d

than

In these cases the forces are 4-d and d-D and we

2

have for the couplet 4-d: d-D::V: v. The densities in the Dv orifices are d and D, and we have dV=Dv and V: = Substi d' tuting this last quantity in the couplet we find

as the formula for the value of d by the new theory when D ex2 ceeds 4. The densities in the chamber computed by these formulæ are placed in the third column of the table.

Density of the Atmosphere during Experiment 30.

Density in the receiver.

Density in the cham-Density in the cham-Density in the cham-Deviation of the
ber as found by ex-
ber due to the new

periment.

ber due to the old experiment from the new theory.

theory.

theory.

The affinity of the experimental results to those derived from the new theory, is obvious upon inspection of the table; and the want of affinity to those derived from the old theory, is not less evident. The comparative relation of the two theories to the results of experiment, is more readily seen in the annexed cut,

where they are respectively delineated by a curve. The upper curve represents the densities or elastic forces in the chamber, as found by experiment; the next curve those due to the new theory, and the lower curve those due to the old theory.

Notwithstanding the near approximation of the experimental results to those due to the new theory, there is yet a small but distinct deviation, which holds throughout. This deviation indicates either that there is some cause affecting the flow which the theory does not take into the account, or that in the structure of the apparatus or in trying the experiment, there was some failure to comply with the requisite conditions.

Although the apparatus was rude in its structure, yet care had been taken to secure a compliance with the conditions on which the experiment was based; and in conducting the experiment I was assisted by my friend, Prof. A. C. Twining, a gentleman distinguished for his accuracy in such matters. The experiment, moreover, was several times repeated, with no important difference in the results. For these reasons, in seeking the cause of the deviation, my first inquiry was whether it might be attributed to a change in the ratio of elastic force to density; the theory being predicated on the assumption that this ratio is constant. It has been ascertained by experiment, that when air is condensed and then suffered to lose the heat evolved by condensation, the ratio of its elastic force to its density will be diminished. Hence it is certain that a part or the whole, or possibly even more than the whole heat evolved by condensation will be required to prevent that ratio from being diminished. Still, however, it has generally been assumed by philosophers (I know not on what grounds) that if air is suddenly condensed, so as not to allow the heat evolved by condensation to escape, the ratio of elastic force to density will be increased. This assumption was made by Laplace when he attributed to this cause, in part, the velocity of sound. Let us suppose then, for the present, that in sudden condensation the ratio of elastic force to density is increased. It will then fol low that in sudden expansion, the ratio of elastic force to density will be diminished. But if that ratio were diminished, then the deviation in the table should be in the opposite direction; that is, the experimental results, instead of being greater than the theoretical, should be less. The deviation, therefore, is not accounted for by this supposition; on the contrary, the experiment seems to prove that the ratio is not diminished by expansion, and therefore cannot be increased by condensation, as Laplace supposed.

Let us next take the contrary supposition, viz., that the ratio of clastic force to density is increased by expansion. This would cause a deviation in the same direction as we find in the table. In order to ascertain whether the deviation in question is due to this cause, we must next inquire whether a deviation arising from

this cause, would vary in the same manner throughout the table, as does the observed deviation. Now if we go through the table and assign for each observation severally, the manner in which the ratio of elastic force to density must increase, in order to satisfy that observation, we shall find very nearly one and the same increment of the ratio demanded for all the observations. Hence if we attribute the deviation to this cause we should be obliged to conclude that one and the same change in the ratio takes place, whether the expansion be greater or less. But such a conclusion is obviously inadmissible. We cannot, therefore, attribute the deviation in question to a change in that ratio, either by increase or diminution.

Nor can we ascribe the deviation to that which is the chief cause of deviation from theory in the case of the flow of liquids, viz., the contraction of the stream in passing an orifice. For if that cause operated, it would affect the flow in the same ratio in both orifices, and therefore would not, in this case, affect the indications of the mercurial columns. Moreover, I think it can be shown, from considerations a priori, that the cause which produces the contraction of the stream in liquids, could not operate to affect the flow of expansible fluids.

Having satisfied myself that the deviation was not due to the causes above named, my next inquiry was, whether a difference in the sizes of the orifices (hitherto assumed to be equal) would cause a deviation corresponding to that in the table. In examining this point, I found that the experimental results would be very nearly satisfied throughout the table, by the assumption that the area of the second orifice was less than that of the first, in about the ratio of 933 to 1. As the two orifices had been made as nearly equal as they could be by forcing the same steel plug through both, I was confident that, as originally formed, they could not differ to this extent. But it occurred to me that some accidental circumstance might have occurred to diminish the inner orifice, and I suspected that the workman, in handling the brass plate after the orifice was made, had got dirt into it, and had omitted to cleanse it before soldering on the outer plate. To ascertain whether such was the case, I divided the tube near the second orifice, and, upon examining it with a microscope, discovered that there was dirt adhering around its inner periphery sufficient, I think, to cause a diminution of its area to the extent above nained. Unfortunately this discovery was made after the arrangements for trying the experiment had been removed; and I have not since found leisure to replace them and try the experiment anew. But for this accidental circumstance no doubt there would have been a still nearer approximation of the experimental results to those derived from the formula. The coincidence, however, is sufficiently near to establish the truth of the new SECOND SERIES, Vol. XII, No. 35.-Sept., 1851.

25

theory, so far as respects those points of difference between the two theories specified in the first part of this article.

The fifth column of the table shows the several differences between the experimental results, and those due to the new theory. It will be noticed that these differences increase slightly between density 10 and 13 in the receiver, before they begin to decrease. This, I think, indicates a slight obstruction to the flow through the second orifice, when the density in the receiver becomes equal or nearly equal to that of the effluent stream. This increment at its maximuin amounts to 088, corresponding to the pressure of that portion of an inch of mercury, and is, I think, the measure of the obstruction or resistance due to that circumstance. If this view of the subject is correct, then there would have been a deviation to this extent in this part of the table, even if the orifices had been equal.

It is desirable that further experiments of this kind should be tried by those who have better means at command than I had to do justice to the subject. To such as may be disposed to undertake it, I would suggest that a perfect equality of the two orifi ces might be secured by interchanging the discs, varying the sizes of the orifices until they gave the same indications in both posi tions.

If, after thus securing the equality of the orifices, there should still be a deviation in that part of the table where the elastic force in the chamber is constant, such deviation. I think, must be attributed to a change in the ratio of elastic force to density; and if so, its amount would furnish the means of determining the law according to which that ratio varies.

I would also suggest that a modification of this experiment would furnish perhaps the best possible means of determining the law according to which the ratio of elastic force to temperature varies, when the absolute amount of heat is constant. In an arrangement for this purpose, the bulb of a thermometer should be inserted into the chamber; and the outer orifice should be so constructed that it may be enlarged or diminished at pleasure. With this arrangement, we may cause the air in the chamber to assume, almost instantly, any elastic force we may choose, between the elastic force of the atmosphere, and a little more than twice the elastic force in the receiver; and we may keep that force constant in the chamber during any time that may be required to cool the thermometer down to the corresponding temperature, the continual flow through the chamber in the mean time carrying off not only the heat which flows in from extraneous sources, but also that derived from the thermometer itself. We may thus ascertain the relation of elastic force to temperature at as many points as we please within this range, and thereby determine the law of their variation when the absolute amount of heat remains constant.