75-76] 



BOKDAS 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 dxfds = cos 6, and therefore s = log sec 0, we get 



x = sin 2 1(9 -log sec J0, y = -J0 + Jsin (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. 



21 = log f, -s^coshsj, w = logz. 2 ............ (1), 



A T A 



-I' 



