OF THE IRK, LOCOMOTIVE ENGINE. 519 
Let W=the given weight in pounds. 
a=length of the beam, in feet. 
b=its breadth, in feet. 
e=its depth, in feet. 
Let A B B' c A‘ represent any lamina of the beam, parallel 
to its plane of deflexion; and let acb be the line, which passes 
through the centre of pressure of every part of the beam. 
Let aCb be the position of ach before the deflection of the 
beam. 
Through ¢ draw erd parallel to bCa, and though « draw xy 
perpendicular to cd, meeting the curve beya, in y. 
Let ¢ be the origin of the co-ordinates ; 
and let z=ca, 
Y=ury. 
