CONSTRUCTION OF THE TABLES. 
XV 
The Second Series of Tables is calculated by the equation 
W= -——,= one-fourth of the breaking weight in cwts., suspended from 
Ij 
the middle (8). 
In the Miscellaneous Tables, 
I? 
Table I. is calculated by the equation b — (9). 
Table II. „ by „ S = '03287 X—.,. (10). 
d 
Tables III. to IX. inclusive, are formed from and by inter- 
polating the First Series of Tables. 
THEOREM. 
( Corollaiy from Equations, page xiii.) 
Let W = one-fourth of the breaking weight, uniformly loaded, of a scant- 
ling of the strength 1344, of which the length in feet is L, and 
depth in inches d. 
L5 = deflection of the same, when uniformly loaded with the weight 
c= deflection of a scantling 1 inch square and 1 foot long of the 
same strength, when uniformly loaded with one-fourth of the 
breaking weight : which for Red Pine is c=^-^. 
We have then the following relation, viz. : 
WhenW'=W, L = — (a). 
For Red Pine L = 30-423 X d8. 
If d = 14" and B = then L = 10-648. 
Therefore, if a Red Pine beam be 14 inches deep, and less than 10 feet 
7-77 inches long, the weight which produces a deflection of ^ of an 
inch to the foot, exceeds one-fourth of the breaking weight. 
