stancy of flow suggested by Rankine is this: as the jet leaves the straight tube and flares out, its section is constantly greater. The calculation made by theory assumes that the less pressure you are flowing into is that of the orifice of the tube. Therefore, you use the section of the orifice, and the fact is, probably, that this is not the place where the lower pressure exists. The lower pressure belongs to some section a little below the tube, just as has been found with nozzles through which water flows. The true section to take is some section yet unlocated beyond the orifice, having a cross-section greater than the orifice of the tube, and what we want is, to make such tubes as that and take the pressure along the jet; make a tube that does not confine the jet, and determine the pressure along that jet. Find where the lower pressure used in the formula is situated, and use that cross-section. Now, Rankine's suggestion at once explains why the coefficient of flow varies-why the coefficient of flow must vary according to the density of the atmosphere it flows into. I should like to see Professor Peabody add to this paper a column showing velocities and flow, because I find a great many people don't appreciate this paradox. The velocity of flow is always greater as the lower pressure is less, but the weight of the flow is itself constant. The velocity is the same, but the weight of flow bas this peculiar constancy, which only direct experiments pointed out. I should like to see some one investigate it from that point of view, and certainly this maximum 242 in the table is something I never saw before. I shall go over the ground myself as soon as I return.

Prof. Peabody.-In answer to Professor Denton's question concerning the coefficient of flow, it is to be said that the term is carefully avoided in the paper, since the method of calculation used is known to be defective, in that the quantity Q, in the first equation, is assumed to be zero, while we have reason to believe that it has an appreciable, but as yet unknown, value. There is also reason to believe that heat is given by the steam to the tube at or near the entrance, and that the tube gives heat to the steam near the exit. There is also a question whether steam may not be condensed on the surface of the tube near the entrance, and the resulting water blown through the tube in the liquid state, though this suggestion raises a question as to how the tube could in such case dispose of the heat given to it.

I do not think that the area of the stream of steam under consideration can be in question, because the tube was purposely

made long enough to avoid confusion with the flow through an orifice or a short tube. I would like to ask Professor Denton whether the experiments to which he refers were not made on the flow of steam through an orifice.

The calculation of the velocity of the steam in the tube by the second equation can be readily made, but it was not set down in the table, since it did not appear to throw any light on the problem. The actual velocity cannot be determined till the per cent. of moisture in the steam in the tube can be determined in some way; a determination based on the equations in the paper must have the same defect as the calculation by them of the flow, and I know of no experimental method.

Prof. Denton.—The experiments I quoted were made with tubes just as Mr. Peabody has made them-one reservoir with another connected by a tube.

Mr. Babcock.-Mr. President, I wish to say but just a word in regard to this point: that, though the experiments do not seem to carry out the theory upon which Professor Peabody started, they do seem to sustain very closely the acknowledged theory that the amount of steam flowing from one pressure into any other less than three-fifths of the initial pressure, is practically constant, and bears a very close approximate ratio to the total pressure. The first seven experiments are under these conditions. If, now, we take the flow in the fourth column and average it for the first seven experiments, we find an average of 232.8 pounds per hour. Inspection will show that the different experiments did not vary greatly from this average, with the exception of the third experiment, which varied about four per cent., but that should have been a little more on account of the pressure. Now how nearly this corresponds with the rough-and-ready rule of Professor Rankine is readily ascertained. His approximate rule is that, under those conditions, the flow in pounds per second is 1 of the absolute pressure per square unit of area, the same units being used for area of opening and area of pressure. Applied to the flow per hour, this rule would be 51.57 times the pressure multiplied into the area of opening. But we must notice that the pressures given in the table are gauge" pressures, so we must add 14.7 to get the absolute pressures. The average pressure in the first seven experiments was 70.2, making 84.9 for the absolute pressure; multiplying, therefore, 84.9 by .058, the area of the opening, and by 51.57, we have 253.94 as the flow per hour. But

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we are told that this theoretical flow must be reduced by a coefficient, representing the contraction of the area and friction, which coefficient is given as .93 for a short tube. Multiplying, therefore, 253.94 by .93, we have a flow of 236.16 pounds per hour, which is within 1 per cent. of the average flow obtained by the experiments. The difference is probably due to the fact that the tube used was not properly a short tube, being thirty diameters in length, so that the coefficient would have to be slightly smaller. It would only be necessary to reduce it to .9167 to give exactly the same flow as was shown by the experiments. The third experiment, not falling into a common curve with the others, is probably an error, which may be due to the pressure not being carefully observed. These experiments were made under varying boiler pressures, the average being taken from several observations, and it is quite possible that the average pressure might have varied considerably from the observed pressure; it would only have to vary about three or four per cent. in order to have made the difference shown in the table.

The Chairman.-If there is no other discussion, Professor Peabody has the reply.

Prof. Peabody.*-As the best and simplest way of replying to the discussion of this paper by Professor Denton and Mr. Babcock, I wish to add another diagram (Fig. 74), reduced from a plate in Mr. Buttolph's thesis, in which points are plotted to represent the several experiments, with differences of pressure for abscissæ and flow in pounds per hour for ordinates. Two series of points were plotted, one showing the actual flow and the other the cal culated flow under the conditions of each experiment. Had the boiler pressure been the same for all of the experiments, the points representing the calculated flow would have fallen on a curve with no more irregularity than that coming from the tables of the properties of saturated steam used in the calculation. The deviation of the points from the curve in the figure is due to the fact that the boiler pressure was not the same for different experiments, though it was very nearly constant for each individual

test.

It is noticeable that the points representing the actual flow vary from the mean curve drawn through them in the same direction, and to about the same amount as the points representing the calculated flow under the same conditions differ from the mean

* Added since the meeting.

curve of the calculated flow. This at once answers Professor Denton's query regarding experiment 3, and shows in another way what is brought out in Mr. Babcock's discussion.

It will be observed that both calculated and actual flow have a

maximum; the maximum calculated flow occurs at about 35 pounds difference of pressure, or at about of the absolute pressure, and the maximum actual flow occurs at about 55 pounds difference of pressure, or at about of the absolute pressure. This last agrees fairly well with the tests quoted by Professor Denton. It appears to me, however, that after making allowance for the change of boiler pressure from experiment to experiment, there is clearly a maximum to the actual flow, and that beyond that point the flow decreases with the increase of the difference of the pressures, though much more slowly than the calculated flow decreases under like conditions.

It must be observed that this maximum flow occurs only when

the superior pressure is maintained constant, and the difference of pressures is increased by lowering the inferior pressure, and that it does not occur when the inferior pressure is constant and the superior pressure is raised. Calculations under the latter assumption, and according to the method used in the paper, show that the flow from a boiler into the atmosphere increases as the boiler pressure is increased, and the experiments of Mr. Brownlee, given by D. K. Clark in his Manual of Rules and Tables, show the

same.

The suggestion made by Rankine, and mentioned by Professor Denton in his discussion, that the pressure in the lower reservoir is that of the expanded jet of steam beyond the tube, and not that of the steam in the tube, is not inconsistent with the tests made by Mr. Buttolph. Should it be true that the pressures in the tube were higher than that in the discharge chamber, then the less difference of pressure would naturally be accompanied by a larger flow after the maximum calculated flow had been passed. I intend to extend our experiments to cover this point.

While I accept Mr. Babcock's calculations in his discussion as correct and his conclusions as just, I must beg leave to say again that the theory on which the calculations are based was known to be imperfect before the experiments were begun, and that the amount of the divergence was the object of the search; still I am ready to confess that the amount of the divergence much exceeded my anticipations. The rule referred to, i. e., that the flow per second is of the absolute pressure per square unit of area, appears to me to be only a rough empirical rule, and not properly a theory at all.

It is our present expectation that the investigation shall be carried further in our laboratory, and that attention will be given to the points raised in the discussion.