\magnification=\magstep2

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

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

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

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

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


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


\bye
