96, 97.] FLOW FROM A CANAL. 105 



The equations (61) and (62) combined give the form of the 

 boundary of the issuing jet. They are obtained in the above 

 manner by Lord Rayleigh*, who has also given a drawing of 

 the curve in question. 



Since s = log cos 0, the radius of curvature of the boundary 



ds 



is -571 = tan 6, and therefore vanishes at the edge. Kirchhoff has 

 do 



shewn that this is a general property of free boundaries. 



97. Example 11. Fluid escapes from a large vessel by a 

 straight canal projecting inwards. This illustrates one of the cases 

 of the tube, spoken of in Art. 31. 



An inspection of Fig. 8, giving the forms of the boundaries in 

 the planes of z, w&amp;gt; f, and of a new variable V will shew that 



Fig. 8. 



J 



this case may be obtained from the preceding by merely writing 

 V? for f, so that we now have 



dz 



=i 



2e- 2w -l + 2e-&quot;Je- 2w -l (63). 



* Phil. Mag. Dec. 1876. 



