xiv 
CONSTRUCTION OF THE TABLES. 
THIRD SERIES OF TABLES. 
Let P = pressure, 8 = deflection in the direction of the depth ; 
Let Q = pressure, 8' = deflection in the direction of the breadth ; 
then from ( 1 ) 
from which we have 
X L^ 
X L^ 
(4), 
(5) 
which are general equations for determining the scanthngs to have any 
given deflections. 
If 8 = S' ; and Q — ?^.P ; 
^=(^)*x(l)* 
b = ^/^\d (7) ; 
by which equations the 6 Tables in the Third Series are calculated ; 
c being = ; P = pressure in lbs. upon each foot in length ; and 
8 = ^ of an inch to the foot, as before. 
P in (6), is assumed as are the terms of the progression, 
14; 24; 2-54; 34; 3-54; 44; 4-54; 54; 9-54; 104. 
In the Tables, in Cols. L to VL, P = H; 24; 2-54; 34; 3-54; 44; 
and in Cols. VII. to XVIII., 
P = 4-54 X 40 X 8'; 64 X 40 X 8' ; 104 X 40 X 8' ; 
in which 8' = -f^; -rs^ as before. 
Substituting the values of d and bin (6) and (7), in the equation 
]Vi = the multipliers M are evidently independent of b and d ; 
and in Cols. VI. to XVIII. constant for the same length. 
