F R I 



tience the value of a vanishing- fraction may bo found by differentia- 

 tion, as in the following examples : 



r 2 _ yt 



Ex. 1. Required the value of - when x . 

 rfP Zxtl-x 



Ex. -2. Required the value of ' ' __ ' . when x 1. f 



But if it so happen that on substituting a instead of x in -r^y this 



fraction also becomes , we must treat it in the same manner as the 

 o 



first, and so on, till we arrive at a value of which one term at least is 

 finite. 



p a a' 2 4- a c 2 2acx o 



Ex. Let TT = ~T -TV -- r~r- 5 > which = when x c. 

 O bxZ ^_ 2bcx -|- ic 2 o 



<f P 2 ao 1 2 c ... o 



Hcrc TQ = ^--gftc wluch also = V whcn * f r> 



But ^ = -7- which is the value of -^ in this case. 

 d*Q b Q 



FREEZING. See Congelation. 



FRICTIO N. (Play fair. ) 



The following must only be considered as a short abstract of the most 

 interesting general results on the subject of Friction, as deduced from 

 experiments made by Coulomb and others. 



1. The retardation which friction opposes to motion is nearly uyform, 

 or the same for all velocities. 



2. The force of friction is the greater, the greater the force with which 

 the surfaces, moving on one another, are pressed together, and is com- 

 monly equal to between | and of that force j but it is very little affect- 

 ed by the extent of the surfaces. 



M. Friction may be distinguished into two kinds, that of sliding, and 

 that of rolling bodies. The force of the latter is very small compared 

 with that of the former. 



I, Hie distance to which a given body will be moved by percussion in 



