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 



(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 + IT) 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 Jamina, so that for an arbitrary 

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



P= ^-pqjl (10)*, 



or { &quot; 



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. 



/ 



^ 



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



* Kirchhoff, 1. c. ante p. 102 ; Lord Rayleigh, &quot; On the Resistance of Fluids,&quot; 

 Phil. Mag., Dec. 1876. 



