98.] IMPACT OF STREAM ON A LAMINA, 109 



and (66) by 



(68). 



Multiplying (68) by p, and eliminating &amp;lt;f) , we obtain for the total 

 excess of pressure on the anterior face 



IT?^ ........................... (69) - 



If the stream be oblique to the lamina, making an angle a with 

 its plane, the condition (a) is replaced by 



f=e-* for &amp;lt;/&amp;gt; = +*, 

 which gives 



A : G= cos a 1 : cos a + 1 ; 



(b) is unaltered, whilst (c) is no longer applicable, there being no 

 longer symmetry as regards the line ^ = 0. The former conditions 

 however reduce (63) to the form 



which shews that the value of the remaining constant K only 

 affects the scale of w. If we assign to it any real value, we make 

 the cusp f = 1 of the lune in the plane of f correspond to some 

 definite point of the boundary in the plane of w. The simplest 

 assumption is K= 1, which gives, after some reduction, 



f=cosa + - + A/ (cos a H ) -1. 



*Jw V \ vW 



For the discussion of this result, and the calculation of the result 

 ant pressure on the lamina we must refer to the paper by Lord 

 Rayleigh, already cited (I. c. Art. 96). 



