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As stated in the paper, the causes for this gain are-first, the subdivision of the power at suitable points; secondly, a greatly reduced weight of shafting and the complete annihilation of all large belts.

In the steam mill, power was measured at the engine by means of indicators; in the electric mill it was read from the meter, and these were the units used.

The balance of discussion does not cover the ground stated in the paper, because the object of the paper was to present facts as nearly as possible as they existed under the conditions of operating the two plants, and distinctly raises the point as to whether it would be possible for the saving represented by the method of transmission used in the electric mill to be exceeded in frictional horse-power by direct coupled engine and generator.

With regard to Mr. Main's discussion, we can say that it will take about 850 horse-power to drive the steam mill when it is fully equipped. As was stated in the paper, all the shafting is in for the complete mill, and the friction of 226 horse-power, as given in the paper, represents the power used for all other purposes otherwise than driving the cotton machinery when doing work. In this there is in each plant about 10 horse-power in pumps, of which no account has been taken, and this would reduce the frictional horse-power that amount.

When the mill is completely filled with machinery, the horsepower will not increase to quite 10 horse-power. The author estimates about 8 horse-power. Assuming that it will reach the full 10 horse-power deducted for the pumps, still gives us a figure of 226 horse-power, which is about 26 per cent. of the total power ultimately required to drive the full mill. Of course, this includes driving all loose pulleys on the machines.

The author agrees with Mr. Main that the transmission through generators and motors is very nearly the same in friction as direct transmission; but from reliable figures in the author's possession, taken from plants actually constructed, and from estimates from reliable machinery builders, the extra cost of erecting a steam generator and putting in the motors is very nearly the same as installing the plant direct with belts or ropes, and the gain in flexibility due to the electric plant is certainly a great advantage.

With regard to Professor Carpenter's discussion, I would say that he is very much in error in proportioning the different

powers in the mill. All we need say is, that in a 1,000 horsepower mill the power would be distributed as follows:

Total Power. 1,000

Looms and Shafting.
416

Friction.
248

Spindles.
584

Looms. 168

There is in this friction the same allowance for pumps as in the paper, no deductions having been made for it. Professor Carpenter labors under the same misapprehension with regard to the generating plant as Mr. Kent does; and, as stated in the reply to Mr. Kent's discussion, I will simply say that the author cannot assert exactly what power would be consumed in driving the generator to operate a plant of this size, not having any data at present to cover these cases, and distinctly leaves it an open question in his paper for further consideration by those having such data in their possession.

DCCLXXI.*

THERMODYNAMICS WITHOUT THE CALCULUS.

BY GEORGE RICHMOND, NEW YORK CITY.

(Member of the Society.)

IN giving, by request, a brief outline of the method of treating heat relations, which, on account of its extreme simplicity, is coming more and more into general use, it must not be supposed that there is any disposition to undervalue the importance of the higher branches of mathematics. The contention is simply that the use of the calculus is no more essential to an intelligent use and understanding of such thermodynamic problems as ordinarily concern the engineer than it is necessary in order to find the horse-power of an engine from the indicator diagram. This diagram, in fact, affords a most striking illustration of the advantage of graphical representation, not only in fixing our ideas, but also in facilitating calculations. A mere inspection of it conveys an amount of information which, if clothed in mathematical formulas, would be unavailable to many, and perfectly intelligible to few, if any. Conversely, we may expect that when the heat relations we are accustomed to see expressed in formulas are presented in graphical form, they will be very much more intelligible. Results are thus rendered available to the non-mathematical reader, and an almost equal benefit accrues to the mathematician.

Since the indicator diagram is so familiar, and as every change of position on it is accompanied by the addition or removal of a definite amount of heat, it would at first glance seem very convenient to represent these heat changes on this diagram itself. Rankine, indeed, pointed out that the mechanical equivalent of the heat transferred to or from a substance, in passing from the condition represented by one point on the indicator

* Presented at the New York meeting (December, 1897) of the American Society of Mechanical Engineers, and forming part of Volume XIX. of the Transactions.

diagram to another, was represented on the same diagram by the area included between the line joining these points and two adiabatics drawn to infinity, one through each of them. He does not seem to have recommended this as a practical means of representing heat areas, for which it was obviously ill-adapted, but, in view of the fact that Rankine divides with Clausius the honor of elaborating the conception of entropy, it is astonishing that he failed to see the advantage of a diagram on which temperature and entropy are the coördinates.

If, instead of referring to a diagram* in which neither of the quantities involved were represented otherwise than as mathematical abstractions, he had used them as coördinates, the temperature-entropy diagram would have now been in use for forty years; incalculable labor would have been saved, and the confusion of ideas connected with entropy would have been impossible. As a more practical method of representing heat changes, Rankine suggested a pressure which he writes as pr and defines as pressure equivalent to expenditure of available heat. He did not make any practical use of it, and the only graphical result left us by Rankine in his text book is a mere picture.‡

Professor Cotterill, however, elaborated Rankine's idea with considerable enthusiasm, and under his treatment the quantity Pr served as the means of obtaining a variety of useful results. Having undoubtedly obtained all that was to be had from exploiting this idea, Professor Cotterill admits, with admirable candor, that it is less available for the purpose than the temperature-entropy diagram, which he uses to a certain extent.

Professors Ayrton and Perry, § recognizing the importance of supplementing the indicator diagram in their investigations on the gas engine by concurrent information as to changes in temperature and heat supply, proposed another method of indicating these variations on the indicator diagram itself.

For the purpose of representing the interchange of heat

*A Manual of the Steam Engine and other Prime Movers, 13th ed., par. 265, 266, and 267.

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The Steam Engine Considered as a Thermodynamic Machine. James H. Cotterill, 1890.

The Gas-Engine Indicator Diagram. Ayrton and Perry, Philosophical Magazine, 1884, vol. ii. An excellent description of this method will be found in Robinson's Gas and Petroleum Engines, April, 1890.

* de

between steam and the cylinder walls, Dwelshauvers-Déry vised still another method of supplementing the indicator diagram by heat areas. Probably other examples could be found, but these are sufficient to indicate the desire for some method of graphical representation of heat changes. This being the main purpose of their introduction, it is irrelevant to compare their relative merits and originality. They have not been used to any great extent by others than their originators, which, however, is not in itself a proof that they are not adapted to the special cases that called them forth.

The temperature-entropy diagram, on the other hand, is to be found in nearly every text book on thermodynamics or allied subjects published within the last ten years, and, what is peculiarly significant, the more recent the edition, the greater the use made of it. It will be a surprise to many to learn that Zeuner uses it throughout in his masterly treatise,† and that more entropy-temperature diagrams are to be found here at this early date than in any similar subsequent publication. Unfortunately he uses them as illustrations only; his calculations are all analytical, and refer to the pv coördinates. He recognizes the value of showing the results in diagrammatic form, but is indifferent to the fact that in many cases these results could be obtained with the same rigor by mere inspection of the heat diagram. A very little editing of this monumental work, which is at once our admiration and despair, would render it—or at least the greater and most important part of it-perfectly simple to those of us who find no comfort in differential equations. The most complete treatment of the subject hitherto published is to be found in the treatise of J. Boulvin. In this case the results are obtained directly from the heat diagram, and very useful auxiliary diagrams are introduced, which have been recently reproduced with modifications by Professor Reeves. I

* Dwelshauvers-Déry: Étude calorimétrique de la machine a vapeur. See also Table of Properties of Steam, by same author, Transactions A. S. M. E., vol. xi.,

1890.

Technische Thermodynamik, von Dr. Gustav Zeuner. Erster Band, 1887 ; zweiter Band, 1890.

Cours de Mécanique appliquée aux machines 3me fascicule théories des machine thermiques. J. Boulvin, Paris, 1893.

The Entropy-Temperature Analysis of Steam-Engine Efficiencies. Sydney A. Reeve, 1897.

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