484

HISTORY OF ENGINEERING.

Book I.

particulars, I proceeded, with a view to answer this third question, to calculate the propor-tional weight at the extremity of every fifth foot from the crown of the bridge, the weightat the crown being supposed to be one. These are put down in the following table : thefirst column contains the length of arches in feet from the crown ; the second column containsthe weights at the extremities of these lengths; the length of arch and the weights at theextremity of that length being in the same line, and adjoining to one another. If thereforeit be determined upon that the weight at the crown shall be any number as n, the weightat the extremity of every fifth foot may be obtained by multiplying the number in thesecond column of the first table by n. As the length of half the arch is 309*299, the lastlength is not a complete multiple of 5.

If the weight over a portion of the arch at the abutment be given, the weight at thecrown may be ascertained. Thus if the weight over a portion of the arch of 10 feet at theabutment be x , the weight x divided by 11 *9911 w-ill give the weight at the crown.

Is/ Cot.

2d Col.

Is/ Col .

2d Col.

Is/ Col.

2 d Col.

Is/ Col.

2d Col.

5

1-00007

85

1 -0209

165

1-0816

245

1 -1909

10

1 -00027

90

1-0211

170

1 -0866

250

1-1997

15

1 -00063

95

1 -0262

175

1 -0923

255

1-2088

20

1-00114

100

1 -0290

180

1-0979

260

1-2181

25

1-00178

105

1-0321

185

1-1039

265

1 -2277

30

1 -00256

no

1 0353

190

1-1099

. 270

1 -2375

35

1 -00367

115

1 -0386

195

1-1162

: 275

1-2477

40

1 -00458

120

1 -0422

200

1-1226

I 280

1 -2582

45

1 00581

125

1 -0451

205

1-1293

285

1 -2689

50

1-00717

130

1*0497

210

1-1371

i 290

1 -2799

53

1*00870

135

1 *0537

215

1 *1433

295

1 -2913

60

1-01034

MO

1 *0579

220

1-1507

300

1 -3030

65

1-01210

145

1 *0623

225

1 -1583

305

1-3150

70

1-01410

150

1 -0669

230

1-1661

309-299

1-3256

75

1-01620

155

1-0716

235

1-1741

80

1-01850

160

1 -0765

240

1-1824

From the form of the bridge, and the law by which the weights over the several partsmust be regulated, it is evident from the table, that proceeding from the crown to eitherof the abutments the quantity of metal must be less and less in proportion than the spaces•occupied ; or, in other words, if I may use the expression, the metal must become more andmore rarified. It therefore follows, that proceeding from either abutment to the crown,the metal must become more and more condensed. The limit of condensation at thecrown, however, is that of solidity, and therefore a greater weight cannot be laid over agiven portion of the arch at the abutment, than that which, regulated according to theestablished law, will render it necessary to use solid blocks of metal at the crown.

Mr. Playfair replied, that the distribution of the weight, so that these wedge-form framesmay be in equilibrio, and may support themselves even if they were not connected but bytheir mutual pressure, can easily be determined, but will give a construction hardly ap-plicable in practice. The equilibrium of the parts would require that the weights of thewedge, at the spring of the arch, should not exceed the weight of that at the crown, in agreater proportion than that of six to five, and that at all the intermediate points, this dif-ference of one-fifth should diminish, as the square of the distance from the crown diminishes.Thus the crown wedge being of the weight a, the wedge at the abutment should be of the

weight a + - ; the first wedge from the crown, a + —-— ; the second a + ——— ; the* 5 ° 5 + 31* 5 + 31*

third a + —-—5 + 31*

and so on for all the other thirty-one frames that compose one-half of the

bridge, computing the distance from the crown by the space between the crown and themiddle point on the base of each frame. This is obviously so remote from the proposedfigure of the bridge, and from any that it can possibly have, that the notion of makingthe parts balance one another, or support themselves by their weight alone, must be entirelyabandoned. It may be abandoned too without any loss to the firmness and stability of thebridge, agreeably to what has been already remarked. The perfect balance of the partsis only necessary, if the frames are unconnected and free to slip on one another; the momentthat any connection by diagonal braces or other means is established between them, the prin-ciple of equilibrium is in effect departed from, and therefore has never been had recourseto in any instance of an iron bridge hitherto constructed. When therefore it is assertedthat the iron bridge over the Thames is not meant to stand on the principle of equili-brium, I do not mean in the slightest degree to object to its construction.