121.-Hence, we have this convenient rule for finding the volume or space the steam of a cubic foot of water occupies, when the steam is of any given elastic force and temperature.

RULE. TO 459 add the temperature in degrees, and multiply the sum by 765. Divide the product by the force of the steam in inches of mercury, and the result will be the space in feet the steam of a cubic foot of water will occupy.

Example. If the force of the steam be four atmospheres, or 120 inches of mercury, the temperature to that force being according to Mr. Southern's experiments 295°, (art. 77.) then 459 +295 = 754; and

Its volume found by experiment was 404; and considering the difficulty of ascertain

From this table it appears that one volume of water produces more vapour than an equal volume of any other substance in the list.

ing the volume, on account of the allowances to be made for escape of steam of such a high temperature, it agrees very well with the calculated result. According to Dr. Ure's experiments the force of steam at 295°, is 129 inches, which gives 446 for the times the volume is increased by converting into steam of that force and pressure.

122.—It is a well known fact that common water contains a considerable portion of air or other uncondensible gaseous matter, and when water is converted into steam, this air mixes with it, and when the steam is condensed remains in the gaseous state. If means were not taken to remove this gaseous matter from the condenser of an engine, it would collect so as to obstruct the motion of the piston. But even when means for removing it are employed, a certain quantity constantly remains in the condenser of an engine, and in order to determine its state, we must consider the effects produced by mixing air with steam, or vapour, at different temperatures and pressures.

Let us suppose that we have air and vapour of the same temperature t, and elastic force p; and that the volumes are v and v'. If they were now put one on the other in a closed vessel of the capacity v + v', it is plain they could preserve an equilibrium; because, the temperature is the same, and the mutual pressures are equal; but this equilibrium would not be stable.

Experience proves that these gases would gradually mix together till they became completely intermixed. It further shews that during this operation heat is neither evolved nor absorbed; so that after a certain time the mixture is perfectly homogeneous, the two gases holding the same proportion in every part, and the temperature and pressure being t and p. From these facts, established by observation, we may deduce another equally well verified by experience.

123.-If two gases, or a gas and vapour, mixed together at the temperature t fill a volume v; and if p and ƒ denote the pressures they would separately exert when separately occupying the same volume v, at the same temperature t, the pressure of the mixture will be p+f.

In effect, let us suppose that the two gases at first are distinct, and let ƒ be greater than p; then dilating the gas under the pressure f, until ƒ changes to p, its volume will be

come

P

provided the same temperature t has been preserved. Placing the two gases now one on the other, their united volume is

124.-These gases, according to what we have said above, will equally intermix without changing their temperature or common pressure p. Now according to the law of the volume being conversely as the pressure, which is as true of mixed as of simple gases, if we compress the mixture without changing its temperature until its volume

becomes v, the pressure p will become p+f, the same as we had to prove. Equally good would the principle hold with three or more gases, or with a mixture of gases and vapour; in all cases the united pressure will be equal to the sum of all the pressures which the gases or vapours would singly exert, when separately occupying the same volume v at the same temperature t.

When a change of temperature takes place either after or during the mixture, and the first temperature being t; then

125.-This is compared with General Roy's experiments in the following table, formed from the mean results which he obtained.* Commencing at zero, 1000 parts of air, in contact with water, and under a pressure of 32-18 inches, increased in volume by the formation of vapour, and increase of temperature as shewn in the second column of the table; while the third is the force of vapour at these temperatures by our rule; the fourth is computed by the rule in the preceding article.†

* Philosophical Transactions, Vol. LXVII. p. 653.

+ An erroneous formula for this purpose has been copied into several works; it is

the volume; and does not at all agree with the experiments. I gave an analysis of the correct rule in my work on warming and ventilating, p. 291. It has also been investigated by M. Poisson, whose mode of illustration have followed in the above.

The agreement with experiment is in this case very near, and it adds further confirmation of the accuracy of the formula for the force of steam below the boiling point.

126. In the condenser of a steam engine the vapour will be of the elastic force corresponding to its temperature, and that temperature is determined by that of the fluids which condense it.

It will also always become, after a few strokes of the engine, mixed with as much air as it will saturate at the given temperature and pressure; and by the preceding inquiry it appears, that this saturation will take place when there is an equal mixture of air and vapour in the condenser; consequently, only half the quantity drawn out by the air pump at one stroke will be air, the rest will be uncondensed vapour; and the quantity of air drawn out at each stroke must be at least equal to all the air which enters both from the boiler, from the injection water, and from leakage at the joints in the time between stroke and stroke; a slight variation on either side, however, will not, it may easily be proved, have much effect in retarding the engine.

As the volume the air and vapour occupies determines the air pump to be of a large size, and consequently expensive both in construction and power, in order to lessen its bulk, a second injection might be made within the air pump. But the utmost that could be gained by this method would be very little more than the difference of volume due to temperature, not perhaps one-tenth of the volume of the pump in any case.

It is important to remark, that in steam from salt water, the same quantity of air will occupy more space, on account of the steam being of less elastic force at the same

temperature; but perhaps this is much more than compensated for, by salt water containing less air.

Of the Motion of elastic Fluids and Vapours.

127.-A knowledge of the principles and circumstances which affect the motion of elastic fluids is of considerable importance in assigning the relative proportion of the parts of a steam engine. It is a subject that has been very little studied in discussing the theory of this invaluable machine, and therefore, it is one which will engage a considerable share of our attention in this work. Steam is in motion during its action; it must move through passages to perform its office, and be forced through others as it retires; and the effect of disproportion it is difficult to determine from practice alone, because the result depends on so many contingent circumstances.

The best method, therefore, must be to separate the effects, and study each independently; there is then reason to hope that they may be united into a perfect system; and at least it shall be our endeavour to forward this desirable end to the extent of our power.

128. The condition of free elastic fluids, has been shewn to be regulated by the pressure and temperature of the atmosphere. And, when an elastic fluid is confined in a close vessel, its condition as to temperature and pressure must be similar to that it would be in, if in an atmosphere of the same fluid capable of producing the same pressure upon

it.

129.-The most convenient method of investigating the motion of an elastic fluid is, to find the height of a homogeneous column of the same fluid, capable of producing the same pressure as that to which the fluid is subjected. For then the fluid would rush into a perfect vacuum with the velocity a heavy body would acquire by falling through the height of the homogeneous column, when a proper reduction is made for the contraction of the aperture.

130.-If a pipe of communication be opened between two vessels containing elastic fluids of different elastic forces, the velocity of the efflux through the pipe at the first instant, will be that which a heavy body would acquire by falling through the difference between the heights of homogeneous columns, of the fluid of greatest elastic force equivalent to the pressures. And it would be as the velocity acquired by falling through the difference between the heights of the columns equivalent to the pressure at any other instant; the height to be ascertained for the instant at which the velocity is required. After