\magnification=\magstep2

$$
t_r \quad = \quad t_1 + t_2
$$

$$
t_r \quad = \quad  t_b \gamma \quad = \quad t_b \thinspace 
        { {1} \over { \sqrt{ 1 - ( {{v^2}\over{c^2}}} )  } }
$$
       

$$
\eqalign{
t_b \quad &= \quad {{2 H} \over {c} }   \cr
\cr
t_r \quad &= \quad {{2 H} \over {c} } { {1} \over {1 - ({{v^2}\over{c^2}}) } } 
         \quad \neq \quad
             {{2 H} \over {c} } { {1} \over {\sqrt{1 - ({{v^2}\over{c^2}}) } }} 
  \cr
}
$$

$$
H \quad = \quad {H} \thinspace {\sqrt{ 1 - ( {{v^2}\over{c^2}}) } }  
        \quad = \quad {H} \thinspace { {{1} \over {\gamma} } }
$$
 

$$
L = v  {{1}\over{2}} {(\Delta t)}_{\rm red}
$$

$$
R \quad = \quad \sqrt{ H^2 + ( {{1}\over{2}}  v {\Delta t}_{\rm r} )^2  }
$$

$$
{\Delta t}_{\rm r} \quad = \quad  {{ 2 R }\over{c}} \quad = 
            \quad { {2 \sqrt{ H^2 + ( {{1}\over{2}}  v {\Delta t}_{\rm r} )^2  }} \over {c} }
$$

$$
{\Delta t}_{\rm r} \quad = \quad  {{ 2 H }\over{c}} 
            { {1} \over { \sqrt{ 1 - ( {{v^2}\over{c^2}}} )  } }
$$

$$
\gamma \quad \equiv \quad { {1} \over { \sqrt{ 1 - ( {{v^2}\over{c^2}}} )  } }
$$


$$
\eqalign{
{\Delta t}_{\rm b} \quad &= \quad {{2 H}\over {c}} \cr
\cr
{\Delta t}_{\rm r} \quad &= \quad {{2 H}\over {c}} \gamma \cr
}
$$


\bye
