effect that air must, in such circumstances, experience in acquiring such a velocity would be from 287° to 268° absolute temperature, or 19° Cent.

The effects of fluid friction in different parts of the stream would require to be known in order to estimate the reduced velocity in any narrow part, according to either the density on the high-pressure side or the density on the low-pressure side. We have not as yet made any sufficient investigation to allow us to give even a conjectural estimate of what these effects may be in any case. But it appears improbable that the "reduced velocity," according to the density on the high-pressure side, could ever with friction exceed the greatest amount it could possibly have without friction. It therefore seems improbable that the "reduced velocity" in terms of the density on the high-pressure side can ever, in the narrowest part of the channel, exceed 644 feet per second, if the temperature of the high-pressure air moving slowly be about the atmospheric temperature of 13° Cent. used in the preceding estimate.

29

1000'

Experiments in which we have forced air through apertures of 1880, 153, and 84ths of an inch in diameter drilled in thin plates of copper, have given us a maximum velocity reduced to the density of the high-pressure side equal to 550 feet per second. But there can be little doubt that the stream of air, after issuing from an orifice in a thin plate, contracts as that of water does under similar circumstances. If the velocity were calculated from the area of this contracted part of the stream, it is highly probable that the maximum velocity reduced to the density on the high-pressure side would be found as near 644 feet as the degree of accuracy of the experiments warrants us to expect.

As an example of the results we have obtained on examining the temperature of the rushing stream by a thermo-electric junction placed th of an inch above the orifice, we cite an experiment, in which the total pressure of the air in the receiver being 98 inches of mercury, we found the velocity in the orifice equal to 535 and 1780 feet respectively as reduced to the density on the high-pressure and that on the atmospheric side. The actual velocity in the small aperture must have been greater than either of these, perhaps not much greater than 1780, the velocity reduced to atmospheric density. If it had been only this, the cooling effect would have been

k-1/178

exactly Tk-1

2

that is, a lowering of temperature amount

2 1115

ing to 150° Cent. But the amount of cooling effect observed in the experiment was only 13° Cent.; nor have we ever succeeded in observing (whether with thermometers held in various positions in the stream, or with a thermo-electric arrangement constituted by a narrow tube through which the air flows, or by a straight wire of two different metals in the axis of the stream, with the junction in the place of most rapid motion, and in other positions on each side of it,) a greater cooling effect than 20° Cent; we therefore infer that a body round which air is flowing rapidly acquires a higher temperature than the average temperature of the air close to it all round. The explanation of this conclusion probably is, that the surface of contact between the air and the solid is the locality of the most intense frictional generation of heat that takes place, and that consequently a stratum of air round the body has a higher average temperature than the air further off; but whatever the explanation may be, it appears certainly demonstrated that the air does not give its own temperature even to a tube through which it flows, or to a wire or thermometer-bulb completely surrounded by it.

Having been convinced of this conclusion by experiments on rapid motion of air through small passages, we inferred of course that the same phenomenon must take place universally whenever air flows against a solid or a solid is carried through air. If a velocity of 1780 feet per second in the foregoing experiment gave 137° Cent. difference of temperature between the air and the solid, how probable is it that meteors moving at from six to thirty miles per second even through a rarefied atmosphere, really acquire, in accordance with the same law, all the heat which they manifest! On the other hand, it seemed worth while to look for the same kind of effect on a much smaller scale in bodies moving at moderate velocities through the ordinary atmosphere. Accordingly, although it has been a practice in general undoubtingly followed, to whirl a thermometer through the air for the purpose of finding the atmospheric temperature, we have tried and found, with thermometers of different sizes and variously shaped bulbs, whirled through the air at the end of a string, with velocities of from 80 to 120 feet per second, temperatures always higher than when the same thermometers are whirled in

exactly the same circumstances at smaller velocities. By alternately whirling the same thermometers for half a minute or so fast, and then for a similar time slow, we have found differences of temperature sometimes little if at all short of a Fahrenheit degree. By whirling a thermo-electric junction alternately fast and slow, the same phenomenon is most satisfactorily and strikingly exhibited by a galvanometer. This last experiment we have performed at night, under a cloudy sky, with the galvanometer within doors, and the testing thermo-electric apparatus whirled in the middle of a field; and thus, with as little as can be conceived of disturbing circumstances, we confirmed the result we had previously found by whirling thermometers.

Velocity of Air escaping through narrow Apertures*.

In the foregoing part of this communication, referring to the circumstances of certain experiments, we have stated our opinion that the velocity of atmospheric air impelled through narrow orifices was, in the narrowest part of the stream, greater than the reduced velocity corresponding to the atmospheric pressure; in other words, that the density of the air, kept at a constant temperature, was, in the narrowest part, less than the atmospheric density. In order to avoid misconception, we now add, that this holds true only when the difference of pressures on the two sides is small, and friction plays but a small part in bringing down the velocity of the exit stream. If there is a great difference between the pressures on the two sides, the reduced velocity will, on the contrary, be less than that corresponding with the atmospheric pressure; and even if the pressure in the most rapid part falls short of the atmospheric pressure, the density may, on account of the cooling experienced, exceed the atmospheric density.

We stated that, at 57° Fahr., the greatest velocity of air passing through a small orifice is 550 feet per second, if reduced to the density on the high-pressure side. The experiments from which we obtained this result enable us also to say that this maximum occurs, with the above temperature and a barometric pressure of 30 14 inches, when the pressure of the air is equal to about 50 inches of mercury above the atmospheric pressure. At a higher or lower pressure, a smaller volume of the compressed air escapes in a given time.

*Received June 19, 1856.

Surface Condenser.-A three-horse power high-pressure steamengine was procured for our experiments. Wishing to give it equal power with a lower pressure, we caused the steam from the eduction port to pass downwards through a perpendicular iron gas-pipe, ten feet long and an inch and a half in diameter, placed within a larger pipe through which water was made to ascend. The lower end of the gas-pipe was connected with the feed-pump of the boiler, a small orifice being contrived in the pump cover in order to allow the escape of air before it could pass, along with the condensed water, into the boiler. This simple arrangement constituted a "surface condenser" of a very efficient kind, giving a vacuum of 23 inches, although considerable leakage of air took place, and the apparatus generally was not so perfect as subsequent experience would have enabled us to make it. Besides the ordinary well-known advantages of the "surface condenser," such as the prevention of incrustation of the boiler, there is one which may be especially remarked as appertaining to the system we have adopted, of causing the current of steam to move in an opposite direction to that of the water employed to condense it. The refrigerating water may thus be made to pass out of the condenser at a high temperature, while the vacuum is that due to a low temperature; and hence the quantity of water used for the purpose of condensation may be materially reduced. We find that our system does not require an amount of surface so great as to involve a cumbrousness or cost which would prevent its general adoption, and have no doubt that it will shortly supersede that at the present time almost universally used.

IV." On the Stability of Loose Earth." By W. J. MACQUORN RANKINE, Esq., C.E., F.R.SS. L & E., Regius Professor of Civil Engineering and Mechanics in the University of Glasgow.

(Abstract.)

The object of this paper is to deduce the mathematical theory of that kind of stability which depends on the mutual friction of the parts of a granular mass devoid of tenacity, from the known laws of friction, unaided by any hypothesis.

The fundamental principle of the internal stability of such a mass has already been published in the 'Proceedings of the Royal Society' for the 6th of March, 1856, viz. that the ratio of the difference to the sum of the greatest and least pressures at each point of the mass must not exceed the sine of the angle of repose.

The principles of the general theory of the internal equilibrium of a solid mass are expressed in a form suited to the special subject of the paper. For the purpose of determining the conditions of equilibrium under its own weight, of a solid mass whose upper surface is that generated by the motion of a horizontal straight line along a line of any figure described on a vertical plane at right angles to the generating line, the mass is supposed to be divided into layers of equal horizontal thrust by a series of surfaces, which layers are subdivided into elementary horizontal prisms by vertical planes normal to the vertical plane first mentioned. For independent variables there are taken the horizontal coordinate in this plane, and the total horizontal thrust from the upper surface down to a given surface of equal thrust. The condition of equilibrium of any one of the before-mentioned elementary prisms being expressed by a differential equation in terms of those variables, the integration of that equation gives the vertical coordinate of any surface of equal thrust in terms of the total thrust down to that surface and of the horizontal coordinate. The integral obtained belongs to a class first investigated by Fourier.

An approximation to the forms of the surfaces of equal thrust is obtained by a simple graphic process, first employed by Prof. William Thomson in connexion with the theory of electricity.

It is shown incidentally how the same integral may be applied to determine the intrados from the extrados of any arched rib, loaded only with its own weight.

The pressure on a surface of equal thrust is vertical; the pressure on a vertical plane at a given point is parallel to the surface of equal thrust traversing that point. When the upper surface of the mass of earth is one plane, horizontal or inclined, the surfaces of equal thrust are planes parallel to it. When the upper surface presents elevations and depressions, the surfaces of equal thrust have corresponding elevations and depressions, gradually vanishing as the depth increases.