E L A 



2. Elasticity and resistance of solid materials. 



Here we suppose that all solid bodies may be considered as made up of 

 elastic fibres capable of extension and compression ; and that the resia- 

 tance to extension is proportional to the extension in each fibre. 



When a solid body is acted on by any 

 force, it may be partly extended and 

 partly compressed. Thus let a mass 

 A B Q P be acted upon by a force F 

 .compressing it in the direction EF. 

 The surface P N Q may be brought in. 

 to the direction p N q j in this case all 

 the fibres R R' which are on one side 

 of N are shortened ; all those on the 

 other side of N are lengthened. N N' 

 remains the same as in the natural 

 State. N is called the neutral point ; 

 and the line which separates the parts fT ^ 



of the body which are compressed from those which are elongated is call- 

 ed the neutral line. 



1. When a rectangular prismatic mass is compressed by a force paral. 

 lei to the direction of the axis : to find the neutral line. 

 Let P M = M Q = cr, M F = h, M N n, then 



Cor. 1. If h | a, n a, or the neutral point is in the surface, and 

 the whole beam is compressed. 



2. When a rectangular prism is acted upon by any force in any direc- 

 tion ; to find the neutral point at any part. 



Let a force/ act in the line y F on a prism A B P Q, then the same no, 

 tation being retained, we have as before 



Cor. If the force act perpendicularly to the axis, A is infinite, n = o, 

 and the neutral point is in the axis. 



3. When a rectangular prismatic beam is made to deviate a little from 

 a straight line by the action of a f*iven force perpendicular to it, to find 

 the deflexion, 



