FLU 



In a plane figure, 



Res. on base I that on the curve ". y ' fl. ~- 



And in a solid, 



Res. on base : that on the surface :: # 2 : fi. ---35 



l +7&* 



Ex. 1. Let the curve be a semicircle. 



Res. on base I res. on curve \\ y I y ^-^- t which, when y r> be- 

 comes as 3 : 2. 



Ex. 2. Let the solid be a sphere, 



Res. on base : res. on surface : : | y* '. | y* i 1 " ' * 2 I 1 wheny = r. 

 Hence resistance to a cylinder is double that of the inscribed sphere. 



Cor. Hence if n density of a globe, whose radius is r, and the speci- 

 fic gravity of the fluid be 1, 



R *r*v* lienv* 3v* 



and R' =. = ; -- = -- - - = ^r - ; or if ar space fallen 

 w 4>g 3 IGgnr ' 



through to acquire the velocity 



4. Let a sphere of given diameter be projected in a resisting medium, 

 whose specific gravity is to that of the sphere as 1 : n. Having given 

 the velocity of projection, to find the velocity of the sphere at any dis- 

 tance x y and the time of description. 



Let e = No. whose hyp. log. = 1, and suppose when x o, # = a, 

 then 



V 2ga 



5. Let a spherical body descend in a fluid from rest by the action of 

 120 



