26 Mr. T. K. Chinmayam on the Flow of 



and this varies from point to point along each line of flow, 

 being a maximum and a minimum respectively where it cuts 

 successive curves 2r0 2 =fnX/2. This variation of the current 

 of energy along its own line of flow can be explained only 

 .as due to the change in cross-section of the tube of flow 

 formed by two lines of flow close to each other. The con- 

 ception of energy as flowing through tubes must therefore 

 give us a better idea of what happens in the field. 



The curves which are at every point normal to the lines 

 of flow, i. e. the curves analogous to the equipotential curves, 

 can easily be obtained. For these curves 



n 

 1-2/ccos-2?'<9 2 + k 2 



tan (f>= '- fcomp. eq. 18). 



26( f c 2 -,ccos n 2r6 2 ') 



The differential equation in terms of 6 and r is found to be 

 {dr-ad0) + ~^cos-2r0*[(a-2r0)d0--dr'] = O (approx.). 



In the immediate neighbourhood of a point, we can as 

 before leave out all variations other than the periodic one 

 and integrate. Then we get 



2k x . ir m [a-2r l 6 l 1 ~| 

 r — a&+ — „sin- 2r0 2 — — = const., (27) 



1 + Kl c L 4*0- 20*~ J 



c c 



which cuts the successive loci of maxima and minima of 

 illumination at points lying on the curve 



r-aO = const., (28) 



which is hence the mean curve about which the actual curve 

 crinkles round. In the rectangular coordinates (#, ?/), 

 •equation (28) becomes approximately ?/ = const., i. e. the 

 mean curves are nearly straight lines parallel to the #-axis. 

 One of these curves is shown in fig. 6 in relation to the lines 

 of flow and to the loci of minimum illumination. Suppose 

 it cuts two successive minima loci at points A and B. Then 

 by (27), there is one complete crinkle between A and B. 

 Consider the tube of flow bounded by the lines of flow 

 which pass through A and B. Since the flow of energy 

 •should be everywhere normal to the wavy curve AOB, 



