32

■he peincifles of bridges.

TKACt 1 .

therefore, in general, ~ tang. = the cotang, is = h thehorizontal thrust, and in the present instance the half of thecotangent 22-903766 is 11-451883 the same value of thehorizontal thrust as before.

Hence then the constant number II’451888 is to be mul-tiplied by the tangents of all the vertical angles, to give theweights of the semiarch, in the 4th column, and by the se-cants of the same angles, to give their oblique pressures, asin the 3d column; or else, to work bv the logarithms, thelog. of the constant number li '451883, which j,s P0588769,is to be added to all the log. secants and tangents of the saidangles, then the corresponding natural numbers taken, andranged in the 3d and 4th columns of the table.

The differences of the numbers in the 4th column aretaken, and ranged in the 5th or last column, for the weightsof the single wedge pieces taken separately, making thewhole of the first or key wedge equal to 1.—The table isas follows.

No, ofsections.

Verticalangles ofthe joints,or Z S o.

Oblique pressures,= /lX SCCiZ.0.

Wts.of half arches,— //Xtan;Z_0.

Wts.of the sec-tions or wedges;

1

decrees.

1 1-46272

0-5

i-

2

n

11-55070

1-50767

1-00767

3

I2i

11-72993

2-53882

1-03115

4

ni

12-00763

3-61076

1-07194

5

2 vf

12-39543

4-74352

1-13276

6

27 i

12-91065

5-96147

1-21795

7

32i

13-57837 '

7-29565

1-33418

8

3ii

14-43478

8-78734

1-49169

9

42f

15-53267

10 49372

1-70638

10

47t

16-95094

12 49753

2-00381

11

52f

18-81177

14-92439

2-42686

12

57f

21-31377

1 7’97585

3-05146

13

62 4

. 24-80112

21-99886

4-02301

14

67k

29-92521

27-64727

5 ’6484 i

15

721.

38-08334

86-32073

S-67346

16

1

* * T

52-91028

51-65611

15-33538

17

82k-

87-73628

86-98568

35-32957

18

874-

262-54 1 1 8

262*29 i 25

175-30557