FOR 



gravity (the rest as before), to find the velocity at any point of the do 

 scent, and the time of description. 



Here V = J 8 r - n ~ l x J 



\\ 



J -"^ 



71 r/ 2 r 1 + 1 P fi i- 



r^rrr X hyp. log. -JL-.-L^-glJLL- 

 3*-l / --3.v 



1 "" 1 e 8 u r 



Cor. 1. If or be increased sine limite, vanishes, and V 



fJIQgr. n 1 _ t j ie g rea test velocity that can be acquired by a spheri- 



3 

 cal body descending in a fluid. 



FLUID elastic. '-See Atmosphere. 



FLUXIONS. See Differentials. 



FORCES, the composition and resolution of. ( Wheu'ell,) 



\. If any two forces act at the same point, the force, which is equiva- 

 lent to the two, is represented in direction and magnitude by the diago- 

 nal of the parallelogram, of which the sides represent the magnitude and 

 direction of the component forces. 



Cor. If p and q be the component forces, which contain an angle 6, the 

 resultant will be V/> 2 -f- 2 p q cos. 8 -j- #2. 



2. Forces may be represented by lines parallel to their direction, and 

 proportional to them in magnitude. 



Cor. 1. If two sides of a A taken in order represent the magnitude and 

 direction of two forces, the third side will represent a force equivalent 

 to them both. 



Cor. 2. If three forces, represented in magnitude and direction by the 

 three sides of a A taken in order, act on a point, they will keep it at rest ; 

 and conversely. 



Cor. 3. If three forces keep a. body in equilibrium, and three lines be 

 drawn making with the directions of the forces three equal angles to- 

 wards the same parts, these three lines will form a A, whose sides will 

 represent the three forces respectively. 



Cor. 4. If three forces keep a point at rest, they are each inversely as 

 the sine of the ^ contained by the. other two. 

 121 G 3 



