---- - - - 1-- - - - - shy
~
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
__________ i
- ---------shy --shy
_---i---~--~-_-=-= -----shy
11 L tYL__ -15 _amp- (e-V-) J ----~ shy __1 ( 0 1-1 - 13b _ _ 2 _---- ---I shy
- t1middot= _
_ middot~middotfmiddot ~--~--_ -=-j~-- -3middotlt gu middot 0 0 _ _~l~
Imiddot L I 1 -+7shy L 2 _L 1 _ -ILL
2 I 0 1 2 I 0 I LL ~-1 -_LlL
1 - 11shy111-- -( _~~C4 ltpound01[-1gt of~i~ -n__~o_
-r11-- I-I --_ __0 - I ___ _ E - b rZ z- e~V- __
1=~l=~~~ _-middotFi lr~ _ I bullbull _ IJod_TJmiddotT ~_J~ - f l Ihlt w _ - V cJYl I
bull ~ ~~_ 1_middotmiddot v ___~-_ i~__idLfJr --= _Itgt--l 2_ - ~j_ ---==--R-=j~1~Ct~~~0~y- -=
I
-r bull ~pL~-(teltp[C~~J~)
~ LI egt-F [- II middot 1 ~ hI CrloVk) J
- - shy - -~ - shy - - - - -
-j~ ~ -~~~le-~ b-~- ~----
_ _ _rLfuLCamp-_f1 5 _ _ 1 ~ L) _ _ ~ _i
r-t----- -~plusmnrd~-tI cgt 1 ol7-_tf~J-----II----+_ _
_ _ _ _ q~----_------~---I ----__--E-----+--~----
-middot- -~1-- H- I------------------~------- - - - - - - lt- -=-----EfQl-l11-- - --1---- --shy- middot----- t1--- -shy c pound
----- 1+-1- - --- --- - ---- - - - 1-- - - - - shy
~
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
11 L tYL__ -15 _amp- (e-V-) J ----~ shy __1 ( 0 1-1 - 13b _ _ 2 _---- ---I shy
- t1middot= _
_ middot~middotfmiddot ~--~--_ -=-j~-- -3middotlt gu middot 0 0 _ _~l~
Imiddot L I 1 -+7shy L 2 _L 1 _ -ILL
2 I 0 1 2 I 0 I LL ~-1 -_LlL
1 - 11shy111-- -( _~~C4 ltpound01[-1gt of~i~ -n__~o_
-r11-- I-I --_ __0 - I ___ _ E - b rZ z- e~V- __
1=~l=~~~ _-middotFi lr~ _ I bullbull _ IJod_TJmiddotT ~_J~ - f l Ihlt w _ - V cJYl I
bull ~ ~~_ 1_middotmiddot v ___~-_ i~__idLfJr --= _Itgt--l 2_ - ~j_ ---==--R-=j~1~Ct~~~0~y- -=
I
-r bull ~pL~-(teltp[C~~J~)
~ LI egt-F [- II middot 1 ~ hI CrloVk) J
- - shy - -~ - shy - - - - -
-j~ ~ -~~~le-~ b-~- ~----
_ _ _rLfuLCamp-_f1 5 _ _ 1 ~ L) _ _ ~ _i
r-t----- -~plusmnrd~-tI cgt 1 ol7-_tf~J-----II----+_ _
_ _ _ _ q~----_------~---I ----__--E-----+--~----
-middot- -~1-- H- I------------------~------- - - - - - - lt- -=-----EfQl-l11-- - --1---- --shy- middot----- t1--- -shy c pound
----- 1+-1- - --- --- - ---- - - - 1-- - - - - shy
~
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
~ LI egt-F [- II middot 1 ~ hI CrloVk) J
- - shy - -~ - shy - - - - -
-j~ ~ -~~~le-~ b-~- ~----
_ _ _rLfuLCamp-_f1 5 _ _ 1 ~ L) _ _ ~ _i
r-t----- -~plusmnrd~-tI cgt 1 ol7-_tf~J-----II----+_ _
_ _ _ _ q~----_------~---I ----__--E-----+--~----
-middot- -~1-- H- I------------------~------- - - - - - - lt- -=-----EfQl-l11-- - --1---- --shy- middot----- t1--- -shy c pound
----- 1+-1- - --- --- - ---- - - - 1-- - - - - shy
~
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
--shy ---t--+-----I~ --~_
-rlt)~-amp~_ ~~__ f CJYl~~_ [if l~H~nf1--~-ltA-OYu rtl--f- ~ __~_ ~_ ~JLblt7u_ 5 j 1 ~_) __~ _
il--Nu-flJlj H~__L_ _ oJ~-tf fI J -I-r __ --IF --- ------r---- -~--- fJ-L -----shy-uf--_shy
1----- __ r ~v~ __L )tljE~ - -Efoil =1 i
- ---- -- - --- --- -------------1----shy__l _
I
~ L-------tt~-L ----I--f_1-------_-- E--- -- ----shy
Er f -~-(-1 ~ f+ bull(- ff rlIeV- C-~)-I
I ) (I)~
fk - ft ~ f- bI -0 ~1
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
L7iL6 ~ I~poundVl of ~Ye-k~ e 5~ ) (ro4
~to ~ ~tt~ -R-i 0 bull j60pound bulltJ~fl li~ ----- -~~~~-expc-f1) _=-~~-l el(f(rjJ~-~-
_ _j9 _
H -cZ eKp [=fr1~]
(~_Io~rcfJ_~ u- _gJ~ crf bullbull laquoJ sda-f~~1---- --- - --_ - -------
_ ---1--1- f IJ-Il-lvlHJJ$ f-JJ--1J-U~ _ _ - 1---- - -- - - --- ----- shy _un - - __
__ ~_n~- ~~=Ie)l~p [_~rn1-Iyen]
dl1t- 11( ofmiddotmiddot
sri middot5~-sbled-~l~~)-~~t(i----~~ Of2u-f ~-JJO cP -~~-3--)--
- - ----- - - ---- __- - - ----shy
Cj z ~tLjje- -shy
-3+sb 1 ~i e-J2_~ of--(J-1-j r[Xltds~ ___i cR~ e c4ffew~ Jl si-J wt c ulod _us ~-4-fk- ~ - - -shy~ i r - -- --shy
____rplusmn_-k0n~_~_~ 5f----7- ekd~middot_ _ _ _ -_ --- ----=- --___ __
dJ--~ -- -~ P -~--1JPev ---shy~~ -I-Pu- Cltnw1 h Hv w ryU llj sf4 ~lo(e ~ -fe-+- ~ J
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
i I I
- -----shy
d~ meJvJ
d(T I
n
- ------ - ---- - -- - - -- ----- -shy
1k~ z (YI tr -p 1 0=- Yl1 J vL
u= d3e(~ ~iJ ~
I iI i
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
----------
- bull nT( _~r- ~ ) ri ) (2f(iJN~----i2- middot-middot-I--I--e- - C~ftrn~ middotmiddote~(mJlplusmn fI -e---Jz -1r--n-l-- ---~-~gt -- f =--ir e ---shy
__- __ -_ - _ ---_ - - __ ~
TT II __
-- CI regshy~ =a~c nt~9~1~IT _____+- __ ___ _m __ _ bullbull __ bullbull _ bullbull
i - -- - - rt- -- ------ -- - - - ---- --- --- ---- - - - - - -- -----_
~ N 0+ f fllS ~ca J~-L We Y)amp_1f _ -t_eKfll$S ~H _
cshy ~e~~-f-J~t~~QL1d gt ____ 1 1- ~~_~ t_e~p_t01i~]j
in) a ------- ---t --t------------ --- --- - ------- ------ ------ ------ ------------ -- --- -- -shy
ToM_h~~l~~f-qfDC-YL=21 nJshyj - I
- - - - d - - - - --- -_---shy
- _ (~ --- _75-- f )11 m bull n -(L -~--6 -ef-L ~ ~
i -----~I--lmiddotL -- - -------------shy
i - -----h_--~--~-iTf-=r~l~ i- n~ci~ -+_____ _ __ 1 _ _ ___ ~
ltl11 ~Jb (113) --shy
CltOshy
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
----------- --- - ------ - ------
-r-( ---- r~- ()e
---------- __ z -- --- -- -2f (JrI1eItT~~-r-C--------- -- u-- _--=-=~~~-u -_~- _ --ftgt- J~-_~__RTjshy~
- -------------shy II __ __
-- -_ ------ --- -shy
- G-~ Y1_) T ~-f Q _l+ _12_s+M1fJ~ _
~
~ k~~ r- ~pound +v-o ~ w t l ~ (lltgt u laquo-dLVO -+alaquo-12
of I 5 ~C-~ ~ f C4-~ ~I
e ~Llt~--
poundOb l-- - - shy
nb - 3 Itgt [_(f-E)l ~ 1----shy--l - ~ egtlp -fl-r j
ss eo T CAL~ rlb [n
~1
-
j
I
---~
--hcHI~_middotmiddot~_
---nGHo)
0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
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wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
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~
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ss eo T CAL~ rlb [n
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-
j
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Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
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C~~~=~)) i
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-- J (S qJfJtJ~
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~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
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11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
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th D ~ ~ ~ -shy
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---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
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l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
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t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
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~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
j
I
---~
--hcHI~_middotmiddot~_
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0 -
T
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
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5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
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l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
Jd1 1+ Iu~ r rJuJ-CJ 111 yc1 ~ T fU-Ultgt +0 ~ 4S1JO k j )-) rJ [W) _ ~ L J T~ (dl
(l Cf) nH)
[-1~ p~ 15 ~Klt~jl an kfLlthlaquo htM ~e1lp=-rJ
~tYlel7fgt- OU~[1J) =Ofl~-rr )
ampvb 000000~G ~ m ~ 0 ( ~V ~
MM~ tV f shyA~ -
_ -I
v p l
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
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bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
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---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
II L t1f 5-f-rtvnyfPl
C~~~=~)) i
( ) 5 0 Tlaquo vte ltllt2vl J J-IWM( W du c ~ 0Y1 _
h~J wiJcA~ 1o-eVfjgtarl I I k CIlUVu- 6 f Q ( ~ IY1Y-l LQ~ r VI vtpoundad_ I
-- J (S qJfJtJ~
c ) I3uh- ~ cLJ 1Sa(~ I~ s+R~ k~ 4J1~ ck~ Ie j TL qrnl-r
~I
0 10(11
I l-2 t-~ 1 hi
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
~ ) ltt4- I z~ t1lt-_ ~ampUaltu
bull flt~~ ~~~ LJ~b1~
B~~~ ~~ ~ iVlT~~ ~ t~ ~~ oft AlIUlltl nri
~ til -- (l1- r to
n 0 h
11 ~
L~ raquo gt ~I ~ ~ X ( f I Vlt ft po
Pvv~c-fc 1J ~ ~ f-VlciM kda -+0 a (ht(L-1 fYllt- W
x I I
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
VI et-t)I YlC H) i s s ftL- d
th D ~ ~ ~ -shy
~ ~ -te~ )C 0
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
---
501Rshy
A-bu ~ u- iJ ~~( CltJ f6 (-4
(I) n[I+ t1ltcf- ~ I-- sol i n(HO)
Flwirs~ r c 112a-l~
(14 ~ (J n(H~ __ 1 _ U -shy
n 1)(11) nrHI_
I 0jn - ()1 _ 1 e p - rr - o gt l)l 10-9
--shy~- shy-hof
) tl1-I~if =lt-3_ il
c ~14014~ c
= ~ I -eIi l IL caJ _-er o~)I (0laquo ~ -shy
(clrl - 2-f2( t=C(t_ ~rrme~T)Jh eo p(-JcaJ r1 c~r) 1 e h l --Rl- --ILl]
Ji -Ib ill fdx V1 (Ca rr) 7--gtc(WXlU-b r~XIO) 2middot) r--rrx rJ~1V gtdlx(j J~1(16 -iiI nCCJ1) ~ middot)ll (b ~U(0- ~j lshyI) [1
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
- -
-----shy -shy _shy -- _shy
cJ lclP
nl-Cw) _ n (cxJ
n rI cor - bull (1 c ( rlcJl ) Vl c
5~ I1H~111f I ) ()CQil In I) 11 VlCJrI1 -
+d-- ~ rr-rtH)C) ~ Yhflil
crr - ( I ) bull ( I) CIlcolnM) (cN-) 6- -
l- lt b (XIO-q=2lfo-S~ Cc) gt2 ltIQ-b Ci~)cJ 7-(fD-amp
i lt4 ~~f W tv ~ I f1Lj ~ niX ~ ~ ligt unrhA-(JIo~ ~ 104 WI4t-1d (lt-if -tfClt+ it ~ foe ud- -o V~ 2- ~~ 10 117 4 ~u
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
I b_C)l f)-O 8_deg04 C1ltj I 2 If
-E--~
t 6 l Vl b1lJa5 amprn~ amp~ 9)10 -lur 1) a IL ~rv I-k t-Il-~
iCu ~ I deg10 t2 lt-At suo ~D~ ~ 5~~
au i~ en ~~ ~~ J~ ~ ~IWS
~J ~--fs (2d J~ ~ fJ1J2
~ ~ ceJ (J~ on laquos
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
(0 M5 I I
35
Classical Cepheds
4045
05
50
3
6
4
5
o
-1
-2
o - J
2(J o
log T
FrGURE i4 Schematic Hertzsprung-Russel diagram The lincsoonstantslopercpre
stars hlhg dlJllic[I rcdi i (see Section + 13)
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
I) ~~eaQ t+Rshy-I+R rr1)
L ~ T e
) rA~fm-eO~ vi 1 - (VIv ~ 6c
Be 15 -0~ I-- e-n IL(J- 1 T e-C 13- v)
Q9 ~~ftE0s~
(VI v fl c lll ~pound LL 0-- ~ I
+ -(7 -clIg +- ()V Imiddot 2-)
1-8middot9 -(- 8 T 7- )l- 1)071
_ I (Mo~-fi()w) LIL 19 0 110 =-11--70
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
~ -f- RO~J ~t=l(~TG ~ R~ 6-ltJ~ +AJ
VI 5 1P ~ ~ 5 kepl(jshy~ Tel
(Jj) TjN C4 ~ OYL U~ lI1 5 s ~ (vlv1s) tVU ~~ eraquo
Y$ S~
t)Ui~ T3 ~ flA~ IS tt kgtocd to X C-2 ~ i6vk ~ ~ ~ 1115 ~~J
a lo owl IA G~ ~ C7 - - 0 I VI ~eee kv1 R
M~ t~M ~~ ~ ~jvfc
-I gt- i 0( jY13 -
~
~~(Jro) f~r~~l
~ -
~(f1()lgD 1 -I -I I
bull
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20
OI-f~M S --
- wL-I- Ie ~~~~ cIr- RCt-lt -10 PWS 5~ - I-Ivlt-ltr do ~~ kt-5 ~ Iv ~~ fhSLJ~7
wtdL ]) ltj~ ~~ Te hdshy~ (l75o~ ~ s~
~ M- n dvt-L(A m I 01-lt 5 ~ ~ eau-ee Te I S I~ 0)
~ ~te~ J2 loW f2 2c to-2-f20