thirds of the weight of a column of air, of a length equal to the height due to the velocity; the height of a column of water nearly equivalent to the force of resistance may be found, by taking the square of of the velocity in a second, in English feet.*

Thus, if the velocity were 1000 feet in a second, the resistance would be equal to a column of water on the same surface, 25 feet in height; and the resistance to a sphere about half as much.

For another example, if we had a cubic foot of a substance equal in specific gravity to water, and were desirous of knowing the greatest velocity that it could acquire by falling through the air; the height of the column of water is here 1, and its square root 1, which, multiplied by 200, gives 200 feet in a second for the velocity, when the resistance would be equal to the weight, which, of course, is the limit beyond which the velocity could never pass. Hence, we may form an idea of the utmost velocity that a stone, of moderate sizę, could acquire in descending from the upper regions of the atmosphere, or even from the neighbourhood of the moon, a velocity that would be much less than that of a bomb or a cannon ball even when it may be followed by the eye. Again, Mr. Garnerin's parachute contains about 860 square feet of surface, and weighs, together with the aeronaut suspended from it, about 230 pounds. Here the weight is of a pound for each square foot, which is equivalent to of a foot of water; multiplying the square root by 200, we have about 13 feet in a second for the utmost velocity; which is the same as if one leaped from a height of between 2 and 3 feet. Mr. Garnerin, however, finds the mean velocity of descent only eight feet, which agrees better with the experiments of Borda, in which the resistance appeared to be of the weight of the column due to the velocity, and exceeded this proportion as the surface increased in magnitude.

* See p. 70.

For estimating the discharge of a siphon, the head of water must be reckoned equal to the difference between the levels of the surface of the water and of the lower orifice. The author observes that the theory of waves has been treated in a new and improved manner by Lagrange, in his Mécanique Analytique. The problem is, however, not yet completely solved: Lagrange's Formula includes the depth of the water agitated as a given quantity, but it does not inform us how to determine this depth from theory.*

CHAPTER XVI.

Of Sucking Pumps.

The length of the sucking pump must never be greater than 30 feet below the movable valve: and there may be a loss of time in the ascent of the water, unless it be made even a few feet shorter. The motions to be produced, and the resistances to be overcome, are considered in detail; but the author refers, for still further information, to Langsdorf's Treatise on Machinery.

* The theory of the tides, and the propagation of waves in the ocean, has lately been very fully investigated by Dr. Young, in Napier's Supp. to the Encyclo. Brit. aft. "Tides."

The velocity of the stroke should never be less than four inches, nor greater than two or three feet in a second; the stroke should be as long as possible, to prevent loss of water by the frequent alterations of the valves; the diameter of the pipe should be about or of that of the barrel. The lifting pump is also here described; it only differs from the sucking pump in having the lower valve movable, and the upper one fixed. A number of valves and pistons are described in this chapter, chiefly from models of English manufacture.

CHAPTER XVII.

Of Forcing Pumps.

In describing the different kinds of solid piston, the author gives the preference to that which has a conical leather projecting on each side; but remarks that there is another form, which has the advantage in the situation of the ring for receiving the rod, which is precisely in the centre of the piston, and is, therefore, fitter for communicating motion in each direction. He says, that where the barrel is well polished, the piston may be used without either wadding or leather. The first pump, invented above a century before Christ, by Ctesibius of Alexandria, to whom, also, music is indebted for the organ, and whose name Mr. Eytelwein mentions in speaking of sucking pumps, was in reality a forcing pump, as may easily be collected from its description by Vitruvius (L. x. chap. 12.)

CHAPTER XVIII.

Of mixed Pumps, or the Combination of Sucking and Forcing Pumps.

When the lower valve is above the surface of the water, the forcing pump can only raise the water by suction, but the construction remains the same; such is Mr. Buchanan's patent ship pump. De la Hire's pump is more complicated; both the ascending and descending strokes of the piston being made effective, by means of a double apparatus of valves and pipes.

CHAPTER XIX.

Of acting Columns of Water.

The mechanism of a pump may be employed for converting the weight of water descending in its barrel to the purpose of working another pump. The author describes a machine of this kind, invented by Mr. Höll, and improved by Langsdorf. A similar arrangement, used in Cornwall, has lately been described in Nicholson's Journal, by Mr. Trevithick. The only objection to it appears to be the magnitude of the friction.

CHAPTER XX.

Of the Spiral Pump.

If we wind a pipe round a cylinder, of which the axis is horizontal, and connect one end with a vertical tube, while the other is at liberty to turn round and receive water and air in each revolution, the machine is called a spiral pump; it was invented, about 1746, by Andrew Wirz, a pewterer in Zurich, and was employed at Florence with Bernoulli's improvement, in 1779. At Archangelsky, near Moscow, a pump of this kind was erected in 1784, which raised a hogshead of water in a minute to a height of 74 feet, and through a pipe 760 feet in length. The force employed is not mentioned; we may, therefore, conjecture that it was turned by water. Mr. Eytelwein enters very minutely into calculations of the machine under different circumstances; and the results of the theory, as well as of experiment, are such as to induce us to expect that it will in time come into common use, instead of forcing pumps of a more complicated and expensive construction. The water-tight joint presents the only difficulty; the pipe may form either a cylindrical, a conical, or a plain spiral, and it appears to be uncertain which is the most advantageous; the vertical pipe should be nearly of the same dimensions as the spiral pipe, which may without difficulty be made of wood.

effect of such a