4l!^ THE STRENGTH 



Equation (2) depends on the equality of the 

 products of the forces multiplied by their 

 leverage. This may be expressed in a different 

 way thus: — if we suppose the neutral line AB 

 to be an axis round which the beam in bending 

 revolves, the weight W, multiplied by the length 

 of the beam to the part ACBD, must be equal 

 to the sum of the products of the forces of 

 tension and compression multiplied by their 

 distances from the neutral line, or 



W X length = F X F P +/' X P/. (3) 



In this theorem the form only is varied, for 



from equation (1), Y —f\ and since length = 

 G/, we have 



W X G/ z= F X (FP + P/) = F X F/, 

 as in equation (2). 



In the foregoing formulae, adapted as below, 

 equation (1) may be used to find the position of 

 the neutral line; and equation (2) or (3) may 

 either of them be taken at pleasure to determine 

 the strength of a body. 



6. To find values for the expressions in the 

 equations above, supposing the forces to be 

 as the extensions and compressions. Call PD 

 z= a, PC = h^ any double ordinate ah on the 

 surface of tension = X, its distance from AB 



