renewing the gudgeon, without injury to the shaft. (Ed.)

134. Cast-iron shafts are sometimes made hollow cylinders, and sometimes they are made solid, and of various figures. It is demonstrable, that a hollow cylinder is much stronger, with the same quantity of matter, than it would be if made into a solid of the same length. This law is very observable in the beautiful economy of nature; for instance, the stalks of plants, the quills of birds, the bones of animals. But, in the works of art, numberless obstacles to perfection continually occur. In this particular case, the expense of making small shafts hollow, would be very great; and another objection is, the difficulty of making such castings perfect. Shafts of a small diameter are, therefore, commonly made solid.

135. Fig. 6, Plate II. represents a castiron cylindrical shaft. It consists of three parts, the body, A BCD, and the two gud

1

geons, A EC, and BPDG. The gudgeons are turned, and carefully fitted into the ends of the body, which is bored and turned to receive them. They are then fixed with screw-bolts, which pass through the flanches, as may be seen by the figure.*

This kind of shaft will obviously be variously constructed, according to circumstances. That represented in the figure was made for a cast-iron waterwheel. The use of the small projections H, H, &c. is to prevent the eye of the arms from shifting round on the shaft. When cylindrical shafts are not used, what are called feathered shafts are often adopted.

136. Fig. 7, Plate III. represents this construction of a shaft. It probably took its

*In this construction, the resistance to twisting depends entirely on the bolts, and some difficulties appear to be encountered in casting without corresponding advantages, either in strength or beauty. (Ed.)

name from its resemblance to the feathered part of an arrow. It may be here remarked, that shafts of this species, as often constructed, are by no means calculated to withstand the twist brought upon them by the strain of the machinery. From the breadth of the feathers, their strength to withstand lateral pressure, is, no doubt, considerable; but wanting substance between the feathers, they are liable to continual tremour. Where feathers are applied to shafts, I would prefer keeping the body of the shaft fully as strong as the gudgeon, or journal*, and apply the feathers merely to prevent bending in the middle, as Fig. 7, No. 4. But the simple square, Fig. 8, is more easily made, and, I believe, has been found in practice, at least as advantageous as any other form that has been tried for solid shafts.+

* Journals, or journeys, are gudgeons subject to torsion.

+ It is easily proved, that the best form for a revolving shaft is a cylinder, and that in any other form the

Having given this general account of shafts, I come next to consider the causes from which the stress on them arises.

SECTION II.

Of the Kinds of Stress to which Shafts are subject.

137. There are two kinds of stress to which shafts are liable: first, lateral stress, by which they may be broken across secondly, stress arising from torsion, by which they may be wrenched or twisted.

flexure will be irregular, and consequently produce irregular wear on the gudgeons and brasses; but when a shaft is to be adapted for placing wheels on any part of its length, a square section is convenient; in all other cases, the section ought to be circular with projections, as at H, H, Fig. 6, Plate II. By making four of these projections continue throughout the length upon a cylindrical shaft, all the advantage and convenience of a square one would be obtained, with very little irregular flexure. The projections should not be greater than is necessary to fix the wheels firmly on the shaft. (Ed.)

All horizontal shafts are liable to the first kind of stress, viz. lateral stress; and some have no other strain whatever; as for instance, a water-wheel shaft, where the motion is communicated from teeth, on the shrouding. See Plate III. Fig. 9.

In Fig. 10, the stress on the upright shaft, arises from torsion only; excepting what may proceed from the inaccuracy of the teeth of the wheels, which, if great, will occasion a considerable lateral thrust.

A vertical shaft, which gives or receives motion, by means of a pulley, has thereby a lateral pressure brought upon it.

In Fig. 11 and 12 the stress is compounded of lateral pressure, arising from the weight of the wheels A and B, and that of the shaft itself, and of the torsion or twist produced between the wheels A and B.

The following letter, with which Mr. JOIN ROBERTON, engineer, favoured me, as it relates to the subject of this Essay, and contains much useful matter, will, I hope, be acceptable to the reader :