arcs than for small (supposing F to be unchanged): if the action began after it, the contrary effect would take place. If we take for F a force sufficient to counteract the resistance of the air supposed to be as the square of the velocity; since the diminution of the arc from that cause=ma', and the increase from the action Fc mn2 a3 n2 a' C

of F=

Fc
we must have = ma2, or F =
n'a

AF

;

is

independent of a, and the clock's rate would be the same under all variations of the maintaining power. If the resistance be supposed to follow any other law, the clock's rate will not be independent of a, except the action takes place as is above described.

The advantages which this escapement seems to offer are as follows:

1st. It would not require greater delicacy of workmanship, perhaps less, than the common dead-beat.

2d. It possesses in theory all the advantages of the detached escapement in watches.

3d. The clock would never be out of beat.

Whether the shortness of the pendulum for a given rate of beat would be any disadvantage, I do not know. The construction would, however, I apprehend, be very convenient for a portable clock. It is evident that by a repetition of this construction, the clock might be made to beat at every vibration : but several advantages would be lost by this complication.

TRINITY COLLEGE,

Nov. 10, 1827.

G. B. AIRY.

IV. On

On the Pressure produced on a flat Plate when opposed to a Stream of Air issuing from an Orifice in a plane Surface.

BY ROBERT WILLIS, B. A.

FELLOW OF CAIUS COLLEGE, AND OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY.

[Read April 21, 1828.]

THE singular and apparently paradoxical result obtained by opposing a flat plate to a current of elastic fluid issuing from an orifice in a plane surface, has lately excited considerable interest, especially on the Continent, where it was first brought into notice. In its simplest form the experiment consists in this. If we blow through a tube, the aperture of which terminates in a flat plate, and apply a circular disc of card or any other convenient material to the aperture, we find that as long as the blast is continued, the disc is attracted to the plate instead of being repelled, as might naturally have been expected. Some pins must be fixed into the plate, to prevent the disc from slipping off sideways.

This appears to have been first discovered, apparently by accident, at the iron-works of Fourchambault, where one of their forge-bellows opened in a flat wall, and it was found that a board presented to the blast was sucked up against the wall. It was there exhibited to Messrs. Thenard and Clement Desormes, in October 1826, and shortly afterwards a paper appeared in the Bulletin Universel, in which the latter gentleman considered a similar Vol. III. Part I.

R

phenomenon with respect to the escape of steam under high pressure, and the danger of failure to which the common safetyvalves of steam-boilers were exposed, by this singular fact. M. Hachette then succeeded in simplifying the form of the experiment, so that it might be performed by a pair of common bellows, or a stream of air from the mouth. He also produced the same effects by using a stream of water instead of air. (The particulars may be found, Bull. Univ. E. vII. pp. 41. 104. Ann. de Chimie, 1827, T. XXXV. p. 34, and T. XXXVI. p. 69. Quarterly Journal, 1827, Vol. I. p. 472, and Vol. II. p. 193. Some similar phenomena may, however, be seen in Young's Nat. Phil. Vol. I. pp. 298, 778.)

My object in the present Memoir is to detail some experiments which were undertaken for the purpose of examining some of the laws of this phenomenon more minutely than has hitherto been done.

In order to put it into a shape more convenient for investigation, some tubes of different diameters, terminating in flat plates, were connected to the wind-chest of an organ capable of furnishing a regular blast of any pressure not exceeding six inches of water, and a balance of light wood about six feet long, together with a number of discs of tin of various diameters, which could be attached by means of a screw to one of its extremities, being provided; then, by adding weights to the other extremity, and counterbalancing these by placing known weights on the centers of the discs, the effects of varying the orifice, pressure, &c. could be measured. The balance was made of considerable length, that the parallelism of the discs might not be sensibly affected by its motion.

Let CBD, Fig. 1, be a section of the lower plate provided with its tube AB, through which a constant blast is maintained. Bring the upper disc GH gradually down to CD, preserving its

parallelism with the lower plate, and keeping its center perpendicularly over the center of the orifice. It will be at first violently repelled by a force which will be found to increase till the disc reaches a point k, thence the force diminishes to a point, where the disc appears in a state of unstable equilibrium. Bringing it still lower it will be attracted by a force which increases, reaches a maximum at m, and diminishes till the disc is placed in stable equilibrium at n, and will be repelled if pressed still further down.

This table shews the distance of these points of stable and unstable equilibrium from the lower plate, in the case of an orifice .25 in diameter, and a pressure of 6 inches. The measures throughout this paper must be understood of inches, unless otherwise expressed. The next table shews the weight in grains required to pull discs of various diameters off the lower plate. It must be observed, however, that it is extremely difficult to ascertain the exact weight required to do this, and this difficulty is increased by a certain tremulous motion which the disc is apt to acquire. The general results are, that when the diameter of the disc is something less than twice that of the orifice, it is blown off*, that upon increasing the diameter of the disc larger

* This fact has been also observed by R. Younge, esq. in the Phil. Mag. April 1828, p. 282.

weights are required to pull it off, till we reach a certain point beyond which the same or a rather less weight is required, however the diameter of the disc be increased. Also that the weights increase with the increase of the orifice, or of the pressure.

To understand these phenomena more perfectly, it is necessary to have some means of estimating the pressure on the lower surface of the disc at any required distance from its center. I shall proceed, therefore, to describe an instrument which is adapted to this purpose.

Fig. 2, a section.

Fig. 3. Plan of the lower surface of FG seen from below. ABCD is the lower plate having a tube B opening at its. center, and communicating with the wind-chest.