62
THE PRINCIPLES OF BRIDGES.
TRACT. I.
The Table for Constructing the Curve in this Example.
Valueof K I
Valueof I c
Value
Of KI
Valiuof 1 c
Value
of K I
Valueof I c
ValueOf K I
Valin-of 1 c
| Valueof KI
Valueof I c
0
0000
1.5
8-120
24
1 1-911
33
18-627
42
29-919
2
6-033
16
8-430
25
12-489
34
19-617
43
31-563
4
6 H4
17
8*766
2 6
13-106
35
20-G65
44
33-299
6
6-324
18
9-168
27
13-761
36
21-774
45
35-135
8
fi-580
19
9-517
28
14-4.57
37
22-948
46
37 07.5i
10
6-914
20
9-934
29
15-196
38
24-190
47
39-126
12
1-330
21
10-381
30
1.5-980
39
25-505
48
41-293
13
7*571
22
10-8.58
31
16-811
40
26-894
49
43-581
14 .
7-834
23
11-368
32
17-693
41
98-364
50
46-000
The above numbers may either be feet, or any otherlengths, of which Da is 40 and aA is 50. But when Da is toqa in any other proportion than that of 4 to 5, or when dk isnot to Da as 6 to 40 or 3 to 20; then the above, numbers willnot answer; but others must be found by the same rule, toconstruct the curve by. In the beginning of the table, asfar as 12, the value of ki is made to differ by 2, because thevalue of ci in that part increases so very slowly. After-wards they differ by units or 1.
Other examples of given extrados might be taken; but asthere can scarcely ever be any real occasion for them, andas the trouble of calculation would be, in most cases, verygreat, they arc omitted.
As the theory for arch vaults, before laid down, will soeasily apply to the arches for domes or cupolas also, a pro-position or two may be here added for that purpose, asfollows.
PROP. XII.
When a regular Concave Surface Dome, or Vault, formedby the rotation of a curve turned about its axis, is kept in equi~librio by the pressure of a solid wall built on every part of it ;then the Height of the wall over any part, is directly proportionalto the cube of the secant of elevation there, and inversely pro-portional to the radius of curvature, and to the diameter or•width of the dome at the same part.
i