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The shadow projection shows why it is called a chair.*|{&@8 8  ` Z ?? k  ` Z h+??n6 ` S  ? 3333 RJd(  dv d N ??55V d C A! -?  -v d N ??Tb d c &A" .?P}  .6 d S  ? 3333 RJh(  hv h N ??Sb h c &A# 0? 9  0v h N ??88V h C A$ 1?  16 h S  ? 3333 , ++2>l_+(  l l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif  l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$5N   l j  l T ??* l  `= ??* ^ . "  t l  ` ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " #  ( l  `T ??* ^ . "   l T ??*  l  ` ??* ^ . "  K  l  `( ??2* )Newman projection of chair cyclohexane. L) '& " #    l  `[ ??*2 ^ . "   l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif   l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$5N  l j  l T ??* l  `dl ??* ^ . "  t l  `ȏ ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " #  ( l  `< ??* ^ . "   l T ??* l  `@ ??* ^ . "  K l  ` ??2* )Newman projection of chair cyclohexane. L) '& " #   l  ` ??*2 ^ . "   l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif  l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$5N  %l j  l T ??* l  `` ??* ^ . "  t l  `@ ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " #  (  l  `  ??* ^ . "   !l T ??* "l  ` ??* ^ . "  K #l  ` ??2* )Newman projection of chair cyclohexane. L) '& " #   $l  `h, ??*2 ^ . "   'l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif  &l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$5N  0l j  (l T ??* )l  `F ??* ^ . "  t *l  `u ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " #  ( +l  ` ??* ^ . "   ,l T ??* -l  ` ??* ^ . "  K .l  ` ??2* )Newman projection of chair cyclohexane. L) '& " #   /l  `x ??*2 ^ . 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P0 (Newman projection of chair cyclohexane. .) 2' B p s *޽h ? 3333 TLt(  t| t NH=??: The cyclohexane ring has two different kinds of hydrogen atoms. In the chair conformation the six hydrogens pointing perpendicular to the ring are designated axial and the six hydrogens near the plane of the ring are called equatorial. (0x2 f R 3 ' N!0O!0v t N ??S t S A't ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex4.gif 6 t S  ? 3333 ~vx (  x x T|$ ?? nUSSNs]p (  2v x N ??Ab x c &A( P?  P x TH>$ ?? ; These two conformations are not equivalent in energy. The equatorial conformation is more stable than the axial by 7.5 kJ mol-1. 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Polycyclic Hydrocarbons 4 "  < Z ??@ +2 !<+2  <  `8 ??%, VName 4 "  < Z ??+2@ + 2 #<+ 2  <  `> ??1, Z Structure 4   " "< Z ??+ 2@  2 %< 2  <  `C ??, d 4 "  $< Z ?? 2<@ >+D '<>+DZ  <  `H ??D%> Prismane hp f  &"# &< Z ??>+Dl@ +> D )<+> D  < Z ??1D> (< Z ??+> D@  >D +< >D <  `P ??D> d 4 "  *< Z ?? >D:@ P+V -<P+VX <  `xV ??V%P Cubane zep f &"# ,< Z ??P+Vl@ +P V /<+P V < Z ??1VP .< Z ??+P V@  PV 1< PV <  `^ ??VP d 4 "  0< Z ?? PVJ@ b+h  3<b+h h <  `d ??h%b  Housane ?bp h &"&#T 2< Z ??b+h l@ +b h  5<+b h  < Z ??1hb  4< Z ??+b h @  bh  7< bh  <  `< Z ?? + l@ +   A<+   < Z ??1   @< Z ??+  @     C<    <  ` ??   d 4 "  B< Z ??   @  + E< + <  `\ ??%~ V<Dodecahedrane ASNbp mp. 0450!   &"#&'#,  T D< Z ?? +`@ +   G<+  ~ < N ??1~ F< Z ??+  @    I<   <  ` ??~ d 4 "  H< Z ??   K< Z h+??B < s *޽h ? 3333 NF@(  @@ @ Tĺ ??0,$D 0 4.3 spv'`( 8 2 H @ T ??`,$D 0 *spۏLN_pN7hvSf[S^ O 0 2v @ N ??y @ S A  ?? b 8  $D 0v @ N ?? @ S A ??p P`g8 $D 0B @ s *޽h ? 33338 D~(  D D N ??X,$D 0 D s ,A ??  8 $D 0B D s *޽h ? 3333  HL(  Hv H N ??x H S A ??p8 $D 0v H N ??X H S A ??  8 $D 0B H s *޽h ? 3333 tl0L (  L L N ??M!M,$D 0 L s ,A ??"8 $D 0 L TT ??,$D 0 , 2` L T ??0*,$D 0 0(S.'lS sNp NSq_T M|N:S+RN) B 2333333" L Tt ??p ,$D 0 jOY.(2v L N ??}W} L S A ??`  8 $D 0B L s *޽h ? 3333 ;3@P(  P@ P T ??,$D 0 5.3 sv~g< (2!  P T ?? ,$D 0 (1885t^BagyercQN _Rf[0 d 2& R P Tl ??`,$D 0 D60 90 108 120  E 2E33Dv P N ??c P S A ?? 8 $D 0S P T( ??` 0Z ,$D 0 E +2444 +944 +044 -516  F 2FEB P s *޽h ? 3333 h`PT(  T T Td ?? ,$D 0 ` 1sNp (2 T N$??@`,$D 0 R s-NC-C.b_bNy/_.~g,xs.҉:N105.5o,H-C-H.҉114 :* 2 6v T N ??c T S A *?? 8 *$D 0B T s *޽h ? 3333 NF`X(  XF X Tp ?? ,$D 0 2sNpTs bpvga@ (2%    X N??P~,$D 0 np sNpNsNpv??0,$D 0  (Ws]pRP[-N CSP[/fSP3BgS0mQ*NC N(W TNs^b C-C.9Y҉Oc10928,Vdks_3z[0vQ gNygPga D02 Z ` S A n ?http://www.uis.edu/~trammell/organic/alkanes/chair.jpge  e,$D0=z n  ` P  ,$D 0!@ k  `kl@  ` ` Z ??  ` Z ??]@  k  ` k{ `  `L ??e {This model shows the gauche-butane interactions of chair cyclohexane. The shadow projection shows why it is called a chair.*|{&@8 8  ` Z ?? k  ` Z h+??nB ` s *޽h ? 3333z *"d(  d d N ??55,$D 0 d S A! -?? e8 -$D 0 d N ??T,$D 0 d s ,A" .??8 .$D 0B d s *޽h ? 3333 hX(  hv h N ??S h s ,A# 0??P@`8 0$D0v h N ??88 h S A$ 1??P Pp8 1$D0B h s *޽h ? 3333/ u/m/2>l /(  l l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif ,$D 0 l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$,$D 0y   l j ,$D 0 l T ??* l  ` c ??* ^ . "  | l  `h ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " # " ' l  `o ??* ^ . "   l T ??*  l  `t ??* ^ . "  S  l  `y ??2* )Newman projection of chair cyclohexane. L) '& " # "   l  ` ??*2 ^ . "   l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif ,$D 0  l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$,$D 0y  l j ,$D 0 l T ??* l  ` ??* ^ . "  | l  `d ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " # " ' l  `` ??* ^ . "   l T ??* l  `@ ??* ^ . "  S l  `Л ??2* )Newman projection of chair cyclohexane. L) '& " # "  l  ` ??*2 ^ . "   l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif ,$D 0 l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$,$D 0y  %l j ,$D 0 l T ??* l  `ԧ ??* ^ . "  | l  ` ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " # " '  l  `4 ??* ^ . "   !l T ??* "l  ` ??* ^ . "  S #l  ` ??2* )Newman projection of chair cyclohexane. L) '& " # "  $l  ` ??*2 ^ . "   'l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif ,$D 0 &l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$,$D 0y  0l j ,$D 0 (l T ??* )l  ` ??* ^ . "  | *l  `| ??* RChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. LR P& " # " ' +l  `x ??* ^ . "   ,l T ??* -l  `X ??* ^ . "  S .l  ` ??2* )Newman projection of chair cyclohexane. L) '& " # "  /l  ` ??*2 ^ . "   2l S A%t ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex2.gif ,$D 0 1l S A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gifv1$,$D 0 =l N ??G2G,$D 0 l T ?? @ ,$D 0 QChair and boat conformations of cyclohexane. Hydrogen atoms omitted for clarity. .R 2P 'B l s *޽h ? 3333 php(  pv p N ??  p s A&t ?http://www.uis.edu/~trammell/organic/alkanes/cyclohex.gif ,$D0L p T ?? P0,$D 0 (Newman projection of chair cyclohexane. .) 2' B p s *޽h ? 3333 tV(  t t N\??:,$D0 The cyclohexane ring has two different kinds of hydrogen atoms. In the chair conformation the six hydrogens pointing perpendicular to the ring are designated axial and the six hydrogens near the plane of the ring are called equatorial. (0x2 ^ R 3 ' N!0O!0v t N ??S t S A't ?http://www.uis.edu/~trammell/organic/alkanes/cyclhex4.gif ,$D 0B t s *޽h ? 3333q !x(  x& x Th ??,$D 0 nUSSNs]p (  2v x N ??A x s ,A( P?? 8 P$D07 x T ?? ;,$D 0  These two conformations are not equivalent in energy. The equatorial conformation is more stable than the axial by 7.5 kJ mol-1. This energy difference corresponds to an equilibrium mixture composed of 95% equatorial methylcyclohexane at room temperature. <02 B x s *޽h ? 3333G |(  |v | N ??0 | s A)r ?http://www.uis.edu/~trammell/organic/alkanes/mec6-2a.gif> ,$D 0 | T| ??P @`6,$D 0  The stability of the equatorial isomer relative to the axial is attributed to steric strain due to interaction of the axial methyl with the axial hydrogens on C-3 an C-5. 02,S= B | s *޽h ? 3333 V(  &  T( ??  ,$D 0 nYSNs]p (  2v  N ??  s A*t ?http://www.uis.edu/~trammell/organic/alkanes/dimec6-c.gif3,$D 0v  N ??M  S A+t ?http://www.uis.edu/~trammell/organic/alkanes/dimec6-t.gifp#,$D 0B  s *޽h ? 3333 f^(  v  N ??_V_  s ,A, Q??`-8 Q$D0.  Tl3 ?? ` ,$D 0 vf z-1 2-N2uWs]p S-1 2-N2uWs]p 4 23333333333333333333333333t  T> ??@ : ,$D 0 > 5226.4KJ/mol 5220.1KJ/mol6?(2>'$ B  s *޽h ? 3333  >(  v  N ??:  S A- R??@p 8 R$D 0B  s *޽h ? 3333p  0(  (  TM ??G,$D 0 p \ ~ . 2  T0Q ??p\,$D 0 :1 s]pYCQSNirg3z[ga/fe-SNWgYvga0 j02 $   TX ??0  ,$D 0 82 s N g N TSNWe 'YSNW(We.vga3z[0 j02$ B  s *޽h ? 3333f P(     `A. y??? `8 y$D 0   fA/ z? ??P\ 8 z$D 0   fA0 {? ?? 0 8 {$D 0B  s *޽h ? 3333 `1(  &  T ??@ `,$D 0 n 'YsSO| , 2  N??I,$D 0 ) Rings made up of seven and eight carbon atoms, called medium rings, possess steric strain due to van der Waals interaction with nonbonded atoms. The floppy nature of these medium rings can be shown by examining models of their conformations. Large ring systems are also possible. Muscone, a natural product found in the scent gland of the musk deer, is used in musk perfumes and fragrances. This molecule possesses a 15 membered ring. 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8 P$D 0 x TdJ  ??  ,$D 0 ? 02B x s *޽h ? 3333  ___PPT10 +X~D ' = @B D ' = @BA?%,( < +O%,( < +D ' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xD' =%(DM' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B-randombar(horizontal)*<3<*xD' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-6B%slide(fromBottom)*<3<*x+p+0+x  ++0+x  + K0   ` (    c $; 33 ?  2 d  c $; 33P,$D  0 .s^a g)RN-CH3YNe.vga(ORga)06 T  c $h; 33<,$D 0 h [gaRg]Z&  BAI ?d?pQ8 $D  0  c $x; 33p > 2 j  c $L; 33,$D  0  ^.ޏ\O(u NSW [NSW F 2FA  c $,; 330 `P ,$D  0 <s^O.2uWs]pkvz.2uWs]p3z[7.1 kJ/mol 2   c $^33  ,$D  0 p2) NSNs]pvga 2     0AJ ?? 8 $D  0H  0޽h ? ̙33@8___PPT10+7$D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(DE' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%strips(downRight)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DA' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-}6B!slide(fromLeft)*<3<* ++0+9  ++0+9  ++0+9  ++0+9  ++0+ 9  +2+K0 9 1  (    c $X; 33 a  2    c $9 33 ,$D  0 0Ջkz_TS_ 1,4-N2uWs]pv3z['`002$    0AK ??`pp 8 $D 0  0AL ??@8 $D  0  0AM ??X 8 $D  0,  c $D 9 330 A,$D 0  ea.WJ 0P2&     c $x9 33  ,$D 0 ee.W:0P2  c $ 9 33   ,$D 0 taa.W,0P2  c $9 33 ,$D  0 D 2uWee.W_gSOk2uWea.W_gSO3z[0V# 2 @ H  0޽h ? ̙33!!___PPT10a!+{D- ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D?' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-{6Bslide(fromTop)*<3<*D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* ++0+  ++0+  ++0+  ++0+   ++0+   +!K0  i(    c $B 33 a  2    c $B 33,$D  0 `[] 2  c $PB 33Mpm,$D  0 ,1. cQ NRga_gSO-NTN*N/fORga0 2s  0AN ??8 $D 0  0AO ??` ]8 $D  0  0AP ?? 8 $D 0  0AQ ?? 8 $D 0   c $tB 33  ,$D  0 b ORga 2  H  0޽h ? ̙33___PPT10z+xVD' = @B Dq' = @BA?%,( < +O%,( < +D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D?' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-{6Bslide(fromTop)*<3<*DR' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DC' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-{6Bslide(fromTop)*<3<* ++0+B  ++0+B  ++0+ B  +  |(  |v | N ??0 | s A)r ?http://www.uis.edu/~trammell/organic/alkanes/mec6-2a.gif> ,$D 0 | T^  ??P @` ,$D 0 > 02B | s *޽h ? 3333C ; ___PPT10 ++D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*|D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*|D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*|D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*|+8+0+|  + @8(  X  Tz  ?? ,$D 0 5.5sSTirvzS_gF(2'     0  T  ?? ',$D 0 x NCQs::(2#v  N ??PYP  S A2 |??P 8 |$D  0B  s *޽h ? 3333  ___PPT10 +=DDe ' = @B D ' = @BA?%,( < +O%,( < +DW ' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D1' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-m6Bbox(in)*<3<*+p+0+  ++0+  +G7K0 c [   (    c $L33 a  2    c $D33,$D  0 XAS"lS 2  0AR ??`P8 $D  0  0AS ??@^8 $D  0   c $`)330 P,$D 0 Ns[4.4.0]xvp& 2 $  <AT ?d?0 8 $D 0  <AU ?d?F  8 $D 0   s *hZ33q ,$D 0 hz_. 2&   s *`f33@ ,$D 0 XS_ 2&   0AV ?? 0~8 $D  0   c $k33@ ,$D   0 `z_ gga_gSO 2    c $8q33 `,$D   0 f S_ega_gSO 2  H  0޽h ? ̙33t,l,___PPT10L,+D*' = @B D*' = @BA?%,( < +O%,( < +Du' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-u6Bwipe(right)*<3<*D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-{6Bslide(fromTop)*<3<* D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<*%(!/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D' =%(DL' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-{6Bslide(fromTop)*<3<* D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<*%(+/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D\' =%(D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +P+0+B  ++0+B  ++0+ B  ++0+ B  ++0+ B  ++0+ B  + K0 (    c $ 0 33 ?  2   0AW ??Ppd8 $D  0  0AX ??p\ 8 $D  0  0AY ??P 8 $D 0H  0޽h ? ̙33  ___PPT10 +D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+R TL (  L  TH  ??p`0,$D 0 5.6spv6Rl @  2    P  T@  ??` ,$D 0 1. eSTirR"l B  2 v  N ??  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