56 



EXAMPLES. 



4. Let the body be a cylindrical pontoon,* with plane 

 ends, and having its axis horizontal. Required to find the 

 load requisite to sink the pontoon 

 to a given depth. 



Let AD be the intersection of the 

 plane of flotation with the end 

 which is a right section. Put A = 

 the area ADK, the plane surface of 

 immersion, and I = AB, the length 

 of the cylinder; and let W= the 



required load that will sink it to the depth HK. Then, 

 calling p' the density of the fluid, we have 



and 



volume of displaced fluid = Al, (I) 



weight of displaced fluid = gp'Al', 



.-. W = gp'Al. (2) 



A may be found as follows: let r = CK, and 6 = angle 

 ACK ; then we have, from mensuration, 



A = 



which in (2) gives, 



+ 8in2S 



'). 



135 + 1 



which is the required load. 

 COB. 1. If 6 = 165, we have, from (4), 

 IF = fcrpV 2 (V* + 1) I. 



(3) 



(4) 



(5) 



* Pontoons are portable boats, covered with balke, planks, etc., for forming 

 floating bridges over rivers. They are now usually made of tin, in the shape of a 

 cylinder, with hemispherical ends. (Tate's Mechanical Philosophy.) 



I 



