77-78] RESISTANCE OF A LAMINA. 109 



must multiply by dx and integrate between the proper limits. 

 Thus since, at the face of the lamina, 



we find 

 i 



(9). 



This result has been obtained on the supposition of special 

 units of length and time, or (if we choose so to regard the matter) 

 of a special value (unity) of the general stream-velocity, and a 

 special value (4 + 7r) of the breadth of the lamina. It is evident 

 from Art. 24 (7), and from the obvious geometrical similarity of 

 the motion in all cases, that the resultant pressure (P , say) 

 will vary directly as the square of the general velocity of the 

 stream, and as the breadth of the lamina, so that for an arbitrary 

 velocity q Q , and an arbitrary breadth I, the above result becomes 



or '4tQpq Q z l. 



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

 say, with its plane, the problem is altered in the manner indicated 

 in the figures. 



11' 



A' 



r 

 The first two steps of the transformation are the same as before, viz. 



* Kirchhoff, I. c. ante p. 102 ; Lord Eayleigh, "On the Resistance of Fluids, 

 Phil. Mag., Dec. 1876. 



