EXAMPLES TO THE THIRD SERIES. XXXvii 
Example 19. — The data in other respects being the same as in the 
last Example, — Required the ScantUng of the Brest-summer Q, 12 
feet long, to support the same pressures, and deflect each way of an 
inch. 
P= 12 X 12-25= 147 cwts.; 0=^%. 
P 147 
= -7" = 147 X 10 = 1470 cwts. uniform pressure. 
To" 
By Col. XIV. p. 120, — = 1462-85 cwts. Scantling, 14-28 X 14-28. 
If the same pressure be in the middle of Q, — 
By Col. XVI. ~ = 1464-50 cwts. Scantling, 16-06 X 16-06. 
Example 20. — Required the Scantlings, for any given length, of the 
Brest-summer Q, Fig. 6. 
Having drawn the figure, let the relative pressures measure as fol- 
low, viz. : — 
Ec = 1-00 ; Ed = -60 ; dc = -40 ; da = eb = -22. 
Pressure p = F,d = -60; pressure q = da = -22, 
Least pressure g "22 
G7^i^;S^s-^=7 = -60 = *^^' scanthngs are given by Table III. 
If the pressure upon Q be uniform, and the weight of AC be 9-9 cwts. 
to the foot, the greatest pressure {p) upon 
Q =z -60 X 9-9 = 5-94 cwts. to the foot. 
The scantlings are given by Col. IX. p, 107. 
If the length be 1 0 feet, the scantling is 9-73 X 5-84. 
If the length be 11 feet, the scantling is 10-45 X 6-27. 
Deflection each way, -/y of an inch to the foot. 
Breaking weight, upwards of 7 times the pressures upon Q. 
X 
Example 21. Fiff. 6.— Let the weight of AC, resting upon the middle 
of Q, be 80 cwts. Length of Q, 12 feet ; Deflection of Q each way, ' 
of an inch. Pressures as in the last Example. 
The greatest pressure {p) upon Q, is Ed X80=-60 X80 = 48 cwts. 
P = 48 cwts. D = i . 
P 48 
'^ — 'Y~ '^^^ pressure in the middle. 
By Col. XL p. 108, ~ = 398-45 cwts. Scantling, 13-18 X 7-91. 
