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



Table III. 

 Fringes behind the cylindrical " edge." 



n. 



x n x x 

 in uams. 



y=0'l cm. 



y=Q-3 cm. 



y=0'5 cm. 



?/=0'7 cm. 



Obsd. 



Calcd. 



Obsd. 



Calcd. 



Obsd. 



Calcd. 



Obsd. 



Calcd. 



2 





0-0159 



00158 



0-0250 



00251 



0-0341 



00326 



0-0370 



0-0370 



3 ... 





0-0284 0-0284 



0-0439 



00450 



0-0580 



0-0580 



00660 



0-0661 



4 ... 





0-0385 0-0390 



0-0600 



00609 



0-0776 



0-0782 



0-0887 



0-0897 



5 ... 





0-0483 0-0480 



00740 



0-0750 



0928 



0-0938 







6 ... 





0-0568 00570 



00867 



0-0879 



0-1116 



0-1134 







7 ... 





00651 ;0-0650 



00990 



0-0997 











8 ... 





00715 |0-0723 



0-1108 



0-1110 











9 ... 





0-0794 0796 















10 ... 





0-0862 



0-0863 















The agreement between the calculated and the observed 

 values is very close and confirms the theory. 



4. Hie Loci of Maxima and Minima of Illumination. 



These curves have an interesting property which may be 

 briefly considered here. The equation to the loci is obviously 



r(l— cos20)=m\/2 or r6 2 = m\/4z approx., . (14) 



where r is the distance o£ the point from the surface of the- 

 cylinder, measured along the reflected ray which passes 

 through the point. The shape of the curves is indicated by 

 the thick lines in fig. 4, for the case a = 5 inches, X = 0*016 

 inch, X being taken so large for convenience of representation 

 to scale ; only the first, third, fifth, &c. loci are drawn. 



The equation to the loci can also be got in terms of and 

 x or y. Thus on eliminating y from equations (3) and (4)< 

 we get 



m\ aO 2 , H _ 



"' = W~"2~' (i5) 



which gives the abscissae of the points at which the loci cut 

 the straight lines = const. The ordinates of these points- 



