\magnification=\magstep0

Time for journey with-and-against the wind
$$
\eqalign{
{ {D}\over{v+u} } + { {D}\over{v-u} } \quad &= \quad
    {{D (v-u) }\over{(v+u)(v-u)} } + { {D(v+u)}\over{(v+u)(v-u)} } \cr
 \cr
                                            &= \quad
    {{D (v-u) }\over{v^2-u^2} } + { {D(v+u)}\over{v^2-u^2} } \cr
 \cr
                                            &= \quad
    {{Dv - Du }\over{v^2-u^2} } + { {Dv + Du}\over{v^2-u^2} } \cr
 \cr
                                            &= \quad
    {{2Dv}\over{v^2-u^2} }  \cr
}
$$



Time for journey across the wind
$$
\eqalign{
{ {D}\over{\sqrt{v^2-u^2}} } + { {D}\over{\sqrt{v^2-u^2}} } \quad &= \quad
    {{2D}\over{\sqrt{v^2-u^2} } }  \cr
}
$$

$$
{\rm if \ }\epsilon \ll 1, \qquad\qquad 
{ {(1 + \epsilon)}^p } \quad \simeq \quad { 1 \thinspace + \thinspace \thinspace p\epsilon  }
$$



Time for journey across the wind (again)
$$
\eqalign{
    {{2D}\over{\sqrt{v^2-u^2} } }  \quad &= \quad
    {{2D}\over{\sqrt{v^2 (1 - { u^2 / v^2 }) } } }  \cr
  \cr
                                   \quad &= \quad
    {{2D}\over{ v \sqrt{ (1 - { u^2 / v^2 }) } } }  \cr
  \cr
                                   \quad &= \quad
    {{2D}\over{ v } }  { (1 - { u^2 / v^2 }) }^{-1/2}     \cr
}
$$

\medskip 
Time for journey with-and-against the wind (again)
\smallskip
$$
\eqalign{
    {{2Dv}\over{v^2-u^2} }   \quad      &= \quad
           {{2Dv} \over { v^2 (1 - {u^2 / v^2}) } } \cr
  \cr
                                        &= \quad
           {{2D} \over { v}} { (1 - {u^2 / v^2})^{-1} }  \cr
}
$$


$$
\Delta t \quad \simeq \quad 3.7 \times 10^{-16} \quad {\rm seconds} 
$$

$$
\Delta t \quad \simeq \quad 7.3 \times 10^{-16} \quad {\rm seconds} 
$$

$$
\eqalign{
{\rm wavelength\ \ } \lambda \quad &\simeq \quad 550 {\rm \ nm}  \cr
{\rm frequency\ \ } f \quad &\simeq \quad 5.45 \times 10^{14} {\rm \ Hz} \cr
}
$$


\bye
