communicating with a horizontal tube A B, at the extremities of which A B are two apertures in opposite directions. When water from the mill-course M N is introduced into the tube TT, it flows out of the apertures A B, and by the reaction or counterpressure of the issuing water the arm AB, and consequently the whole machine, is put in motion. The bridgetree a b is elevated or depressed by turning the nut c at the end of the lever c b. In order to understand how this motion is produced, let us suppose both the apertures shut, and the tube TT filled with water up to T. The apertures A, B which are shut up, will be pressed outwards by a force equal to the weight of a column of water whose height is TT, and whose area is the area of the apertures. Every part of the tube A B sustains a similar pressure; but as these pressures are balanced by equal and opposite pressures, the arm AB is at rest. By opening the aperture at A, however, the pressure at that place is removed, and consequently the arm is carried round by a pressure equal to that of a column TT, acting upon an area equal to that of the aperture 4. The same thing happens on the arm TB; and these two pressures drive the arm AB round in the same direction. This machine may evidently be applied to drive any kind of machinery, by fixing a wheel upon the vertical axis CD.

Barker's mill

Cour.

In the preceding form of Barker's mill, the length Improveof the axis CD must always exceed the height of ment on the fall ND, and therefore when the fall is very by M. Mahigh, the difficulty of erecting such a machine would thon de la be great. In order to remove this difficulty, M. Mathon de la Cour proposes to introduce the water from the millcourse, or reservoir F, by means of the pipe F G H, entering at D, into the horizontal arms A, B, which are fixed to an upright spindle C T, but without any hollow tube TT. The water will obviously issue from the apertures A B, in the same manner as if it had been introduced at the top of a tube T T as high as the fall. Hence the spindle CD may be made as short as we please. The practical difficulty which attends this form of the machine, is to give the arms A B a motion round the mouth of the feeding pipe, which enters the arm at D, without any great friction, or any considerable loss of water. In a machine of this kind which M. Mathon de la Cour saw at Bourg Argental, AB was 92 inches, and its diameter three inches; the diameter of each orifice was 1 inch. The height of

the fall F G was 21 feet; the internal diameter of D was two inches, and it was fitted into C by grinding. This machine made 115 turns in a minute when it was unloaded, and emitted water by one hole only. The machine, when empty, weighed 80 pounds, and it was half supported by the upward pressure of the water. This improvement which was published in Rozier's Journal de Physique for January and August 1775, appeared about 20 years afterwards as a new invention of Mr. Waring's in the Transactions of the American Philosophical Society of Philadelphia, who was probably not aware of the labours of M. Mathon de la Cour.

In the year 1747, Professor Segner of Gottingen published, in his Excercitationes Hydraulica, an. account of a machine which differs only in form from Dr. Barker's mill. It consisted of a number of tubes arranged as it were in the circumference of a truncated cone; the water was introduced into the upper ends of these tubes, and flowing out at the lower ends, produced, in virtue of its reaction, a motion round the axis of the cone.

Another form of this machine has been suggested by Albert Euler. He proposes to introduce the water from the mill-course into an annular cavity in a fixed vessel of the shape nearly of a cylinder. The bottom of this vessel has several inclined apertures for the purpose of making the water flow out with a proper obliquity into the inferior and moveable vessel. This inferior vessel, which has the form of an inverted frustrum of a cone, moves about an axis passing up through the centre of the fixed vessel, and has a variety of tubes arranged round its circumference. These tubes do not reach to the very top of the vessel, and are bent into right angles at their lower ends. The water from the upper and fixed vessel being delivered into the tubes of the lower vessel, descends in the tubes, and issuing from their horizontal extremities, gives motion to the conical drum by its reaction.

History of The excellence of this method of employing the this machine. reaction of water, was first slightly pointed out by Dr. Desaguliers, and no further notice seems to have been taken of the invention till the appearance of Segner's machine in 1747. The attention of Leonhard Euler, John Bernoulli, and Albert Euler, was then directed to the subject, and it would appear, from the results of their investigations, that this is the most powerful of all hydraulic machines, and is therefore the best mode of employing water as a moving power.

Leonhard Euler published his theory of this machine in the Memoirs of the Berlin Academy, vol. vi, p. 311; and the application of the machine to all kinds of work, was explained in a subsequent paper in the seventh volume of the work, for 1752, p. 271. John Bernoulli's investigations will be found at the end of his Hydraulics.

Effect of

Barker's

mill.

Albert Euler concluded, that when the machine had the form given to it by Segner, the effect was equal to the power, and was a maximum when the velocity became infinite. Mr. Waring, in the paper which we have already quoted, makes the effect of the machine equal only to that of a good undershot wheel driven with the same quantity of water falling through the same height. The Abbé Bossut has likewise investigated the theory of this machine, and has found that an overshot wheel, and a wheel of the form given to it by Albert Euler, will produce equal effects with the same quantity of water, if the depth of the orifice below the millcourse in the latter machine is equal to the vertical height of the loaded arch in the overshot wheel; and he, upon the whole, recommends the overshot wheel as preferable in practice. The preceding result, however, proves the inferiority of the overshot wheel, as the height of the loaded arch must be always much less than that of the fall. A new and ingenious theory of this machine has lately been given by Mr. Ewart in the Manchester Memoirs.

Method of keeping off the Back-water from Water Wheels. Mr. Burns of Cartside, in Renfrewshire, seems to have been the first who proposed and executed the method of keeping off the back-water from wheels in time of floods, by directing against it the force of the superabundant current.

This method is shewn in Fig. 8, where CDE is a current of water taken from the mill-lead, and acting against the backwater at F, so as to drive it back and keep it from the wheel. For this purpose, the water C is kept from the wheel by the boarding D BE, a channel being left at E, through which the back-water would rush upon the wheel if it were not driven back by the superior force of the current rushing down the channel 4. Mr. Perkins makes the diameter of B larger than E. The current is made to act in a direction perpendicular to the plane of the wheel, when the wheel has been

already built. The water which comes from the buckets is also carried off through B. This method appears to have been adopted in America, and was recently submitted to the public by the ingenious Mr. Perkins, who was not aware of what had been done in Scotland, and published in the Transactions of the Society of Arts, vol. xxxviii, p. 109. See also the Edinburgh Philosophical Journal, vol. iv, p. 439, and vol. v, p. 222.

SECT. III. On the Force of Wind, and the mode of applying it to drive Machinery.

Considering air as a fluid, it is obvious that its force, when in motion, may be applied to machinery, in the same way as moving water is applied to the float-boards of vertical or horizontal undershot wheels. As the current of air, however, is not limited in magnitude, we must direct it solely upon the float-boards on one side of the wheel, by screening the other side from its action. When the axis of a wheel of this kind is vertical, and consequently the motion of the vanes or floatboards horizontal, the machine is called a horizontal wind-mill. The most common method, however, of applying the force of wind, is to direct it against sails moving nearly in a vertical plane, as shewn in Plate II, Fig. 13. In this case, the machine is called a vertical wind-mill.

On Vertical Wind-Mills.

The vertical wind-mill, as improved by Mr. James Verrier, is represented in Plate II, Fig. 13, where A A A are the three principal posts, 27 feet 7 inches long, 22 inches broad at their lower extremities, 18 inches at their upper ends, and 17 inches thick. The column B is 12 feet 2 inches long, 19 inches in diameter at its lower extremity, and 16 inches at its upper end; it is fixed in the centre of the mill, passes through the first floor E, having its upper extremity secured by the bars G G. EEE are the girders of the first floor, one of which only is seen, being 8 feet 3 inches long, 11 inches broad, and 9 thick; they are mortised into the posts A A A and the column B, and are about 8 feet 3 inches distant from the ground floor. DDD are three posts, 6 feet 4 inches long, 9 inches broad, and 6 inches thick ; they are mortised into the girders E F of the first and second floor, at the distance of 2 feet 4 inches from the posts 4, &c. FFF are the girders of the second floor, 6 feet long, 11 inches broad, and 9 thick; they are mortised into the posts A, &c.

;

and rest upon the upper extremities of the posts D, &c. The three bars G G G are 3 feet 11 inches long, 7 inches broad, and 3 thick; they are mortised into the posts D and the upper end of the column B, 4 feet 3 inches above the floor. P is one of the beams which support the extremities of the bray-trees or brayers; its length is 2 feet 4 inches, its breadth 8 inches, and its thickness 6 inches. I is one of the bray-trees, into which the extremity of one of the bridge-trees K is mortised. Each bray-tree is 4 feet 9 inches long, 9 inches broad, and 7 thick; and each bridge-tree is 4 feet 6 inches long, 9 inches broad, and 7 thick, being furnished with a piece of brass on their upper surface to receive the under pivot of the millstones. LL are two iron screw-bolts, which raise or depress the extremities of the bray-trees. M M M are the three millstones, and N N N the iron spindles, or arbors, on which the turning millstones are fixed. O is one of three wheels, or trundles, which are fixed on the upper ends of the spindles NNN; they are 16 inches in diameter, and each is furnished with 14 staves. fis one of the carriage-rails, on which the upper pivot of the spindle turns, and is 4 feet 2 inches long, 7 inches broad, and 4 thick. It turns on an iron bolt at one end, and the other end slides in a bracket fixed to one of the joists, and forms a mortise, in which a wedge is driven to set the rail and trundle in or out of work; t is the horizontal spur-wheel that impels the trundles; it is 5 feet 6 inches diameter, is fixed to the perpendicular shaft T, and is furnished with 42 teeth. The perpendicular shaft T is 9 feet 1 inch long, and 14 inches in diameter, having an iron spindle at each of its extremities; the under spindle turns in a brass block fixed into the higher end of the column B; and the upper spindle moves in a brass plate inserted into the lower surface of the carriage-rail C.

The spur-wheel r is fixed on the upper end of the shaft T, and is turned by the crown-wheel v on the windshaft c; it is 3 feet 2 inches in diameter, and is furnished with 15 cogs. The carriage-rail C, which is fixed on the sliding kerb Z, is 17 feet 2 inches long, 1 foot broad, and 9 inches thick. YYQ is the fixed kerb, 17 feet 3 inches diameter, 14 inches broad, and 10 thick, and is mortised into the posts A A A, and fastened with screw-bolts. The sliding kerb Z is of the same diameter and breadth as the fixed kerb, but its thickness is only 7 inches; it revolves on 12 friction rollers fixed on the upper surface of