IMP A CT. 1 79 



from which we find W^ = (1 -f- cos ) W, 

 and W z =i(l-cos) W. 



Substituting these values of Wj and PF 8 in (2), we have 



, (3) 



ivhich is the total impulse in the direction of the 

 stream. 



Dividing (3) by sin , we obtain 



CK = P cosec =.- ^ PTsin , (4) 



which is the normal impulse. 

 Multiplying (3) by cot , we obtain 



1J ___ 7? 



CS = P cot a = - - W sin cos 



V - ^tFsinSa, (5) 



which is the lateral impulse. 



Hence, /&e foto^ impulse in the direction of the 

 stream, is proportional to the square if the sine of the 

 angle of incidence, the normal impulse to the sine of 

 this angle, and the lateral impulse to the sine of 

 double this angle. 



Sen. If the oblique plane has no border, the water can 

 flow off in all directions ; in this case the impulse is in- 

 creased, for is the smallest angle which the filaments of 

 water can make with the axis, and hence every filament 

 which does not flow off in the normal plane will make with 

 the axis an angle larger than , and therefore from (3) will 

 exert a greater pressure than those which do. 



