79] 



BOBYLEFF S PROBLEM. 



113 



The definite integral which occurs in this expression can be calculated from 

 the formula 



Tx+J*(i-i*)-i*(i-i*) ( vi )&amp;gt; 



i: 



where *() = d/dt.\ogU(t) 9 is the function introduced and tabulated by 

 Gauss* 



The normal pressure on either half is, by the method of Art. 77, 



rifl* 



dt 



sin ^nrr 

 2a 2 



^ ?r sin a 



The resultant pressure in the direction of the stream is therefore 



4a 2 



Hence, for any arbitrary velocity q Q of the stream, and any breadth b of 

 either half of the lamina, the resultant pressure is 



.(viii), 



where L stands for the numerical quantity (v). 



For a = TT, we have L 2 + 577, leading to the same result as in Art. 77(10). 



In the following table, taken (with a slight modification) from Bobyleff s 

 paper, the second column gives the ratio P/P of the resultant pressure to 





* &quot; Disquisitiones generates circa seriem infinitam,&quot; Werke, Gottingen, 187077, 

 t. iii., p. 161. 



L. 8 



