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Art. II.- An Automatic Mercury Vacuum Pump; by

M. I. PUPIN, Ph.D., Columbia College.

The pump which forms the subject of the following description is a combination of two distinct forins of apparatus. First, a suction pump capable of raising mercury to practically any height and secondly, an ordinary Sprengel pump. The part

connecting the two is a syphon barometer, properly disposed with respect to the two parts which it connects.

Referring now to the diagram I hiu un )

shall describe each part separately and shall then explain the modus operandi of the combination.

h

F

K

1. The Suction Pump. It consists of the reservoir A to which are joined the short tube n and the tube tvm which I shall call the suction tube. A short branch tube vw is connected by a rubber tube wu to the wide tube u X. This wide tube I shall call the valve tube. The suction tube and the valve tube dip in two separate mercury vessels E and D which are provided with specially constructed glass dishes 1, 2, 3, 4 containing concentrated sulphuric acid for drying purposes. The two vessels are connected to each other by means of a rubber tube. A part of the suction tube a b about 20cm long has a cross-section one-half as large as that of the rest of the tube.

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2. The Sprengel Pump. It is of the ordinary type and consists of the reservoir B from which the mercury drops into a long tube pq, the tube of descent. This tube may be given any convenient length; 160cm will be found sufficient for rapid working. The tube of descent carries a lateral extension which is connected to the reservoir B by means of the tube ghi. The object of this conuection is to keep the gas pressure above and below the mercury in the reservoir the same. Two ground joints k and n are made air-tight by the mercury which fills the surrounding hoods. These joints connect this extension to a manometer and the vessel F which is to be exhausted.

3. The Syphon barometer connection. This is the part consisting of the bulb c and the tube cf. The length of this tube is about 80cm.

All the parts are made of glass.

The modus operandi. First a little mercury is poured through z s into A until the reservoir c is about half full, which is considerably more than sufficient to fill the tube cf. By means of a rubber tube, z 8 is connected then to a water-pump or any other suction pump that may be available. Suppose that this auxiliary suction pump is capable of reducing the pressure in A to say 40mm and suppose also that the barometric pressure is 760mm. Owing to the action of the auxiliary suction pump the gas pressure in A is continually reduced and therefore also in F and in all other parts connected with A. Mercury rises in the valve and suction tubes and also in the tube of descent. The extremity m of the suction tube is placed at such a distance below the initial level of the mercury in E and D that when the mercury column in the suction tube is about 60cm long the mercury level in E (which sinks rapidly on account of the rising of the mer. cury into the valve tube) has just reached m. From that moment on no more mercury gets into the suction tube. But owing to the action of the auxiliary pump the pressure in A is being still reduced, hence the column in the valve tube rises still higher and the level in E sinks still lower. In the mean time the column in the suction tube rises bodily owing to the external air pressure until it reaches the narrow part ab when it begins to lengthen out, and since ab is 20cm long and the initial length of the mercury column is 60cm it follows that this column will be lengthened out to 70cm and no more. Hence as soon as the pressure in A has been reduced by 70cm this column will rise with accelerated velocity until it is injected by the external air pressure into the reservoir A. The external air rushes then into A and through tvw into the valve tube. The valve tube column sinks and the level in E rises. But it will rise more rapidly in D than in E owing to the friction of the narrow rubber tube connecting the two vessels E and D. Hence it will continue to rise for a short time even after it has reached m and by closing the suction tube started again the action of the auxiliary suction pump. This retardation of the level in E is of considerable importance, for if the suction tube had no contraction ab and if the two levels in E and D were continually of the same height then the mercury would be sucked up through the suction tube not in form of solid columns but in forın of numerous drops separated from each other by air bubbles. This would render the rapidity of action less satisfactory; besides, it would also cause a rapid oxidation of the mercury.

As soon as the quantity of mercury injected into A brings the distance between the level in A and the point f into the vicinity of the barometric height then the mercury begins to overflow from the syphon tube into the reservoir B and the exhausting of F begins. By squeezing the tube connecting E and D the rapidity of supply to B is varied, hence the quantity of mercury in B can thus very easily be kept within certain desirable limits.

The simplicity and the convenience of the apparatus need n. comment. Suffice it to observe that it has no stopcocks and that it can operate with a much sinaller quantity of mercury than required by ordinary mercury pumps.

My experiments with vacuum tube discharges suggested long ago to my mind a pump of this type; but want of time and of a glass blower at a convenient distance prevented me from giving my ideas on this matter a practical test, until last summer.* I intend to publish soon numerical data concerning the rapidity of working of the various forms of pumps of this type. The vacua obtainable by it are, of course, the same as those obtainable by the ordinary form of the Sprengel pump.

Electrical Laboratory, Dec. 17th, 1894. Columbia College, New York.

ART. III.On Graphical Thermodynamics ; by

RENÉ DE SAUSSURE.

Translated by the author from vol. xxxi of the Archives des Sciences physiques

et naturelles, May, 1894. 1. HEAT is usually regarded as a periodical motion of the particles constituting the material bodies; if this be true, the variations in the physical state of a substance are due to the variations of the state of this periodical motion; in other words, the physical state of the substance is a function of the state of the periodical motion. Since the periodical motion of the particles can be defined by its kinetic energy and by the duration of its period, the physical state of the substance can be completely defined by means of these two data, provided that the weight of the substance remains the same.

* (More particular details of construction will be given to Messrs. Eimer & Amend, 18th Street and 3d Ave., New York, and to Herr Kramer, Glasbläser, Fridrich Str., Freiburg, Baden ]

It is by so defining the state of a body, that Clausius succeeded in demonstrating the fundamental theorems of thermodynamics, with the help only of the laws of mechanics, without making any hypothesis as to the form of the trajectories described by the particles of the body.

But if it is desired to establish the theory of the transformations which take place in a substance under the influence of heat, it is necessary to define the nature of the periodical motions, as well as in the theory of light. We can assume for instance, that this motion is a straight vibratory motion on either side of a fixed center.

By this hypothesis, we still need two data to detine completely the motion of the particles, i. e., the amplitude a and the duration i of one period of the vibratory motion. And since the state of the substance (whose mass is taken as the unit) is a result of the state of motion of the particles, the state of said substance can be considered as a function of the two variables a and i.

2. On the other hand, to define the physical state of a substance by means of experimental data, the variables used are : the volume V, the absolute temperature T' and the outside pressure P (the mass being still taken as the unit).*

Hence, the state of a body can also be regarded as a function of the three variables: P, V and T. But these variables are not independent, that is to say: the same weight of the same body cannot occupy the same volume at the same pressure and at different temperatures, since two variables are sufficient to define the state of the substance. For each body, there is a relation F(P, V, T) = 0 known as the equation of said body, so that the value of either of the three variables P, V or T is a direct result of the values attributed to the two others.

Considering P, V and T as three coördinates, the equation FP, V, T) = 0 represents a surface, any point of which corresponds to a certain state of the body. This surface is therefore a • representative locus” of the different states under which the body can exist, and is known as the " thermodynamic surface.

3. When the physical state of a substance is defined by the first method, i. e., by means of the amplitude a and of the period i of the vibratory motion which constitutes the heat, the variables a and i can also be treated as two coördinates, and the physical state can be represented on a piece of paper by the point corresponding to these coördinates. In this case, the piece of paper itself or a part of it, is the representative locus of the different states under which the substance can exist.

* In the following study. we assume that all the particles of the body are at the same temperature, i. e., that they all have an identical vibratory motion.

It follows that each point of the thermodynamic surface F(P, V, T) = 0 corresponds to a point on the sheet of paper, and conversely. If the variables P, V and T vary continuously, the variables a and i shall also vary continuously, since the variation of the state of the body is itself continuous ; so that the coördinates P, V, T are continuous functions of the coördinates a and i.

P=1(a, i)
V=ua, i)

(1) T= v(a, i) These three equations can be regarded as the general equation to the thermodynamic surface in terms of two auxiliary variables a and i ; hence, by eliminating a and i between them, the result must be: F(P, V, T) = 0.

The variables a and i can be considered as the coördinates of any point on the thermodynamic surface. Any relation between a and i represents a curve traced on this surface, i. e., a cycle of transformations undergone by the substance.

We have just seen that the functions , u must be such as to lead to the relation F(P, V, T) = 0 by eliminating a and i between equations (1); but as long as these functions are submitted only to this condition, the variables a and i are still arbitrary variables and do not necessarily denote the amplitude and the period of the vibratory motion, since there are an infinite number of ways of representing the same surface by means of two auxiliary variables. For instance, the equation of the body: T=f(P, V) can be put under the form:

P=u
V= =V

T = f (16, v) u and v being the two auxiliary coördinates chosen to represent graphically the cycles of transformations.

These coördinates u and v being equal to P and V respectively, the graphical representation thus obtained would be the same as the one first introduced in thermodynamics by Clapeyron, and would have the same property, i. e., the area lying between the axis of V, two ordinates and the path described by the body would be equal to the external work.

If other coördinates are chosen, the properties of the graphical representation will change, for it is evident that these

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