plate forming at once the bottom of the upper and the top of the lower cylinder, the only air-passage between them being a silk valve, v.

"In each cylinder works a valved piston, P, and p, attached to a piston-rod common to both, which passes through a stuffing-box in the plate. The distance between the pistons is such that, when P is in contact with the top of the upper or exhausting cylinder, p is in contact with the top of the small or lower cylinder; and when P is in contact with the bottom of the large cylinder, pis in contact with that of the small cylinder. The pump-plate, E, placed above the large cylinder A, supports the receiver R, or other vessel to be exhausted, from which the air flows through the valve v, during the descent of the piston P.

66

Fig. 403 represents the complete pump, as manufactured for philosophical purposes. The motion of the pistons is effected by means of a short crank with a jointed connecting-rod, converting the circular motion given by the lever handle into a vertical one, which is maintained by means of a cross-head, with rollers working between guides.

"The action of this air-pump is as follows:

"On the descent of the piston P, tending to produce a vacuum in the exhausting cylinder, A, by causing a difference of pressure above and below the first valve, v, in the top of the cylinder, the elasticity of the air in the receiver causes it to pass through the valve v. The air below the piston, P, is at the same time pressed through the valve, v', in the plate separating the cylinders, and enters the cylinder, B, in which a vacancy is simultaneously made for it by the descent of the piston p; and, in consequence of the difference of capacity of the two cylinders, it becomes reduced to one-fourth of its original bulk, its elasticity, according to the well-known law, being proportionally increased. The air contained in the small cylinder below the piston, p, will, in like manner, be pressed through the valves, v, v, into the atmosphere.

"During the ascent of the pistons, the valves, v, v', v", will be closed, and the valves, w, w', in the pistons opened by the upward pressure of the air in the cylinders and atmosphere, admitting the air in each cylinder to pass through the pistons as they rise, in order that, in the following downward movement, the air, which during the previous stroke of the pump issued from the receiver into the exhausting cylinder, may be withdrawn from that into the lower cylinder, while the air condensed in the latter may be finally expelled into the atmosphere. By this construction of the instrument we are enabled to obtain a more perfect vacuum than by any air-pump previously devised.

"In order to prove this, let us compare the action of two air-pumps, one of the improved, the other of the usual construction, assuming that they are equally perfect in workmanship. If an air-pump could discharge the entire quantity of air contained in it at the end of every stroke of the piston, and if the action of the valves were also perfect, there would be nothing to prevent our obtaining a perfect vacuum.* But whoever has tried the experiment will have found that an ordinary philosophical air-pump does not remove much

The inventor of the new air-pump makes the following remarks on this subject:-"It is the opinion of some natural philosophers that the whole of the air could never be exhausted from a closed vessel by means of a pump, even if the apparatus were theoretically perfect. From that opinion, however, I must beg leave to dissent; for, even if the repulsive force which separates the atoms of fluids were itself unlimited (which, however, has never been proved), there necessarily must be a limit where that force and the force of gravity acting on a single particle just equal each other; and if a vessel were emptied of air to this extent, and a further portion were withdrawn, the remainder would no longer be able to fill the whole vessel, but would cover the bottom only, as a non-elastic fluid would, leaving a perfect vacuum above. In this state of things, continual withdrawals of air from the lower part of the vessel would at length cause the last atom itself to be withdrawn."

more than of the atmosphere from the receiver, however long he may have continued to work the instrument. We may conclude, therefore, even when the piston is in contact with the bottom of the cylinder, that there still remains a space equal to of the capacity of the cylinder, through which the piston cannot be depressed, and where the air is merely condensed, expanding and refilling the whole cylinder when the piston is raised. "Now, let us suppose that in the new air-pump the piston, P, leaves of the air in the exhausting cylinder, A, undisplaced, and that the piston, p, cannot be brought within part of the length of stroke of the top or bottom of the smaller cylinder, the working having been continued until no further exhaustion is effected. At this period, the piston, p, will leave in the cylinder, B, during the downward stroke, of its bulk of air of the atmospheric density unexhausted: if it be raised again, this portion of air will expand and fill the cylinder, B, with air, the density of which will be only that of the atmosphere. The piston, P, will at the same time ascend to the top of the exhausting cylinder, A, filled with air of the same density as that remaining in the receiver; but, the exhaustion having reached its utmost limit, during the next downward stroke no air will be discharged from cylinder a into cylinder B: the air above the piston in the latter will, at the termination of this stroke, have expanded 100 times, and, having previously expanded to an equal amount during the upward stroke, it will now be reduced to the density that of the atmosphere. If no force were required to open the valve, v', air would, in this state of things, pass from the upper into the lower cylinder, unless that in the former, 100 times compressed as it would be at the end of the downward stroke, were not still rarefied 10,000 times, or what is the same thing-if it were not, when it filled the cylinder A, 1,000,000 times rarefied. We find, therefore, that by the addition of the second cylinder the vacuum may be rendered 10,000 times more perfect than if the cylinder A had been employed alone in the manner of an air-pump.*

"As the leakage of the valves and piston is a principal cause of the imperfection of the vacuum obtained by means of air-pumps of the ordinary construction, it may be objected that, as we have in the new one two valves and one piston more than usual, the loss of effect from this cause will be proportionally greater. This, however, is not the case. On the contrary, the loss from leakage at the valves and pistons is diminished in the new air-pump nearly in the same ratio as the opposing unexhausted space in the cylinder. The amount of leakage through a given aperture bears a certain proportion to the difference of pressure on each side (increasing as the square root of the pressure); and it will be observed that this difference of pressure, especially in the large cylinder, is very small indeed, and occurs at intervals only, whereas, in the case of an ordinary single-acting pump, the entire atmosphere constantly rests on the piston and exhausting-valve. Besides, in the new air-pump the leakage of the air through the apparatus is opposed by a greater number of obstructions, one after another, between the discharging-valve and the re

999,999

99 100,

the new

*Cæteris paribus, if a well-made pump, of any of the ordinary forms, will rarefy the air to one would carry the rarefaction up to 1,000.00, if the valve, v', could be rendered automatic. Although the reasoning above is in some degree theoretical, it is independent of the consideration of extreme accuracy in the construction of the new air-pump, which will produce a vacuum approaching to the perfection assigned, ir proportion to the smallness of the force required to open the valve,

ceiver. Indeed, the efficacy of the pump would not be impaired in any considerable degree if even the valve, v, were removed altogether, and any one of the others should be in a very leaky state.

"Another circumstance interfering with the power of obtaining a good va cuum by means of a well-made air-pump of any of the forms previously constructed, but which is obviated in the instrument now described, is, that the valve through which the air has to pass from the receiver into the pump is forced into its seat at the end of the reversed stroke by the whole pressure of the atmosphere, minus only that of the air remaining in the receiver. By this the silk valve is soon injured, and, what is even more important, the rarefied air has not power to force it open again, and the exhaustion consequently ceases before the vacuum has attained that degree of perfection to which it might otherwise be carried. One of the most obvious objections to an ordinary airpump, whether single or double acting, arises from the inequality of the force required to move the piston through different portions of the stroke, and from the very great force which is ultimately requisite.

FIG. 404.

"In the diagram (Fig. 404), A is the barrel of a double-acting air-pump which, by the alternate motion of the piston, P, and the valves 1, 2, 3, and 4, produces a partial vacuum in the receiver or closed vessel, R. Let us suppose that five-sixths of the air originally contained in R have been removed, and that the working of the pump is still continued. The resistance which the piston will now have to encounter is readily found from the law of Mariotte, and will be represented by the shaded part of the diagram, bounded by the parabolic curve. At the commencement of the stroke, the pressure on both sides of the piston being equal to one-sixth atmosphere, the resistance is o; it increases gradually in proportion to the diminution of the space below the piston, until the air has been compressed to one-sixth of its original volume, when

its density will have become equal to that of the atmosphere, and the discharging-valve, 4, will be opened. It is evident, in this case, that the force required to move the piston to the bottom of the cylinder must be sufficient to overcome the maximum resistance, which will be about 34 times greater than the average amount that would be experienced if the entire resistance could be distributed over the whole stroke.

"In this illustration we have supposed the pump to be double acting, and have, therefore, deducted from the actual pressure against the piston the uniform ‘aiding pressure' of the air which follows it freely from the receiver through the valve, 1.

"Air-pumps for philosophical purposes are very commonly single acting, the pressure of the atmosphere being constantly exerted on one side of the piston only; but when there are two cylinders, as is frequently the case, having their piston-rods connected with the opposite ends of the same lever, the atmospheric pressure on one piston balances that on the other, and the resistance will be equivalent to that occurring in a pump with one double-acting cylinder. In a single-barrel pump with open top the inequality of load is still greater than in a double-acting or double-cylinder pump. The inequality of load increases as the rarefaction proceeds, but the resultant of the resistance attains its maximum when the vacuum equals 19 in. of mercury in the gauge, or when nearly two-thirds of the atmosphere have been removed from the receiver, after which it constantly diminishes.

FIG. 405.

"It will readily be perceived that in the improved air-pump this great inequality of load does not exist, and therefore a pump of several times greater capacity than any given one on the ordinary construction may be worked with equal facility and speed, because the resisting pressure against the larger piston, P, cannot rise at the termination of the stroke to more than four times the pressure of the air still contained in the receiver, and therefore diminishes as the perfection of the vacuum increases; and even of this greatest resisting pressure, one-fourth part is balanced by the pressure, on the top of the piston, of the air entering the cylinder from the receiver, and another fourth by the increasing aiding pressure' on the top of the small piston, ; and the re