in the July following, each had nearly reached the surface, and was quite immovable; and some had grown over the others. Mr. Stutchbury describes a specimen consisting of a species of oyster, whose age could not be over two years, encrusted by an Agaricia, weighing two pounds nine ounces.* It is stated by M. Duchassaing, in a letter from Guadeloupe, that in two months, some large individuals of the Madrepora prolifera, which he broke away, were restored to their original size.† Since the return of the Expedition, I have received a letter containing some facts on the growth of Actinia from Sir J. G. Dalyell, whose able observations in this department of science are highly curious and important. After speaking of the various conditions and sizes of the young at birth, and of the difference in the rapidity of growth depending on the amount of nutriment at hand, he says, speaking of a Scottish species of Actinia, "The dimensions will generally double in a fortnight from its birth. The diameter of the base being originally about an eighth of an inch, or hardly as much, will be five-eighths in six months, and the tentacles will occupy a circle of an inch and a half in diameter. In twelve or thirteen months, the diameter of the base will reach an inch and the expansion of the tentacles two inches between the tips. An Actinia whose tentacula expanded a quarter of an inch three weeks after it was produced, enlarged so much in five months that they expanded an inch, and the body was then half an inch thick." If we reason upon these data, and assume that the Madrepore polyps may increase lineally in six months as much as the young Actinia, we shall have an elongation of five-eighths or three-fourths of an inch in six months. Taking the still more rapid rate, of doubling in a fortnight, which might be more correct, since the Madrepore polyps are about the size of the Actinia in its earliest state, we should have a lengthening of a fourth of an inch in a month, and three inches a year. The data upon which this conclusion is based, though important, are uncertain, but would probably give too high rather than too low an estimate. And yet it is far below the rate apparently established by the experiments with corals cited in the preceding paragraph. We must admit that the subject requires more accurate investigation. The stay of the expedition near any particular reef in the Pacific was too short for any examinations by us. They might easily be made by those residing in coral seas, either in the manner adopted by Mr. Allan, or more definitely by placing marks upon particular species. By inserting slender glass pins a certain distance from the summit of a Madrepore, its growth might be * West of England Journal, vol. i, p. 50, SECOND SERIES, Vol. XII, No. 35.-Sept., 1851. 24 accurately measured from month to month. Two such pins in the surface of an Astræa, would in the same manner, by the enlarging distance between, show the rate of increase in the circumference of the hemisphere; or if four were placed so as to enclose an area, and the number of polyps counted, the numerical increase of polyps resulting from budding, might be ascertained. It is to be hoped that some of the foreign residents at the Sandwich, Society, Samoan or Feejee Islands will take this subject in hand. There are also many parts of the West Indies, where these investigations might be conveniently made. The applications of the facts reviewed occupy us in our next chapter. ART. XX.-On the Flow of Elastic Fluids through Orifices; with a suggestion of a new method of determining the mutual relations of Elastic Force, Temperature and Density in an Expanding Fluid; by ELI W. BLAKE. IN volume V, Second Series, of this Journal, page 78, I proposed a new theory of the flow of elastic fluids through orifices, differing essentially from that heretofore received. The chief object of the present article is to give an account of an experiment instituted for the purpose of testing the truth of that theory. The fundamental points of difference between the old theory and the new, are as follows: 1. The old theory regards the constant force which expels the fluid as being, in all cases, equal to the difference between the elastic forces of the fluids in the two vessels. The new theory regards it as equal to that difference only when the less exceeds half the greater; and in all other cases as equal to half the greater. 2. The old theory considers the fluid as passing the orifice with a density equal to that in the discharging vessel. The new theory considers it as passing the orifice with a density equal to that in the receiving vessel, whenever this last is equal to or greater than half the density in the discharging vessel; and in all other cases, with half the density in the discharging vessel. The formula for the quantity discharged in a given time, predicated upon the new theory, gives, in all cases, less than that predicated upon the old theory. In the case of a flow into a vacuum, the difference amounts to one half. The scheme devised to test the relative merits of the two theories, was founded upon the following considerations, viz.: When air rushes from the atmosphere into a receiver wholly or partially exhausted, passing on its way through a small intermediate vessel or chamber, entering that chamber and passing out H 3. of it through equal orifices, it will take in that chamber a density somewhere intermediate between that of the atmosphere and that in the receiver. For each relation that may at any moment subsist between the density of the atmosphere and that in the receiver, the density in the chamber will have a certain definite and determinate value, such that the chamber may receive through one orifice and discharge through the other simultaneously the same quantity of air. Now since in order to this equal simultaneous flow the two theories respectively demand quite different densities in the chamber, the object of my experiment was to ascertain the actual densities in such a chamber under various relations of the density in the receiver to the density of the atmosphere, in order to compare the densities thus ascertained experimentally with those demanded by each theory respectively in like circumstances. To try the experiment, I constructed the apparatus shown in the annexed sketch. A is a vessel or receiver of the capacity of about 50 gallons, so arranged that it may be exhausted by the air-pump or otherwise. B is an elbow formed of lead pipe of one inch calibre, one branch of which opens into the receiver, and the end of the other branch at C is covered by a brass plate or disc about th of an inch in thickness, through which is an orifice of about th of an inch in diameter. Another similar plate with an orifice of the same size intersects the pipe at D, thus forming a chamber between the two plates. Two short tubes are inserted into the lower side of the pipe; one on each side of the plate D. With these short tubes two glass tubes m and n, each thirty-three inches in length, are connected by means of pieces of India rubber hose. These glass tubes are open at both ends and terminate at the bottom in a vase of mercury. A rod (not shown in the sketch) graduated to inches and tenths is placed beside the glass tubes, sustained upon a float resting upon the surface of the mercury, so adjusted that zero of the graduation may coincide with the surface of the mercury. If the orifice at C be closed by a stopper and the receiver exhausted, the mercury will rise in the tubes; and if the density of the atmosphere at the time of the experiment be expressed in inches of mercury, the height of the mercury in the tubes as read upon the graduated rod will be equal to the difference between the density of the atmosphere and that in the receiver. If we now remove the stopper from the orifice at C, the column of mercury in the tube m will instantly subside to a point which indicates the difference between the density of the atmosphere and the density in the chamber when an equal quantity of air flows through the two orifices; while at the same time the column of mercury in the tube 'n will only have began to subside very slowly as the density in the receiver increases. Having noted the height of the barometer at the time of the experiment, if we note the simultaneous heights of these two columns of mercury, and deduct them respectively from the height of the barometer, we shall have the density in the chamber necessary to an equal flow through the two orifices under the relation which subsists at the moment of notation between the density in the receiver and the density of the atmosphere. And if we note the simultaneous heights of these columns at various times during the filling of the receiver, so many densities in the chamber shall we find corresponding to different relations of the other two densities. At the time of the experiment the height of the barometer, or density of the atmosphere was thirty inches. In consequence of leaks in the receiver, I was unable to exhaust it so as to raise the column in the tube n higher than twenty-six inches. I noted the simultaneous altitudes of the two columns at the moment when the column n coincided with each successive inch-mark upon the graduated rod, and thence ascertained the densities in the chamber under twenty-six different relations between the density in the receiver and that of the atmosphere. These results I have placed in the table beyond, in which the first column shows the densities in the receiver at the times of notation, and the second the densities in the chamber corresponding thereto. In order to ascertain what these densities should have been according to the old theory, I constructed a formula as follows. Let 4 be the height of the barometer at the time of the experiment, D the density in the receiver, d the density in the chamber, V the velocity through the first orifice, v the velocity through the second orifice. Then according to the old theory the force which drives the air through the first orifice is 4-d and that which drives it through the second orifice is d-D. But since an equal quantity flows through both, these forces are as the velocities, that is 4-dd-D::V: v. Again, according to the old theory the density with which the air passes the first orifice is 4, and that with which it passes the second orifice is d. But since the orifices are equal and the quantities which pass through them are also equal, the products of the dv velocities by the densities are equal, that is 4V=dv and V= Substituting this value of V in the preceding couplet and then finding the value of d, we have the following formula for determining the densities in the chamber according to the old theory, viz., The several densities in the chamber computed by this formula are placed in the fourth column of the table. In order to ascertain what the densities in the chamber should have been according to the new theory, I constructed a formula as follows, preserving the same notation as above. By the new theory the force which drives the air through the Δ first orifice is 4-d whenever d is not less than But d is never 2 2 less than when an equal quantity flows through both orifices, for if it were so the chamber would, according to our theory, be receiving as much as could flow into a vacuum under the pressure 4, and must therefore discharge into the receiver as much as would flow into a vacuum under a pressure 4; in order to which the density in the chamber must be equal to 4, and therefore greater than Consequently, the force which drives the air 4 2 through the first orifice is in this arrangement always 4-d. Again, the force expended in driving the air through the second d d 2 orifice by the new theory is whenever D is not greater than 2 Let us first construct a formula for the cases in which D is not greater than d 2 passes the orifices are respectively 4-d and In these cases the densities under which the air 4 couplet, we have d=4; a constant quantity. Hence while the 2 density in the receiver varies from 0 to 4, the density in the 5 chamber is a constant quantity and equal to 4 4. Let us now 15 construct a formula for finding the value of d when D is greater |