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The numbers given in the last Table, which hasbeen taken from Tree!gold’s work before quoted, areso far within the limits of the actual value of e at thetime the beam takes a permanent bend (as may be seenby comparison with the former results by M. Girard)that there can be no doubt of employing these valuesin any practical case, unless the beam is very defective,and such beams ought in no case to be employed.Two examples will sufficiently illustrate the aboveformulae:—

1. A weight of 5000 lbs. is to be sustained by an oakcolumn 7 feet 6 inches long, 5 inches depth, requiredthe breadth or greater thickness.

Here <? = -001 5,1 = 7-5, d = 5, w = 5000.

Whence b = ~ 3’2 inches.

2. Suppose the same weight were to be supported bya round pillar, six feet long, required its diameter.

Here 1 = 6, e = -0015, w = 5000.

D = 4 y' l "w x T7 e = 4 5 inches.

I 2 =36w =_ 5000180000

1-7

1260000

180000

3060000

•0015

1530

306

4 |/ 459 0 = 4'5 inches nearly.