Fer mat's Laic. 157 



If this is to be consistent with Fermat's law we must 

 have, for light propagation, 



T-V=C (constant) (1) " 



Later on, in §17, he says : — 



" Again, from the principle ot energy 



T + V=C (constant) (3) 



Therefore from (1) and (3) we get 



2T-C+0, 



2V=C'-C. 



But this is meaningless, since the mean potential energy 

 and the mean kinetic energy are alone constant, as these 

 quantities are understood to mean in the above equations. 

 Accordingly, the only conclusion that seems to be consistent 

 with all the equations is that the optical energy is entirely 

 kinetic." 



"Again, if the potential energy of deformation of the 

 sethereal medium involved in light propagation is to be 

 regarded as essentially kinetic, we are led to conclude that 

 all energy is kinetic/' 



3. For a statement of the principle of Hamilton to which 

 appeal is first made we may refer to Lamb's article on 

 Dynamics in the * Encyclopedia Britannica ' *. It is 



sTcT-VjrfteO, 



the time of transit being the same for the hypothetical as 

 for the actual motion, and the initial and final configurations 

 prescribed. But in Fermat's law we have 



f<fc=0, or oj^=0, 



where the co-ordinates are no longer those of particles of 

 matter as in Hamilton's principle, but successive points on 

 the ray as the light-wave travels along, and the velocity of 

 the ray is entirely different from the velocity of the indi- 

 vidual material particles whose motion constitutes the light. 

 Also, while the initial and final points are prescribed in 

 Fermat's equation the time of transit is not. 



* Eleventh Edition, p. 762. 



