Energy in an Interference Field. 295 



the abbreviations C l5 C 2 of § 1) 



p 2 opp p 2 p 2 9P p p 2 



r*! 2 r^a ?* 2 «V ?V*2 r 2 



=2{% 2 +% 2 + ^ C l + cos^)]. 

 ( rx 2 ?- 2 2 r ml r s v y j 



The time mean of this quantity is, by § 1, proportional to 



The truth of the above statements is seen at once from this 

 expression. 



§ 3. The general course of tlie mean energy curves (course oj 

 the beam). 



It is seen from the " microscopical " equation of the 

 energy curves that the points on an energy curve for which 

 r 2 — Ty — mir all lie on the straight line 



r i{pi + pi cos 0) — 1\ (pi 4- p 2 cos 6) + const., 



and the energy curve winds back and forth across this line. 

 The " general direction *' of the energy flow in the neigh- 

 bourhood of the point r 1: r 2 is therefore given by 



dr 2 _ r-f + r 2 2 cos 6 

 di\ r^ + r^ cos 6* 



This is also the general direction of the set of curves of 

 fig. 4, as a whole, i. e. the direction of the "beam/' Now 

 this is exactly the differential equation that would be derived 

 from the expression for S in § 1 if the terms involving 



cos — - (r 2 — )\) were not present, i. e. it is a curve which is 



A, 



tangent at each point to the vector 



But this vector represents the velocity produced in an 

 infinite liquid by two equal sources at A x and A 2 . The 

 " general course" of a curve of mean energy flow {course of a 

 " beam ") is therefore that of a line of flow of an incompressible 

 fluid, produced by two equal sources at A r and A 2 . 



