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



Along the curve rO^-C, dr/cW= — r \d. Hence from (25) 



/da, 2 „ r 2 2ar 



[dO) = a +5i + -3-approx., 



aV_ r __ C 



If I be the " wave-length " of a crinkle, 



'-(a+g)w- (.+£)£, • • • (*> 



Q being the same, Z increases as # decreases, the rate of 

 increase getting larger as the absolute value of 6 diminishes ; 

 Z = co when = 0. Again, as we move away from the 

 cylinder to the right (fig. 1), both C and 6 increase so that 

 I decreases. These points are brought out in fig. 5. 



Turning back to equation (23), the lines of flow near the 

 point (r 1? 0l) are given by 



rO = C— yr - sin ilr... 



0, 47T Y 



The curves will obviously lie between the curves 



— &i 4:7T 



The deviation from the mean line r# = Cisiproportional to 



*i_ f ci •) * 



1 "\0(2r + a0)j ' 



As either r or 6 increases, this will decrease. The 

 " amplitude " of, these crinkles therefor© gets smaller and 

 smaller as r and 6 increase and the crinkles vanish at 

 sufficiently large distances from the cylinder. 



The shape of the lines of flow very near the surface of th& 

 cylinder is of special interest. The energy which comes 

 crinkling down successive loci of maxima and minima of 

 illumination, when it reaches the first maximum, flows down 

 in a smooth curve which will meet the mean line of flow 

 only at infinity. The energy does not crinkle along after it 

 has crossed the first maximum of illumination. 



It is thus seen that the introduction of a perfectly reflecting 

 cylinder into a field through which plane waves are passing 

 has the effect of (1) altering the general direction of flow of 

 energy, and (2) giving a crinkled microscopic structure to 



