xxxiv 
EXAMPLES TO THE THIRD SERIES. 
If the centre of gravity G be in the middle between P and Q, and if 
W = weight of the rafter between P and Q; then if Ec = 1-00, we 
have 
Pressure upon P in the direction E6 = X W (5) ; 
Pressure upon Q in the direction Ea = Ea X W (6) ; 
or twice those pressures, if the rafters are continued to the purlin P', 
and to a purlin Q', at the same distance apart, from P towards C. 
In Figs. 8 and 10, the pressures upon P and Q, arising from the 
WEIGHT OF THE ROOF ALONE, are in the direction of the depth only; 
therefore the scantlings may be found by the First or Second Series 
of Tables. Scantlings fixed by the rule derived from Fig. 4, so as to 
have one pressure only, and that in the direction of the depth, should 
be firmly secured at each end in the required position, with only the 
one bearing surface in contact with AC as shewn in the figures; other- 
wise, the pressures being changed, the equilibrium of the whole will 
be thereby destroyed. 
When ICE is parallel to BA, the position of P is the same as in 
Fig 5 ; but the position of Q not being at right angles to EA, Q in Fig. 
5 is subjected to two pressures p and q, as shewn in the figure; and the 
scantlings for Q to sustain such pressures, may be found by the Table 
page xxxviii., or by the Third Series of Tables. 
To measure the relative pressures, it will be convenient to set off 
Ec = 1 inch, the inch being divided into tenths, or set offEc = 10 feet 
from any scale ; then the various lines in any of the parallelograms 
Fiacb, measured by the same scale, give the relative pressures upon P 
and Q; which relative pressures being multiplied by the weight of AC, 
the actual pressures upon P and Q are given in the several direc- 
tions. 
In Fig. 5, Ec = I'OO, represents the vertical pressure p upon Q; and 
ca = Fib, the pressures q and q'. 
In Fig. 6, Ec being I'OO, Ec? is the measure of the vertical pressure p ; 
Ee is the measure of the vertical pressure p' : 
and da = eb is the measure of the pressures q and q' . 
Since p + j^' = Erf + Ee = Ec ; the sum of the vertical pressures upon 
P and Q, is always equal to the weight of AC. 
In Fig. 9, the purlins P and Q are fixed at right angles to the back 
of the rafter, and are supposed to sustain the whole pressure of the 
roof, in the directions E6 and CA. 
If Ec represent the weight of the rafter between P and Q, then 
