specific gravities of stones, so far as regards their repulsive powers, although the increase is certainly in favour of their specific gravities. But there would appear to be some undefined law in the connection of bodies, with which the specific gravity has little to do. Thus, statuary marble has a specifie gravity above Aberdeen granite, yet a repulsive power not much above half the latter. Again, hardness is not altogether a characteristic of strength, inasmuch as the limestones, which yield readily to the scratch, have nevertheless a repulsive power approaching to granite itself.

It is a curious fact in the rupture of amorphous stones, that pyramids are formed, having for their base the upper side of the cube next the lever, the action of which displaces the sides of the cubes, precisely as if a wedge had operated between them. I have preserved a number of the specimens, the sides of which, if continued, might cut the cubes in the direction of their diagonals.

Experiments made on the transverse strain of cast bars, the ends loose. June 8th, 1817.*

A bar of cast-iron, from a Welsh foundry, which did not yield easily to the file, was laid upon supports exactly three feet apart; the bar was an inch square, and when 308 pounds were put into a scale suspended from the middle of its length, the deflexion was found to be 3-16ths of an inch; whence the height of the modulus of elasticity is 6,386,688 feet. The experiment was made by Mr. R. Ebbels, at Garnons, near Hereford. A joist of cast-iron, nine inches deep, resembling in form the letter I, was laid upon supports 19 feet apart, first on its edge, when the deflexion from its own weight was 3-40ths of an inch. It was then laid flatwise, and the deflexion from its own weight was 3 inches. The castings were from Messrs. Dowsons' foundry, Edgware-road. The iron yielded easily to the file. The height of the modulus of elasticity according to the experiment on the

joist flatwise is

5,100,000 feet,

on the edge is 5,700,000 feet.

The deflexion being very small when the joist was on its edge, perhaps it was not measured with the necessary degree of accuracy, as a very small error would cause the difference in the result. The following tablet contains the value of the modulus for cast-iron, according to the experiments above stated. Height of modulus in feet. Experimentalists. Ebbels.

Cast-iron (Welsh)

Cast-iron

....

Cast-iron, grey French

Cast-iron, soft do.

Cast-iron.

6,386,688

149

Half the second bar..

1

1437

840

3059

1656

....

150 A feather-edged or 1 bar was cast whose dimensions were 151 2 inches deep by 2 wide...

10 0 edge up 2 8

3105

152

Half of ditto

N. B. All these bars contained the same area, though differently distributed as to their forms.

Experiments made on the bar of 4 inches deep by inch thick, by giving it different forms, the bearings at 2 feet 8 inches, as before.

Experiments on the transverse strain of bars, one end made fast, the weight being suspended at the other, at 2 feet 8 inches from the bearing.

155 An inch square bar bore

156 A bar 2 inches deep by 4 an inch thick 157 An inch bar, the ends made fast

280

539

1173

The paradoxical experiment of Emerson was tried, which states that by cutting off a portion of an equilateral triangle (see page 114 of Emerson's Mechanics) the bar is stronger than before, that is, a part stronger than the whole. The ends were loose at two feet eight inches apart as before. The edge from which the part was intercepted was lowermost, the weight was applied on the base above, it broke with 1129 pounds, whereas in the other case it bore only 840 pounds.

Remarks on the transverse strain.

Banks makes his bar from the cupola, when placed on bearings three feet asunder, and the ends loose, to bear 864 lbs.

Now all my bars were cast from the cupola, the difference was therefore 33 lbs. I adopted a space of two feet eight inches asunder, as being more convenient for my apparatus. The strength of the different bars, all cases being the same, approaches nearly to the theory, which makes the comparative values as the breadths multiplied into the squares of the depths. The halves of the bars were tried, merely to keep up the analogy. The bar of four inches deep, however, falls short of theory by 365 pounds. It is evident we cannot extend the system of deepening the bar much further, nor does the theory exactly maintain in the case of the equilateral triangle by

The diagonal position of the square bar, is actually worse than when laid on its side, contrary to many assertions.

The same quantity of metal in the feather-edged bar was not so strong as in the four-inch bar.

The semi-elliptical bar, exceeded the four-inch bar, although taken out of it. The parabolic bar came near it.

The bar made fast at both ends, I suspect must have yielded, although the ends were made fast by iron straps. The experiments from Emerson, on solids of different forms, might be made; but the time and trouble these experiments have already cost, have compelled me to relinquish further pursuits for the present. If, however, in the absence of better, they are worthy of the indulgence of the Royal Society, it will not only be a consolation to me that my

labours merit their attention, but a further inducement to prosecute the investigation of useful facts, which, even in the present advanced state of knowledge, will yet admit of addition.

The science of construction is yet in its infancy, and certainly requires many additions. The first experiments on the strength of materials appear to have been made before the Royal Society; and there can be no doubt that a favourable reception will be given to any others that will tend to elucidate a subject which is likely to form one of the principal branches of an engineer's education; as he must either proceed on the principle of science, or be directed by a feeling of fitness, which is to be acquired only by devoting a lifetime to the practice of his art.

HYDRAULIC ENGINES.

THIS term is applicable to all machines driven by the force of water; consequently we have, under the article "Watermills," already treated of the most extensive branch of these machines. Those which have now to claim our attention, are such as could not with propriety be introduced under that head, and which are, upon the whole, of too much importance, both with respect to the conveyance of water, and as accessions to mechanical combinations, to be entirely omitted.

1. Of all the hydraulic machines invented by the ancients, though Archimedes' screw is the most curious, the tympanum raises the greatest quantity of water at once.

It consists of a great hollow wheel, composed of several planks joined together, and well calked and pitched, forming, as its name imports, a kind of barrel or drum, and having an horizontal axle on which it turns. The interior is divided by eight partitions into as many equal spaces or cells, each of which has an orifice of about half a foot in the rim of the drum or wheel, shaped so as to facilitate the admission of the water: there are, moreover, eight hollow channels running contiguous to each other and parallel to the axle of the wheel, each corresponding to one of the eight large cells, through which the water passes from the cells just mentioned, and after running along the channels to a convenient distance escapes through orifices into a reservoir placed just beneath the axle of the wheel. Thus the water is elevated through a vertical space equal to the radius of the hollow wheel. When the tympanum is used to raise water from a running stream, it is moved by means of float-boards impelled by the stream; but when employed to raise stagnant water, it receives motion from a foot-wheel placed on the same shaft, which is, as we have already described under the article "Foot-mill," turned by men walking inside. The chief defect of this machine is, that it raises the water

in the most disadvantageous situation possible: for the load being found always towards the extremity of a radius of the wheel, the arm of the effective lever which answers to it, increases through the whole quadrant the water describes in passing from the bottom of the wheel to the altitude of its centre; so that the power must act in like manner as if it were applied at a winch-handle, and, consequently, cannot act uniformly.

2. M. de la Faye, to remedy this defect, devised a machine which may here be described, together with the process of reasoning that led to it.

When we develope the circumference of a circle, a curve is described (ie. the involute) of which all the radii are so many tangents to the circle, and are likewise all respectively perpendicular to the several points of the curve described, which has for its greatest radius a line equal to the periphery of the circle evolved. The truth of which is shown by geometricans when treating of the genesis of evolute and involute curves.

Hence, having an axle whose circumference a little exceeds the height which the water is proposed to be elevated, let the circumference of the axle be evolved, and make a curved canal whose curvature shall coincide throughout exactly with that of the involute just formed: if the further extremity of this canal be made to enter the water that is to be elevated, and the other extremity abut upon the shaft which is turned; then in the course of the rotation the water will rise in a vertical direction, tangential to the shaft, and perpendicular to the canal in whatever position it may be. Thus the action of the weight answering always to the extremity of a horizontal radius will be as though it acted upon the invariable arm of a lever, and the power which raises the weight will be always the same: and if the radius of the wheel, of which this hollow canal serves as a bent spoke, is equal to the height that the water is to be raised, and consequently equal to the circumference of the axle or shaft, the power will be to the load of water reciprocally as the radius of a circle to its circumference, or directly as 1 to 64 nearly.

In M. de la Faye's opinion, the machine ought to be composed of four of these canals: but it has often been constructed with eight, as represented in fig. 210. The wheel being turned by the impulsion of the stream upon he float-boards, the orifices F, E, D, C, &c. of the curvilinear canals, dip one ifter another into the water which runs into them; and as the wheel revolves the fluid rises in the canals, f, e, d, c, &c. and runs out in a stream P from the holes at O; it is received into the trough Q, and conveyed from thence by pipes.

By this construction the weight to be raised offers always the same resistance, and that the least possible, while the power is applied in the most advantageous manner the circumstances will admit of: these conditions both fulfilled at the same time furnish the most desirable perfection in a machine. Further, this machine raises the water by the shortest way, namely, the perpendicular, or vertical; in this respect being preferable to Archimedes' screw, where the vater is carried up an inclined path: and besides this, each urved channel in this wheel empties all the water it receives every revolution, while the screw of Archimedes delivers nly a small portion of the fluid it is charged with, being

often loaded with twenty times as much water as is discharged in one rotation; and thus requiring an enormous increase of labour when a large quantity is intended to be raised by it.

The nature and advantages of this wheel evince very forcibly how far the speculations of geometers are from being so unfruitful in useful applications, as is often insinuated by practical men.

3. The wheel just described would, we think, be the most perfect of any that could be employed for raising water, had it not the disadvantage attending the tympanum, which is, that it can only raise water to the height of its semidiameter, As in many cases water is to be raised higher than the radius of any wheel can well be made for practice, we shall next describe a machine called the Noria, common in Spain, which raises water nearly through a diameter.

This Noria consists of a vertical wheel of 20 feet diameter, on the circumference of which are fixed a number of little boxes or square buckets, for the purpose of raising the water out of the well, communicating with the canal below, and to empty it in a reservoir above, placed by the side of the wheel. The buckets have a lateral orifice, to receive and to discharge the water. The axis of this wheel is embraced by four small beams, crossing each other at right angles, tapering at the extremities, and forming eight little arms. This wheel is near the centre of the horse-walk, contiguous to the vertical axis, into the top of which the horsebeam is fixed; but near the bottom it is embraced by four little beams, forming eight arms similar to those above described, on the axis of the water-wheel. As the mule which they use goes round, these horizontal arms, supplying the place of cogs, take hold, each in succession, of those arms which are fixed on the axis of the water-wheel, and keep it in rotation.

This machine, than which nothing can be cheaper, throws up a great quantity of water; yet undoubtedly it has two defects: the first is, that part of the water runs out of the buckets and falls back into the well after it has been raised nearly to the level of the reservoir: the second is, that a considerable proportion of the water to be discharged is raised higher than the reservoir, and falls into it only at the moment when the bucket is at the highest point of the circle, and ready to descend. These inconveniences are both remedied by the contrivance mentioned in the next paragraph.

4. The Persian wheel is a name given to a machine for raising water, which may be turned by means of a stream A B acting upon the wheel CDE according to the order of the letters; (fig. 210.)

The buckets a, a, a, a, &c. instead of being firmly fastened, are hung upon the wheel by strong pins, b, b, b, b, &c. fixed in the side of the rin; which must be made as high as the water is intended to be raised above the level of that part of the stream in which the wheel is placed. As the wheel turns, the