150 
MISCELLANEOUS TABLES, ETC. 
ON THE ADMEASUREMENT OF EARTHWORK IN RAILWAY 
CUTTINGS AND EMBANKMENTS. 
Let Fig. 1 represent the plan of a railroad and cuttings ; Fig. 2, the 
cross section through EH ; and Fig 3, the longitudinal section through 
the middle of the roadway, parallel to BK or CL. 
Fl C I 
•i— — — 1 
e 
F 
E J 
FIG 3 
In Fig. 1, let BK be parallel to CL and at right angles to AD and IM ; let AB = CD ; and 
IK = LM ; bisect CL in F, through F draw EFGH intersecting DM, BK, AT, m !>, ^, 
In Fig. 2, let cd be parallel to ab ; and ae, i/ perpendicular to ah, cd; ce=fd. In ^ig 6, 
let ST, NP, be vertical to SN ; from T draw TO parallel to SN ; bisect SN iu R; and trom 
K draw EZQ paraUel to ST, NP ; intersecting TO, TP in Z, Q. 
Let SN = L; n. RQ,= GH = FE ; then the true content of the whole solid ABCDMLKIA 
= V, may be found by any of the following equations,* viz. :— 
EH2 — FG2 
EGxGH 
3 
w.ZQ,^ 
3 
n.za2 
xL. 
} 
I xL... 
I xL... 
Example to the first equation. 
.(1) 
.(2) 
.(3) 
Let the vertical ordinates in feet, be as in Fig. 4 and 1 chain 
apart; jj = 1-5; width of Roadway FG = 40 feet, then the true 
content of the whole figure by equation (1), is as follows: — 
Middle ordinate. 
Ordinate 
Difference 
RG2 
RG. 
ST or NP. 
ZQ. 
za2. 
25-00 
5-0 
000 
5-0 
25-00 
198-81 
141 
10-0 
4-1 
16-81 
453-69 
21-3 
18-2 
31 
9-61 
707-56 
26-6 
28-8 
2-2 
4-84 
1385-06 
67-0 
1385-06 X 1-5 = 2077-59 = RG^ x n 
67-00 x 40 0 = 2680-00 = RGxFG 
56-26 x -5 = 28-13 = ZG^x^ 
4785-72 X 66 = 315857-520 ubio feet the true content. 
In the same Example if n = 2, i 5487-62 x 66 = 362182 92 Cubic feet, 
tnen the true jcontent is ) 
* See Note, page 152. 
