APPLICABLE TO MATHEMATICS, &C. 373 



These conditions must be fulfilled in all ma- 

 terial bodies, in order that equilibrium may take 

 place. 



If the particles are, by the application of force, 

 compelled to assume the position x^ — h where h 



is a very small quantity, then the force ~-r^^— rcr 



will be called the force of elasticity of the body. 

 And if the compressive force is equal to the 

 tensile at any distance h of compression and 

 extension we must have 



F(.ri+^) _ _ F(^i-^) 



Develop these by means of Taylor's theorem 

 and we have 



F{x,)-\-Y(xi)h+F(x,)h'+&c. -F(x,)-^-F(x,)h-F{x,)h'+&c. 



1-2 ^ 1-2 



(x,+hy (x,-hy 



By the binomial theorem we have 



(x,+A) " = .r, '-2.r ^.A-|-&c. &c. 



(x^-h) '=x,~'+2x ^.h+&c.&c. 



