75-76] 



BOKDA S MOUTHPIECE. 



105 



we have y = JTT, which shews that, on our scale, the total breadth 

 of the canal is 2?r. The coefficient of contraction is therefore J, 

 in accordance with Borda s theory. 



If we put docjds = cos 0, and therefore s = log sec %0, we get 



# = sin 2 10 -log sec J0, y = -%0 + sin0 (7), 



by means of which the curve in question is easily traced. 



Line of Symmetry. 



76. The solution for the case of fluid issuing from a large 

 vessel by an aperture in a plane wall is analytically very similar. 

 The successive steps of the transformation, viz. 



^ 1 = logf, #3 = cosh #! , w = log, (1), 



Z,-loff 5 



A T A 



-I 



