8 DeVVitt B. Brace, 



V, must be very small. Neglecting squares of small quan- 

 tities, we have 



P 



(9) 



p'v 2 7r r 



2 «^ aX^ ' 

 putting for / its value 



2 TT 2 rra 



A very small change in the velocity may produce an ap- 

 preciable retardation of different rays for very great distances. 

 Expressing 7 to the next order of approximation, we have on 

 expanding 



0/0 



neglecting small quantities of higher orders than k-. Since 

 /c is a very small quantity, we may put 



w 



K = — , 



y 



where j is a large quantity, and zv has different but not large 



values. Putting 



y = Vt' = at, 



and substituting, we have 

 or 



/ 

 .'. t — t' = , nearly. 



(10) 



This shows that the relative retardation of the different 

 rays due to viscosity is too small to be observed, even when 

 the time /, necessary for light from the most distant visible 

 object to reach us, is very great. 



8 



