irt + .012 .257 .276 2.55 .366 .75 .5 5.4.155.18 3. .26 .6 .45 5.2.09.11 2.6.24 .45 +82 .22 1.5.235.4 1.55 5.4 .1 .1 .23 1.26 5.5 Note. The pressures greater than the atmospheric are marked and those less 5 6 Pressure at Orifice in inches. .56 .253 .3 .65 .5 2 77 435 .327 .55 .35 .26 .34 1.15 .249 .3 1.57 .7 .27 .28 .01 .05.295.46 | .43 4 783.44 .33 .565 .7 .33 .34 2.3 .247 .29 3.5 .84.262 .276 .8 .33 .52 .59 .79 437 .33 .567.87 .33 .34 2.65.246.29 4.6 .88 .26 .276 1.25 .339.52 .6 .77 435 .33 .57 1.08 .26 .34 3.6 .245 .29 5.7.89 .26 .276 1.8 .34 .52 .6 It appears from this Table that upon varying the pressure the radii of the principal circles remain very nearly constant, while the amount of the minimum pressure varies nearly as the pressure applied at the orifice, except when the plates are very near indeed. The pressure on any circle of the disc is plainly proportional to the pressure indicated by the gage on that circle and to its radius, jointly. The curves in Fig. 6. are constructed on this principle, their abscissæ representing the distance of the gage from the center, and their, ordinates being taken proportional to (pressure) × (distance), the ordinates becoming of course negative when the pressure is less than that of the atmosphere. Hence the area will represent the whole difference between the pressure on the lower surface of the disc and the atmospheric pressure, the upward pressure being proportional to the areas above the axis, and the downward pressure to those below. These diagrams, therefore, shew, by inspection, the variations of pressure at different distances of the disc from the plate. Thus at .5 it is plainly repelled, at about .25 in equilibrium, from .24 to .024 attracted, between .024 and .018 in equilibrium, and from .018 to contact repelled. The center of the orifice is in all these figures at the left hand, and the decimals are the distances of the disc from the plate. 1 To ascertain the effect produced by varying the diameter of the disc, a gage ABCD, Fig. 5, was provided, which terminated in a flat horizontal tube, made so thin that it could be introduced between two plates at a distance of .08 from each other, the upper plate being, for the convenience of seeing the point of the gage, of glass; and sustained by three little knobs or feet, which served to maintain its distance and parallelism with the lower plate, and yet allowed it to be moved about into any position with respect to the orifice. Inferring then that the pressure of the current, estimated at right angles to its direction, would be the same whether measured in a direction parallel or perpendicular to the disc, the end of the gage was placed, as in the figure, at right angles to the radius, and upon moving it to different distances from the center of the orifice, its indications were found actually to agree with those already obtained by means of the gage before described. Now upon keeping this gage fixed at any distance whatever from the center of the orifice, and observing its indications while the upper plate was moved about, it was found that the pressure was not at all affected by such motion, unless the edge of the upper plate was brought very near the point of the gage, when the pressure became slightly diminished. It may be concluded from this that cat. par. the pressure at any point of the disc at a given distance from the orifice, is not affected by increasing or diminishing the diameter of the disc, or otherwise altering its figure, and this may serve to show why the small discs are blown off: for if in Fig. 4, the disc be reduced to the diameter of Aa, there will be no rarefaction, and it must necessarily be repelled. Again, if it be made at all greater than Cc, the rarefaction will not be increased, but the condensation will slightly, and therefore it will sustain a rather less weight upon further increasing it. A good experiment in illustration of all this is one that was devised by Hauksbee, as long ago as 1719. He shewed that when a current of air was made to pass through a small box, the air contained in the box became considerably rarefied. From this and similar experiments it appears that a current of air communicates its motion to the particles in its immediate neighbourhood, and carries them along with it. In our experiment, then, the first portion of air when it issues from the orifice instead of dispersing itself in distinct streams, communicates its motion to the air contained previously between the plates, and carries it away so that the succeeding portions are compelled to fill the whole space. The air may then be considered as issuing in successive concentric annuli from a cylindrical aperture, whose length is the circumference of the orifice, and height the distance between the plates. Now as the particles in each annulus issue with a certain velocity, and in lines radiating from the center, they must necessarily increase their distance from each other, and hence the air in the annulus becomes suddenly rarefied, by which means its progressive velocity and the pressure on the preceding and succeeding portions is variously modified. Some of these modifications I have attempted to develope experimentally, and have ventured to submit these results to the Society in the hope that they may be found useful hereafter in confirming any theoretical views of the subject which may appear, and in the mean time may serve to throw some light on a phenomenon which is doubtless possessed of very great interest. CAIUS COLLEGE, April 21, 1828. R. WILLIS. |