CONSTRUCTION OF THE TABLES. 
EQUATIONS BY WHICH THE TABLES ARE CALCULATED. 
Throughout the Tables, the standard values of S and E for Red Pine 
are, — 
« = ^ = >3-- 
E = —— = 230000. 
If the weight W be uniformly loaded, and L be the length in feet, we 
V 1 184000 bS ) ^ ' 
and if W = weight in lbs. upon each foot in length, and S = ^ of an 
inch to the foot, 
fc3/(_!L. X W (2): 
V 1 4600 b j 
by which equation Tables I. to XXVI. in the First Series are cal- 
culated. 
In equation (2), W is assumed successively as follows, viz. : 
Tables I. to XIV 2^; 2-53; 33; 3-53; 7-53; 83; and in 
Tables XV. to XXVI., 93; 103; IP; 123; 133; 193; 203; 
the depths throughout the tables for the same values of b and L are 
therefore in arithmetical progression. 
In the Tables, the weight in lbs. upon each foot in length is, in 
Tables I. to XIV., as above, viz F; 23; 2-53; 33; 7-53; 83; and in 
Tables XV. to XXVI., 93X40X8'; 103 X 40XS'; 203X40XS'; 
in which 8' = 3% ; T^^, respectively. 
Since the breaking weight in lbs., uniformly loaded, of a scantling of 
the standard strength 1344, is -y—= (suppose) MXWXL, we have 
M = ^ (3) 
Substituting in (3), the value of in (2), we have M=c' X^ -i^; there- 
fore the multipliers M are independent of d and L. 
In Tables I. to XIV., M for the same value of b is in arithmetical 
progression, and in Tables XIV. to XXVI. constant throughout. 
