A simple and ingenious hydrostatic machine, invented more than a century ago, by Dr. Barker, and forming one of the most simple water mills ever constructed. It has been rarely introduced in practice, although it has been warmly eulogized and recommended by most writers on the subject of hydraulics. In the annexed engraving, which is a perspective view of the machine, a b represents a vertical axis, moving on a pivot at b, which would be best made of steel, and to run in a brass step let into a block of stone, as at c; this axis passes freely through the lower mill-stone d, and is then fixed to the upper stone e. To the axis is also fixed the large vertical tube g, the upper part of which is expanded into the shape of a funnel or basin, for receiving the water from the mill-course or pipe i; at the lower part g, this tube has an open communication with the hollow horizontal arms h h, each of which has an opening near its extremity on one side, and so adjusted by stop-cocks for regulating the discharge, that the vertical tube shall always be kept full of water, in order that the utmost force may be obtained, as a lateral pressure will be exerted in all directions in the horizontal arms, proportionate to the altitude of the column.
Now this pressure being removed from the space forming the area of the aperture of the arms, by the water being allowed to issue through it, there will be an excess of pressure on the opposite side of the arm, in which there is no pressure equal to the force with which the water would spout from the aperture, were the machine fixed, and the water permitted to pass through it.
In the preceding form of Barker's mill, the length of the axis must always exceed in height the elevation of the pipe i, which in some cases might render the execution of such a machine difficult. To remove this difficulty, it was proposed by M. Mathon de la Cour, in Rozier's Journal de Physique, for August, 1775 to introduce the water from the mill course into the horizontal arms h k, which are fixed to an upright spindle f, as represented in the annexed diagram, and without any revolving vertical tube, as in the previously described arrangement. The water will now obviously issue from the apertures at the extremities of h h in the same manner as if it had been introduced at the top of the tube, in the former figure; hence the spindle may be made as short as we please. The practical difficulty, in this arrangement, is to give to the arms h h a motion round the mouth of the feeding pipe, which enters the arms without any great friction, or any considerable loss of water. In this form of the mill, o is the reservoir; p the mill stones; l the vertical axis; q r s the feeding pipe, the mouth of which enters the horizontal arm at s.
In a machine of this kind, constructed at Bourg Argental, the tubular arms h h were each 46 inches long, and their inside diameter 3 inches; each of the orifices 1 \ inch diameter, and the height of the head of water above the points of discharge was 21 feet. Though the fall was so great, the consumption of water was small, since it was supplied by a 2-inch pipe; and when the machine was not loaded, and had but one orifice open, it made 115 turns in a minute. Thus a prodigious centrifugal force is produced in the arms, and a corresponding velocity far exceeding that of a simple fall of water with a pressure of 21 feet head.
The machine, when empty, weighed 80 lbs., and it was half supported by the upward pressure of the water. It is to be regretted that no extensive and accurately conducted experiments have been instituted to determine the comparative powers of this machine, and that great difference exists in the opinions both of theoretical writers and practical engineers upon the subject. L. Euler, J. Bernoulli, and A. Euler, consider it to be the most powerful of all hydraulic machines. Whilst the Abbe Bossut reckons the overshot-wheel as upon the whole superior to it, Mr. P. Ewart says, that "the effect of this mill is much superior to that of an under-shot water wheel, consuming the same quantity of water, but inferior to that of an over-shot wheel, in which the water is applied to the best advantage; but Mr. Waring makes the effect to be equal only to that of a good under-shot wheel, when driven by an equal quantity of water falling from the same height.