294 Prof. Max Mason on the Flow of 



The equation then takes the form 



y sin 6{p2+pi cos 0) + .^^(cos 2 — 1) 



= _ ^- 2 (l + cos 0) sin 2tt[?/ sin (9~^(l-co.? 0)]. 



On introducing the parameter 



ol—u sin — <z(l — cos#), 

 the following parametric equations of the curve are ohfained: 



x = 



pip 2 (l + cos 0) sin 2nru (p 2 2 + pi 2 cos fl)« 



+ 



2tt(1-cos6>)( /)2 2 - /0i 2 ) (L-cos^C^ 2 -^ 2 )' 



_ /oip 2 (l + cos 0) sin 27r^ ^(l + cos flk 

 y ^rlm^W-Pi 2 ) sin% 2 2 -p 1 2 y 



The curves may be readily plotted from these equations. 

 The fio-ure (fig. 4) shows a set of curves of mean energy 



flow in the neighbourhood of the point for which p 2 /p l = 4:i3, 

 = tt/2. (The orientation of the set with respect to the 

 centres of radiation is shown in fig. 5, below.) The heavier 

 straight lines give the position of the interference minima, 

 lines given by r 2 —r 1 = const., or " microscopically," by 

 y cos + x(cos — 1) = const. The energy thus "crinkles" 

 through the field, tending to flow along the bright inter- 

 ference bands, and to cut across the dark bands. 



It may be noted that the variation of the energy in passing 

 from a bright interference band to a dark band decreases as 

 we approach the line A : A 2 between A x and A 2 , and there are 

 no interference maxima or minima on the line A 2 A 2 between 

 the sources of radiation. In fact, the energy is proportional to 



Ei 2 + 2(E 1 E 2 ) + E 2 2 + H^ 4- 2(H 1 H 2 ) + H 



2. 

 2 J 



the vectors have the values given in § 1, and the angle 

 between H x and H 2 is 0; so that the above quantity is (using 



