OP IRON BEAMI^. ^37 



thfe beams differed only in depth, we shall find, 

 that in these, the deflections are inversely ad 

 the depths ; for, the products of the depths and 

 deflections were equal in the two experiments, 

 since 4.1 x 1.14 = 6.93 x .67, very nearly. 



- This result seems to be natural, for we may 

 expect that iron of the same quality would 

 stretch the same portion of its length before 

 fracture ; and, consequently, the ultimate deflec- 

 tion would be inversely as the distance of the 

 neutral line from the bottom of the beam: and 

 this distance must in the case before us be nearly 

 as the depth. 



2nd. — For the ultimate deflection in terms of 

 the length. The mean deflection of the beams 

 in experiments 15, 18, and 20, (in which the 

 span was 4 feet 6 inches, and depth 5f inches),' 

 was .51 inch; and in experiment 24 (where the 

 Span was 7 feet, and the depth 5.2 inches, nearly 

 same as the others), the deflection was .79 inch. 

 Hence the ultimate deflection in these was 

 simply as the length; for 4 feet 6 inches : 

 7 feet :: .51 : .79 inch. ^ 



Supposing the ultimate deflections to he 

 inversely as the depth when the length is the 

 same, if we reduce the deflections in experi- 

 3 Y 



