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time, also for measuring the pressure of gas in the chambers, for exhausting the chambers, and for bringing the chambers into direct communication when required. The different temperatures were secured by a stream of steam on the one side, which gave a temperature of 212° F., and a stream of water on the other side, wbich gave a temperature constant for the time, but which ranged during the investigation from 47° in February to 70° in July.
The porous plates tried were of biscuit-ware, stucco, and meerschaum, and ranged in thickness from •06 (1.5 millims.) to .44 inch (11:2 millims). The pressures of gas within the chambers and the difference of pressure on the two sides of the plate were measured by mercury gauges. A special instrument used for reading the differential gauge read to the tooooth of an inch (.0025 millim.).
Several weeks were spent on this apparatus in getting it tight, getting the gauges to work, and getting rid of the disturbing effects of moisture, before any definite results were obtained, but finally the instrument answered extremely well.
The Experiments on Thermal Transpiration. The streams of steam and water having been kept going for several hours, long enough for the condition of temperature in the instrument to be perfectly steady, the tap which established communication between the chambers on the opposite sides of the porous plate having been open, so that the pressure in these chambers was equal, this tap was closed, so that the sole communication was through the porous plate. Any difference of pressure between these chambers was then read on the differential gauge.
Supposing that on the first reading the gas (whatever it might be) within the instrument was at the pressure of the atmosphere, a certain quantity of gas was then drawn out and the experiment repeated. This was done until the pressure within the instrument was as low as 25 inch of mercury.
According to the theoretical deductions, it had appeared that when the sole communication between the two chambers was through the porous plate, and the gas in these chambers was at the same pressure, the difference of temperature would cause the gas to pass from the colder chamber to that which was hotter, until a certain difference of pressure was established, after which there would be no further change as long as the same difference of temperature was maintained, so that the result to be expected as giving evidence of thermal transpiration was a difference in the pressure on the two sides of the plate.
This difference was first obtained with air at the pressure of the atmosphere and a biscuit-ware plate, the difference being 1 inch (2:54 millims).
It further appeared from the theory that the difference which would, cæteris paribus, depend on the difference of temperature, would also depend on the relation between the density of the gas and the coarseness of the plate, so that, cæteris paribus, the finer the plate the greater the difference, and this conclusion was at once verified.
A plate of meerschaum, .25 inch (6.3 millims.) thick, gave a difference, -25 inch with air, and •88 with hydrogen, at the pressure of the atmosphere, while a plate of stacco of the same thickness as the meerschaum only gave a difference of .02 inch with air and •14 inch with hydrogen.
It also appeared from the theory that with the same plate and the same gas, the difference of pressure should be a maximum at some particular density, so that if the initial density was sufficient, the thermal difference of pressure would increase as exhaustion proceeded up to a certain point and then fall off, the density at which the thermal difference would be a maximum depending on the coarseness of the plate and the nature of the gas. These conclusions were verified.
For with the meerschaum piate the thermal difference for air was almost constant at pressures nearly equal to the atmosphere, but fell at an increasing rate as the density diminished (this is shown by the curve for air, fig. 1). From this it was clear that if the thermal difference reached a maximum it would be at some pressure greater than that of the atmosphere. With stucco the thermal difference for air increased as the pressure fell from that of the atmosphere, and reached a maximum only at a pressure of about 8 inches of mercury (shown in fig. 2).
A comparison of these results shows that the density at which the thermal transpiration is a maximum depends on the coarseness of the plate; and that it depends on the nature of the gas appears at once on comparing the results for hydrogen, air, and carbonic acid, which are shown on figs. 1 and 2.
Experiments with plates of various thicknesses gave the thermal difference of pressures independent of the thickness of the plate, so long as the difference of temperature was the same.
Several minor deductions from the theory were also directly verified.
The Law of Corresponding Results at Corresponding Densities. In order to establish this law it was necessary to compare the results obtained with different plates. According to the law, the ratio of the thermal difference of pressure to the mean pressure with a particular plate and a particular gas should be the same as with another plate and the same gas, as long as the densities (or pressures) are in a fixed ratio, which is the ratio of the fineness of the plates.
A simple numerical calculation sufficed to show that this conclusion is approximately verified. On dividing the thermal differences by the mean pressure for both the meerschaum and stucco plates, it
appears that the resulting numbers are approximately equal, so long as the pressure with the meerschaum is six times as great as with the stucco. This is so both for air and hydrogen, and through a range of pressures from 30 to 35 inches with the meerschaum, and 5 to 2 inches with the stucco.
The numerical comparison does not, however, bring out the agreement in nearly as strong a light as the comparison which has been effected by a graphic method.
Graphic Method of comparing the Results. This method consists in taking as ordinates and abscissæ, not the thermal differences and mean pressures, but the logarithms of these quantities, and the curves so formed are called the logarithmic homo. logues of the curves shown in figs. 1 and 2.
Any common ratio which exists between ordinates or abscissæ of corresponding points on the natural curves becomes a common difference between the ordinates or abscissæ of their logarithmic homologues, so that if the natural curves correspond after the manner that has just been described, their logarithmic homologues must be precisely similar curves, such that by shifting the one parallel to itself it can be made to fit on to the other.
In fig. 3 a b and cd are the logarithmic homologues respectively for the air curve and the hydrogen curve with meerschaum, and e f and g h are the logarithmic homologues respectively for the air and hydrogen curves with stucco. By tracing ef and g h together with their axes on the same paper, and moving the paper without turning it, until the traced curves fit the curves for meerschaum, it is found that the fit is perfect, a portion of the traced carve e' f' coinciding with a portion of a b, and a portion of g' h' coinciding with cd.
O'M and O' N, the components of the shift, are the logarithms of the ratios of the corresponding ordinates and abscissæ of the natural curves; and in the particular case to which fig. 2 refersO'N .7
log. 5 O'M .77
log. 5.9 It is thus seen that the reason why the numerical comparison did not
give absolutely consistent results is because the ratio of the corresponding abscissæ is not exactly the same as that of the corresponding ordinates, the difference being found on examination to be owing to a discrepancy in the temperatures, which affected the ratio of the corresponding ordinates, but not the ratios of the corresponding abscissæ. These, therefore, give 5 as the ratio of the coarseness of these parti. cular plates.
The woodcut, fig. 3, merely illustrates the result. The logarithmic homologues of the curves for both air and hydrogen, plotted with the greatest care, the points marking the experiments being so close together that it was scarcely necessary to draw a curve, have been compared, and the agreement is very remarkable, the only slight deviation being that shown in fig. 3, which was found to be owing to some impurity in the hydrogen at pressures below an inch of mercury.
In order fully to appreciate the force of this agreement, it must be noticed that it is not only the portions of the curves which overlap that
agree in direction, but also the distances between the curves for hydrogen and air, which are shifted in pairs.
Nothing could prove more forcibly than this fitting that the difference in the results for different plates depends on a relation between the density of the gas and the coarseness of the plates.
Experiments on Transpiration under Pressure. According to the theoretical deductions the rate at which
would be forced through a tube or porous plate by a difference of pressure bearing a fixed ratio to the mean pressure of the gas in passing, would vary with the mean density of the gas according to a law which would hold with different plates, the corresponding results being obtained at pressures inversely proportional to the diameters of the tubes. The differences in the laws of transpiration which Graham found with different tubes and plates are, so far as they go, in fair accordance with the law as deduced from this theory, but the range of densities over which Graham's results extend is too small to allow a very complete verification, and the chief object in these experiments was to extend this range of densities. The apparatus used was the thermo-diffusiometer, slightly modified, and without the streams of steam and water. The instrument lent itself very well to this part of the investigation. It allowed of the measurement of the time of transpiration of a definite volume of gas, measured at whatever might be the pressure of the instrument, through the porous plate, under a difference of pressure bearing a fixed ratio to the pressure within the instrument.
The times of transpiration of equal volumes of air and hydrogen through plates of stucco and meerschaum were determined at pressures varying from that of the atmosphere to a fraction of an inch of mercury.