14 president's address— section a. 



On the other hand, the use of the Principle of Least Time appears to 

 rest on the assumption of an underlying uniform period in t in the 

 four-dimensional continuum. The question can be discussed from 

 another point of view by looking on the light path as the limit of an 

 orbit. 



The equations arising from hfds = are ; — 



ids) ^ ids) ^ r ^ r' 



ds 



ds 



y -r = ^• 



From these equations we derive 



By the Principle of E(|uivalence, for a light path 



(0 



'^'dt^^'-y <^^ 



where a = h/k. 



The differentia] equation of the path is found from equations (1) 

 and (2). 



On elimination of t by means of (2), (1) becomes 



(1)' + ""•-■/.■ 



Kdcf>J 



where u = 1/V. 

 This leads to 



For a ray grazing the sun m is always less than [697,000] "^ and 

 m = 1 47. Therefore the ratio of 3nin^ to u is of order 10 "I 



Conseciuently we can use approximate methods of solution. If 

 u = A cos cf) is the first approximation, the second is 



u = ^cos.^ 4-|w^^'[3-cos2</,] (3) 



