<P> The right - hand side of the two integral equations above are identical which means </P> <Dl> <Dd> c ∫ t t h e n + λ t h e n / c t n o w + λ n o w / c d t a = c ∫ t t h e n t n o w d t a (\ displaystyle c \ int _ (t_ (\ mathrm (then)) + \ lambda _ (\ mathrm (then)) / c) ^ (t_ (\ mathrm (now)) + \ lambda _ (\ mathrm (now)) / c) (\ frac (dt) (a)) \; = c \ int _ (t_ (\ mathrm (then))) ^ (t_ (\ mathrm (now))) (\ frac (dt) (a)) \,) </Dd> </Dl> <Dd> c ∫ t t h e n + λ t h e n / c t n o w + λ n o w / c d t a = c ∫ t t h e n t n o w d t a (\ displaystyle c \ int _ (t_ (\ mathrm (then)) + \ lambda _ (\ mathrm (then)) / c) ^ (t_ (\ mathrm (now)) + \ lambda _ (\ mathrm (now)) / c) (\ frac (dt) (a)) \; = c \ int _ (t_ (\ mathrm (then))) ^ (t_ (\ mathrm (now))) (\ frac (dt) (a)) \,) </Dd> <P> Using the following manipulation: </P>

The change in direction of the sun's light as shown here is an example of