
$B$3$N$H$-(B$P$$B$H(B$P'$$B$,AjB3$/8rE@$G$"$C$F!"(B$\theta, \lambda$$B$H(B$\theta', \lambda'$$B$,(B$\theta, \lambda$$B$NBP1~$9$kCM$G$"$k$H$9$l$P<!$rF@$k!%(B
$$
  (\theta' + \lambda') - (\theta + \lambda) = 2\pi.
$$

$\theta+\lambda$$B$,(B$u$$B$K4X$7$F$D$M$KA}2C$9$k4X?t$G$"$k$3$H$r;XE&$7$F$*$/!%<B:]!"(B$v$$B$H(B$w$$B$,Hs>o$K>.$5$$$H$-!"<!$N$h$&$K=q$1$k!%(B
$$
  F(u,v,w) = R \sin (\theta + \lambda + h).
$$
$B$3$3$G(B$R=\sqrt{p^2+p_1^2}$$B$O(B$u$$B$N<~4|4X?t$G$"$k!%$3$N$H$-(B$C_1$$B$H(B$A$$B$N8rE@$O(B$F$$B$,%<%m$K$J$k$H$7$FF@$i$l!"(B
$$
  F = F' = 0,
$$
$B$H$7$F(B$C_1$$B$H(B$A$$B$N@\E@$,F@$i$l$k!%$3$3$G(B$F'$$B$O(B$u$$B$K4X$9$k(B$F$$B$NHyJ,$G$"$k!%$3$l$i$O<!$N$h$&$KM?$($i$l$k!%(B
$$ \begin{array}{l}
 F = R \sin(\theta + \lambda + h) = 0, \\
 F' = R' \sin(\theta + \lambda + h) + 
      R (\theta' + \lambda') \cos (\theta + \lambda+h) = 0 . 
   \end{array}
$$

$\theta'+\lambda'=0$$B$J$i!"(B$h=-\theta-\lambda$$B$H$9$k$3$H$,$G$-!">r7o$OK~$?$5$l$k!%$H$3$m$G!"$3$l$OIT2DG=$G$"$k!%$J$<$J$iLL@Q(B$A$$B$OHs@\?($H2>Dj$7$F$"$C$?$+$i!%$7$?$,$C$F(B$\theta+\lambda$$B$NHyJ,$O%<%m$K$J$l$:!"(B$\theta+\lambda$$B$O$$$?$k$H$3$mF1$88~$-$KJQ$o$k!%$3$l$,$$$D$bA}2C$G$"$k$h$&$KD4@0$G$-$k!%(B

$B4X?t(B
$$
 \frac{\displaystyle \theta+\lambda}{\displaystyle \alpha+m},
$$
$B$O>e$N35G0$r>/$70lHL2=$7$F!"4T850z?t(B(argument r\'{e}duit)$B$H8F$V$3$H$,$G$-$k!%NL(B$\alpha+m$$B$O(B$\alpha$$B$H@0?t(B
$$
  m = 
\frac{\displaystyle \lambda(u+2\pi)-\lambda(u)}{\displaystyle 2\pi},
$$
$B$7$+0c$o$J$$!%>e$GA*$s$@(B2$B$D$NNc$N>l9g$K$O$3$l$O%<%m$G$"$k!%4T850z?t$O(B$C_0$$B$r0l<~$9$k$H(B$2\pi$$BA}$($k!%$^$?$3$l$O(B$u$$B$NA}2C4X?t$G$"$k$+$i!"(B$C_0$$B>e$NE@$N0LCV$rDj5A$9$k$N$K;H$($k!%(B$P$$B$O(B$C_0$$B$KHs>o$K6a$$$+$i!"E@(B$P$$B$N4T850z?t$H$=$NJQ49A|(B$P'$$B$N4T850z?t$O(B
$$
\frac{\displaystyle 2\pi}{\displaystyle \alpha+m},
$$
$B$@$10[$J$k!%(B

$B$3$N$h$&$KCV$/$H!"0LCV2r@O$N;kE@$+$i$OLL@Q(B$A$$B$r1_$NLL@Q$HF10l;k$G$-$k!%$7$?$,$C$F$3$NLL@Q$NE@$N0LCV$r6K:BI8$K;w$?:BI8(B$x$$B$H(B$y$$B$N:BI87O$GDj5A$9$k$3$H$,$G$-!"(B$C_0$$B$NJ}Dx<0$r<!$N$h$&$KI=$o$;$k!%(B
$$
 x=a.
$$
$B$7$+$b$3$N6J@~>e$G(B$y$$B$O4T850z?t$KEy$7$$!%$7$?$,$C$F!"$o$l$o$l$NJQ49(B$T$$B$O6J@~(B$x=a$$B$rJ]B8$7!"<!$N$h$&$G$"$k!%(B
$$
  Y - y = \frac{\displaystyle 2\pi}{\displaystyle \alpha+m} = 
{\rm const.}
$$

$B%/%m%M%C%+!<$NDjM}$K$h$l$P!"$3$N$H$-(B$A$$B$NFbIt$KJQ49$NITF0E@$,(B\underline{$B4q?t(B}$B8D$"$k!%$3$N3FE@$K<~4|50F;$,BP1~$9$k!%$=$N$&$A>/$J$/$H$b(B1$B$D$O0BDj$G$"$k!%(B

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$$
  x=0.
$$

$BJQ49(B$T$$B$O$3$N$H$-(B$x=a$$B$rJ]B8$9$k$P$+$j$G$J$/!"FbB&$N6K8B1_(B$x=0$$B$bJ]B8$9$k!%$?$@$78e<T$O(B1$BE@$K=L$s$G$$$k!%(B

$C'_0$$B$OJD6J@~(B$C$$B$N$&$A(B$P_0$$B$rDL$k$b$N$H$9$k!%:BI87O(B$u',v',w'$$B$rF3F~$9$k!%$3$l$O7O(B$u,v,w$$B$,(B$C_0$$B$KBP1~$7$?$N$HF1$8$/(B$C'_0$$B$KBP1~$9$k!%$=$N>e!"$3$N:BI87O$G(B$A$$B$NI=<0$,(B$u'=0$$B$G$"$k$H$9$k!%$3$&$9$k$3$H$O2DG=$G$"$k!%$?$@$7(B$u,v,w$$B$K4X$7$F9T$J$C$?2>Dj$N0lHVL\$rJ|4~$9$k>r7o$N$b$H$G$G$"$k(B($B$9$J$o$A(B$u$$B$H(B$v$$B$rJQ$($:$K(B$w$$B$rJQ$($k$H!"@\@~$NJ}8~$@$1$,JQ$o$j!"B,CO@~$^$?$O50@W$NE@$OJQ$o$i$J$$(B)$B!%<B$r8@$($P!"$3$N2>Dj$OK\<AE*$JLr3d$O2?$b$;$:!"1?F03XE*>GE@$NDj5A$N5-=R$r4JC1$K$9$k$?$a$@$1$N$b$N$G$"$C$?!%$3$N>r7o$N$b$H$G(B$C'_0$$B$N6a$/$N6J@~(B$C$$B$NJ}Dx<0$O<!$N$h$&$K=q$1$k!%(B
$$ \begin{array}{cc}
 \frac{\displaystyle v'}{\displaystyle a'} = \rho' \sin (\theta'+h'), & 
 \frac{\displaystyle w'}{\displaystyle a'} = \rho'_1 \sin (\theta'+h') +  \rho'_2 \cos (\theta'+h') . 
   \end{array}
$$
$B$^$?<!$rF@$k!%(B
$$
  \theta' = \beta u' + \varphi'(u').
$$
$B$3$3$G(B$\varphi'$$B$O<~4|4X?t!"(B$i\beta$$B$OFC@-;X?t$G$"$j!"$=$l$f$((B$u'$$B$,(B$2\pi$$BA}$($k$H(B$\theta'$$B$O(B$2 \beta \pi$$BA}$($k!%:BI87O(B$x,y$$B$rA*$s$G!"(B$P_0$$B$N6a$/$G$O1TIR$G$"$k$h$&$K$G$-$k!%$9$J$o$A(B$x$$B$,Hs>o$K>.$5$$$H$-!"(B$u'=0$$B$N$H$-$N4X?t(B$\rho',\rho'_1,\rho'_2$$B$NCM$rM?$($F(B
$$ \begin{array}{cc}
 \frac{\displaystyle v'}{\displaystyle x} = \rho' \sin y, & 
 \frac{\displaystyle w'}{\displaystyle x} = 
\rho'_1 \sin y +  \rho'_2 \cos y. 
   \end{array}
$$

$B$3$N$H$-(B$u'$$B$,(B$2\pi$$BA}$($k$H!"$9$J$o$A!"E@(B$P$$B$+$iE@(B$P'$$B$K0\$k$H!"(B$y=\theta'+h'$$B$O(B$2\beta\pi$$BA}$($k!%$H$$$&$h$j$O!"$`$7$m(B($2\pi$$B$N@0?tG\$NITDj@-$,$"$k$+$i(B)
$$
  2 \pi (\beta+n),
$$
$B$@$1JQ$o$k!%$3$3$G(B$n$$B$O@0?t$G$"$k!%$7$?$,$C$F$3$N$H$-<!$rF@$k!%(B
$$
  Y - y = 2\pi (\beta+n).
$$

$m$$B$OG$0U$G$J$$$1$l$I$b(B$n$$B$OG$0U$G$"$k$h$&$K8+$($k!%$7$+$7!"LL@Q(B$A$$BA4BN$rF0$-2s$k$H!":9(B$Y-y$$B$OO"B3E*$KJQ$o$k$+$i!"$3$l$K$h$C$F(B$n$$B$,7h$^$k!%(B

$B$3$&$7$?>e$G!"(B$T$$B$r(B$p$$B2s7+$jJV$7$?JQ49(B$T^p$$B$r9M$($h$&!%$3$NJQ49$O(B$x=a$$B$H(B$x=0$$B$rJ]B8$7!"(B$T$$B$HF1MM!"$o$?$7$NK\(B($B>e5-;29MJ88%(B2)$B$G<($7$?86M}$K$h$C$F@5$N@QJ,ITJQNL$r5v$9!%0lJ}$3$NJQ49$K$h$j(B$x=a$$B$N>e$G(B
$$
  Y - y = 2\pi \frac{\displaystyle p}{\displaystyle \alpha+m},
$$
$B$rF@!"$^$?(B$x=0$$B$K$*$$$F(B
$$
  Y - y = 2\pi p (\beta+n) ,
$$
$B$rF@$k!%(B

$B$3$l$O(B$q$$B$r@0?t$H$7$F(B$Y$$B$r(B$Y+2q \pi$$B$KCV$-49$($?$H$-$KF@$i$l$k$b$N$HK\<AE*$K0c$o$J$$!%$J$<$J$i(B$Y$$B$O(B$2\pi$$B$N@0?tG\ITDj$@$+$i$G$"$k!%$3$N?7$7$$JQ49$K4X$7$F!"(B$x=a$$B$N>e$G<!$rF@$k!%(B
$$
  Y - y = 2\pi \left( \frac{\displaystyle p}{\displaystyle \alpha+m} + 
q \right) .
$$
$B$^$?(B$x=0$$B$N>e$G<!$rF@$k!%(B
$$
  Y - y = 2\pi [p(\beta+n) + q].
$$
$BEy<0(B
$$
  (\beta+n) (\alpha+m) = 1,
$$
$B$,@.$jN)$?$J$1$l$P!"@0?t$NAH(B$p$$B$H(B$q$$B$G<!$rK~$?$9$b$N$rL58B8D8+$D$1$k$3$H$,$G$-$k!%(B
$$
 \left( \frac{\displaystyle p}{\displaystyle \alpha+m} + q \right) 
[p(\beta+n) + q] < 0.
$$
$B$9$J$o$A!"(B
$$
 \frac{\displaystyle 1}{\displaystyle \alpha+m} > 
- \frac{\displaystyle q}{\displaystyle p} > \beta + n ,
$$
$B$^$?$O(B
$$
 \frac{\displaystyle 1}{\displaystyle \alpha+m} < 
- \frac{\displaystyle q}{\displaystyle p} < \beta + n .
$$

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$B$3$NLdBj$N$"$k%G!<%?$NCM$KBP$7$F!"6J@~(B$C_0$$B$H(B$C'_0$$B!"$7$?$,$C$FLL@Q(B$A$$B$r9=@.$7$?$H$7$h$&!%<!$K$3$NLdBj$N%G!<%?$rJQ2=$5$;$h$&!%(B$C_0$$B$OO"B3E*$KJQ2=$9$k!%(B$A$$B$bO"B3E*$KJQ2=$5$;$k$3$H$,$G$-!"$=$N:]$=$NK\<AE*$J@-<A!"$H$/$KHs@\?(@-$rJ]B8$9$k$h$&$K$G$-$k!%$3$NE@$r9MN8$9$k$H!"(B$C_0$$B$,B8:_$9$k8B$j$3$l$O$:$C$HB3$/!%$7$?$,$C$F!"(B$C_0$$B$H(B$C'_0$$B$,B8:_$9$k8B$j!"$o$o$l$o$N8@$C$?$3$H$O$9$Y$FJ]$?$l$k!%@0?t(B$p,q$$B$KBP1~$9$k<~4|2r$O(B$C_0$$B$"$k$$$O(B$C'_0$$B$H0lCW$7$F(B
$$ \begin{array}{ccc}
 - \frac{\displaystyle q}{\displaystyle p} =  
\frac{\displaystyle 1}{\displaystyle \alpha+m} & $B$^$?$O(B & \beta+n ,
   \end{array}
$$
$B$,K~$?$5$l$k$^$G$O7h$7$F$J$/$J$i$J$$!%(B

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