EXAMPLES TO THE THIRD SERIES. 
XXXV 
E6, and bd = da are the pressures to be sustained by each of the 
purlins P and Q ; the pressures being twice those, if the rafters are 
continued as in the description to Fig. 10. 
When BC = AB, as in the figure, then = E6; the purlins are 
square, and the scantlings are found by Table VI. in the Third Series ; 
or by Col. X. page xxxviii. 
When BC = \ AB, then 6c? = J E6 ; the sides of the purlins are to 
one another as 1 to or as 10 to 7'07, and the scantlings are found 
by Table IV. Third Series, or by Col. VII., page xxxviii. 
In Fig. 11, the purlin P is at right angles to the back of the rafter, as 
in Fig. 9. cb represents the weight of the roof acting vertically, and 
ac the force of the wind acting at right angles to AC ; completing the 
parallelogram Eac6, Ec is the position of a purlin to resist the two 
pressures be, ac, acting together, so as to have only one thrust, and 
that to be in the direction of the depth of the purlin ; P being the 
position to resist with greatest effect the pressure from the wind alone, 
and Q the position to resist the weight of the roof alone. 
When the two forces act together, Ec? is the pressure upon P in the 
direction ac, and dc is the pressure upon P in the direction dc. In 
like manner Fc' = a'd' -\-b'c' is the pressure upon Q in the direction 
Fc' ; d'c' the pressure upon Q in the direction d'c' ; and by dividing the 
least pressure by the greatest, the scantlings may be found by the Third 
Series of Tables, or by the Table before referred to at page xxxviii. 
THE THIRD SERIES OF TABLES; 
By which maybe found the Scantlings of any description of Timber, to 
have given equal deflections when acted upon by two forces ; viz., 
one in the direction of the depth, the other in the direction of the 
breadth. 
The pressures upon a brest-summer or purlin being ascertained or 
given, and the deflection with those pressures assumed, the scantlings 
are found by the Third Series of Tables. 
If the assumed deflection be the tabular deflection, the scantlings are 
given by inspection of the tables. 
If the assumed deflection be less than the tabular deflection, the 
scantlings are found by means of the expression — at the foot of each 
table. 
