different from those actually obtained by him. I will cite a single example in support of this. One day I had a plate of tinned iron in contact with the surface of water, and noticed that the water became sensibly changed by the oxidation of the iron and other influences that I could not explain. Now this plate of tinned iron and a similar plate of brass experienced an equal resistance on the surface of the water thus changed, while below the surface the resistance encountered by the brass was considerably less than that encountered by the tinned plate.

4. The resistance offered by the surface of liquids to solids may be distinguished into linear and superficial, while below the surface the resistance is superficial only. This distinction, though simple, is important. The resistance which the body encounters when its surface is in contact with the liquid is different as compared with the resistance it meets with at the line of separation between the surface of the liquid and the upper external surface of the solid. I name this latter the linear resistance, the former the superficial. The linear does not exist when the body is totally immersed in the liquid, while the superficial in the case of thin plates so immersed has a value sensibly double that which is experienced at the surface.

The apparent complications and irregularities in the results obtained when using metallic solids of various forms and contours disappeared as soon as I had made the above distinction. With plates of the same material in the same liquid I found, in some cases depending on the form, less resistance below the surface, as happened to Plateau with the needle in the water and numerous saline solutions; while in other cases there was a less amount of resistance at the surface of the liquid, contrary to the results given by Plateau.

The theory is easy, and naturally follows from the phenomena. Let λ be the linear resistance and σ the superficial. The total resistance on the surface of the liquid is λ+o. Below the surface, for thin plates it is 2o. But depends on the contour of λ the plate, σ on the superficies; and it will be understood that whatever be the linear resistance for every unit of length, and the superficial for every unit of superficies, dependent on the relation of the contour to the superficies of the plate, we thus get for one and the same plate, and one and the same liquid, one of three cases:

If M. Plateau will repeat his experiments with a magnetic needle in which the greater diagonal is equal to that of the needle already used by him, and with the minor diagonal equal to the half of the major, he will probably obtain results different

from those already arrived at by him. Such a needle moves more quickly on the surface of water than below it.

It must be remarked that the linear resistance does not depend on the internal contour, but solely on those parts of it which move normally or obliquely to their direction. The contour of a circular disk which turns on its centre experiences little or no resistance. The portions of the contour oblique to the direction of their motion operate sensibly as their projections on the normal to the direction of the motion are at equal distances from the centre.

Further experiments may lead to the introduction of some modifications in the foregoing conclusions.

XXIV. Memoir on Internal Work in Gases.
By M. ACHILLE CAZIN.

[Continued from p. 99.]

§ IX. Influence of moisture in the gas.

SECTIONS V., VI., VII., VIII. indicate what are the indispensable precautions for a good series of experiments. In the following sections I shall adduce several facts which will prepare for a complete explanation of the phenomenon.

I shall first demonstrate that we cannot admit the depression of the curve of the h's to be due to aqueous vapour in the gas. In order to ascertain the possible value of this objection, let us examine the most unfavourable case-that in which the gas in the reservoirs is saturated with aqueous vapour.

The whole apparatus having a capacity of 42.868 litres, contains 7.181 grms. of vapour at 20°, under the tension of 17 millims. of mercury, equivalent to 125 millims. of sulphuric acid. When the whole of the gas in reservoir B is made to pass into reservoir A, there is supersaturation in the latter, and a portion of the vapour there is liquefied and deposited on the sides. If the vapour which remains were condensed during the expansion, forming a mist, the depression of h would have just the value of 125 millims., and the curve would afterwards rise in proportion as the mist disappeared and the water condensed on the sides returned to a state of vapour; but this last effect would be slow, and the depression would maintain itself a long time, probably longer than in my experiments.

Suppose the hygrometric state to be in the gas, and that we compress it to 4 atmospheres in the reservoir A; there would still be saturation in this reservoir, and the depression would still take place; but this time it could not exceed 31 millims. of mercury; and as there would be no water condensed on

its sides, this depression would disappear as rapidly as the mist. Thus we should not observe the effect described; but the presence of aqueous vapour would exercise a considerable influence on the magnitude of the depression. Hence the objection is important, and it was indispensable to be certain that the gas was completely dried.

For this purpose 2 metres of pumice-stone saturated with sulphuric acid were placed between the tubulures H and H'; and after having compressed the gas in A by means of the pump, it was allowed to return to the reservoir B, passing through the long column of pumice-stone as slowly as was wished: it was sufficient to regulate properly the stopcocks r', rl (fig. 2). This manipu lation was repeated several times before Series VII. (on hydrogen) was commenced; and it was ascertained that no appreciable moisture was deposited in a drying-tube, by weighing the latter before and after the passage of the gas. Experiments A, B, C, D of the following series were then made; the minimum of h was between 90 millims. (sulphuric acid) and -102 millims. After this trial a column of anhydrous phosphoric acid of 60 centims. was placed between the tubulures H and H', and the gas was made to pass several times through this substance by the process described. The two experiments and B were then made, and the minimum of h was 108 millims, and -89 millims. The six curves of this series are identical, so that it is impossible to admit the influence of moisture. Hence the drying by sulphuric acid is sufficient. In all the experiments the gas was not only dried during its introduction into the reser voirs, but also afterwards by the process described in the present paragraph.

Series VII. (September 1867).

Dry hydrogen, Metal reservoir B.

p1=3.80 atmospheres, p=0.22 atmosphere. Temperature between 2007 and 21°2.

8X. Influence of the dimensions and nature of the reservoirs. This influence is ascertained by the comparison of experiments in which for the reservoir B either the cylindrical zinc vessel, containing 33.805 litres, or the glass globe of 60-617 litres was taken and the gas in reservoir A compressed under a constant pressure p. Thus we had in both cases the same mass of gas expanding from the same pressure p, to the same final pressure p'. But the mass of gas contained in reservoir B was different, as well as the pressure p2. By increasing the capacity of the reservoir B the pressure p2 was increased, and also the mass of gas compressed during the expansion. Let μ be the mass of the unit of volume of the gas under the pressure p', and v the increase of volume of the reservoir B; the mass of compressed gas was increased by vμ, whatever the pressure p,; it is the mass of 26.812 litres of gas at a pressure but little different from that of the atmosphere,

Series VIII. (November 1867).

Dry hydrogen. Metal reservoir B.

P1=3.80 atmospheres, p=0.24 atmosphere. Temperature

Series II., previously mentioned, and Series VIII. afford an example of comparison. The coordinates of the minimum are h=-124 millims., t=2 seconds (Series VIII., zinc reservoir), and h=-67, t=2 seconds (Series II., glass reservoir). We have traced in fig. 6 the line X'X' which expresses the Series II., and the line XX which expresses the Series VIII.

The first meets the axis of the abscissæ two seconds later than the second; and the maximum of h in the first has scarcely more than one-third of the value it has in the second.

The same result is obtained by comparing Series IV. and I. (air). The coordinates of the minimum are h=-35 millims. (sulphuric acid) in Series IV. (glass), and h=-136 millims. (sulphuric acid) in Series I. (zinc). Moreover the abscissa of the point h=0 is greater, and the curve does not rise so far above the abscissæ in Series IV. as in the other.

The experiment shows thus that the cause of the depression is intimately connected with the quantity of gas which the jet encounters during the expansion. We must attribute this depression to a mechanical or thermic effect counteracted by the gas contained in reservoir B. Let us examine how this can take place.

By distinguishing three parts in the gas in motion as we have done before, we see, first, that the quantity of gas left in reservoir A is the same in each pair of experiments, since the expansion commences at the same pressure p1 and finishes at the same pressure p'. The quantity of gas which passes into reservoir B is also the same, since the reservoir A always contains the gas compressed under the pressure p1. The third part, that which is contained in reservoir B, alone changes; it increases with its capacity. The law of expansion of the first part remains the same; the gas expands by overcoming a pressure equal at each moment to its elastic force. But it is not the same for the other two parts. The second always expands, it is true, from the pressure p, to the pressure p', but by overcoming a pressure less than its elastic force and varying from p2 to p'; and we have seen that p, increases with the capacity of B. The resistance to the flow being smaller than the elastic force of the portion of gas considered, its molecules acquire certain velocities; and evidently these velocities are greater the less the counterpressure p2. This is a difference of mechanical effect about which we can have no doubt.

The state of motion of the second part can only last a certain time; little by little the molecules lose their velocities, producing heat, so that the mechanical effect finally transforms itself into a thermal effect. Such a condition must contribute to the depression observed in experiments where the value of is very small. We are thus brought to recognize one of the causes of this depression. The greater the velocity of the efflux the greater the depression; hence it is due, at least in part, to the fact that the gaseous molecules do not instantaneously lose their velocities.

The character of the third part remains to be studied. It is compressed from p, to p', and consequently its temperature is raised. The compression and rise in temperature, on the one hand, are less when p2 increases; but, on the other, the quantity of gas which constitutes the third part increases more rapidly