under 5,000 pounds liquid pressure per square inch, without the least indication of porousness; that is the highest pressure we have had on any castings. In that case there was about 2 inches of surface exposed to the pressure, but the extreme edge of that casting was not exposed. No porousness whatever was found. You must understand, of course, that I am talking about castings made in a college workshop, which has no skilled men, the casting being done by students who have had all their training in our foundry. Consequently the results that we get are not as good, I think, as should be obtained in other foundries. We have made no castings with sprues larger than 6 or 8 inches. Mr. Almond.-We usually find the porous condition nearer to the centre. The solid part of the casting is more likely to be at the surface, owing to shrinkage in cooling. In the metal shown the porosity would seem to be due to the absorption of gases which come from the sand.

Professor Carpenter.*-I should have to answer the question simply in the light of our experience, and that is that we can make sounder castings with this metal than we can with brass.

The specimen to which Mr. Almond refers is a section of a pig of this metal cast in sand, without any sprue head, and is about 4 inches in diameter. I attributed the small checks near the outer edge to the fact that the outside cooled much sooner than the centre, and that finally the shrinkage of the centre mass caused the outside to check somewhat. It is quite certain that there is no especial difficulty in getting sound castings, even when they are very thin, with this metal.

Since writing the article, a method of rolling and drawing this metal has been perfected, there being no especial difficulty at a temperature of about 400 degrees F.

My attention has recently been called to the fact that many foundrymen have very little skill in mixing metals, by several failures which have been made in attempting to make the simple aluminium-zinc alloy, as described. For that reason I should advise those who desire to use it, to correspond with the Pittsburg Reduction Co., at Pittsburg, Pa., from whom I believe it can be obtained at cost prices.

*Author's Closure, under the Rules.

DCCLXXV.*

WHAT IS THE HEATING SURFACE OF A STEAM

BOILER?

BY CHARLES WHITING BAKER, NEW YORK CITY.

(Member of the Society.)

Ir is a fact which is now generally understood by engineers and all who have to do with steam power plants, that the power of any boiler, or more accurately the amount of steam which it can furnish in a given time, depends first of all upon its area of heating surface. Of course the amount of steam which a square foot of heating surface will produce varies between very wide limits, and is affected by a multitude of conditions. It is also true that heating surface is no more essential than the means for supplying the heat-that is to say, a furnace of sufficient size and grate surface to burn the fuel, and draft sufficient to supply the furnace with the necessary air. The furnace and the chimney, however, are not necessarily parts of the boiler at all; their function is merely to supply the heat, and the function of the boiler proper is to transfer as much as possible of this heat to the water which it contains. Both the amount of heat which it can transfer in a given time and the proportion of the total heat generated which can be transferred vary with the area of the heating surface exposed. In other words, both the capacity and the economy of a steam boiler depend directly upon its area of heating surface.

Evidently, then, the area of the heating surface of a boiler ought to be determined with a fair degree of accuracy. The designer of the boiler must know it, if, with any degree of precision, he is to adapt the boiler to the work which it has to do. The seller of boilers must know it, if he is to be sure of fulfilling his guarantees of capacity or economy; and the purchaser of boilers should know it, in order to determine what he is getting for his

Presented at the Niagara Falls meeting (June, 1898) of the American Society of Mechanical Engineers, and forming part of Volume XIX, of the Transactions.

money. As a matter of fact, a very large proportion of the boilers bought and sold are actually bought and sold by their heating surface. The prices asked for and quoted may be the price per horse-power, but the horse-power is determined directly from the heating surface, the number of square feet allowed to a horsepower varying from 5 to 14, according to the type of the boiler. Again, in comparing the work done by different boilers, the relative heating surface is always taken into consideration.

We need go no further for proof that accurate determination of boiler heating surface is a desirable thing. But we have now to notice the remarkable fact that in computing boiler heating surface, an error of from 7 to 17 per cent. is made by a large proportion of steam engineers and boiler manufacturers. The error to which I refer consists in taking the surface in contact with the water, instead of that exposed to the fire or hot gases, as the heating surface. If the heating surface is flat, of course the areas are the same; but boiler heating surface is in most cases made up of tubes, and the difference between the interior and exterior surface of a boiler tube is as much as 17 per cent. of the interior surface in the case of a 1-inch tube and is about 7 per cent. in a 4-inch tube.

The error arises in the first place from a failure to appreciate the fact that the heating surface exposed to the fire is the actual heating surface of the boiler, on which its capacity depends. A clear understanding of this fact is so important, and it has been and is so generally mistaken by engineers and writers of engineering works, that the writer ventures to submit a discussion of the elementary principles on which this assertion is based.

In Fig. 144, suppose we have an iron plate 1 inch thick, on one side of which is flowing a current of hot gas at a temperature of, let us say, 1,000 degrees, and on the other side is a body of water in a steam boiler at a temperature of 300 degrees (corresponding to a gauge pressure of steam of about 52 pounds).

Now the heat in passing from the hot gas on the side of the plate to the water on the other meets with three different resistances as follows:

(1) Resistance in passing from the gas to the surface of the plate.

(2) Resistance due to the passage through the plate.

(3) Resistance due to the passage from the other surface of the plate to the water.

That one of these resistances which is accurately known is (2), the resistance in the passage through the plate. The heat conductivity of metals has been carefully determined by experiment in physical laboratories, so that if we know the actual temperatures of the two surfaces of a plate and its thickness, we can at once determine how much heat is passing through a unit area in a given time. On the other hand, if we know how much heat is passing through the plate, we can determine what is the difference of temperature of its two surfaces. Let us solve an example of the latter sort: Suppose the plate is transmitting heat enough to evaporate 3 pounds of water per hour from and at 212 degrees per square foot of its area, or about the average rate that the heating surface transmits heat in an ordinary stationary boiler. Since 965.7 heat units are required to transform a pound of water at 212 degrees into steam at the same temperature, the plate will transmit 3 x 965.7 2,897.1 heat units per square foot per hour, or for convenience let us say 2,900 heat units.

=

Now experiments on the conductivity of metals have shown that an iron plate 1 foot square and 1 inch thick whose opposite surfaces are kept at a uniform difference in temperature of 1 degree Fahr. will transmit in an hour 473 British thermal units.* Hence to transmit 2,900 British thermal units per hour, the dif ference in temperature of the two sides of the plate will be 2,900÷ 473 6.13 degrees.

I doubt not it will surprise many to learn that so small a difference of temperature between the two surfaces of an iron plate is sufficient to cause so large an amount of heat to flow through it; but the coëfficient for the heat conductivity of iron on which it is based is the result of many experiments by the most eminent physicists, and is accepted as correct by the best scientific authorities, and there is no reason to doubt its accuracy.†

In studying our present problem, however, the exact accuracy of the coefficient is a matter of no particular importance. We just found that boiler heating surface 1 inch thick, when transmitting 2,900 heat units per hour, will have a difference of temperature on its two sides of 6.13 degrees Fahr. But we never

See Ganot's "Physics," 13th ed., page 378.

+ Many engineering text-books and pocket-books still quote Rankine's formula and Peclet's coëfficients for heat conductivity; but the latter have been found by the more careful research of modern physicists to have been largely in

error,

have heating surface of such thickness in steam boilers. The shell heating surface in internally fired boilers is seldom over 3-inch thick. Furnaces and fire boxes are made of inch to -inch plates, while tube heating surface is from to -inch thick. We see then that the actual difference of temperature between the two surfaces of a boiler tube transmitting heat at the rate already named will be from to of 6.13 degrees, or in round numbers from & degree to less than 1 degree Fahr. As the eminent physicist Lord Kelvin has said, for all practical purposes, we may consider that the heating surfaces of steam boilers conduct heat as if they were no thicker than paper, or as if the metal were of infinite conductivity. It will be seen also that an error of 50 per cent., or even of several hundred per cent., in determining the coefficient of conductivity of iron, even if such an error were probable, would make no practical difference in this conclusion.

There are many facts of practical importance to be drawn from this. For example, in its light we can readily see how little reason there is to expect any greater economy in locomotive boilers with brass or copper tubes and fire boxes than in those of steel. Yet we still hear the superior conductivity of copper urged as a reason why English railways stick to the use of copper fire boxes.

on

Turning again to Fig. 144, we know now that the two surfaces of the plate, (if we conceive its thickness reduced to that of an ordinary boiler tube,) will have only a trifling difference of temperature. Next let us discuss the relative heat-absorbing powers of the water on the one side of the plate and the hot gases the other. It is to be kept clearly in mind that the temperatures of the two sides of the plate which we have just considered are the temperatures of the skin of the plate itself, which is quite a different matter from the temperature of the air or the water in contact with the plate.

If this is clearly understood, it will be easy to understand that the actual temperature of the plate itself depends on the relative heat-transmitting power of the fluids on its two sides. If these fluids were the same on the two sides, and were at the same temperature and under the same conditions as respects mobility, then the plate temperature would be a mean of the temperatures of the fluids on its two sides. But in the case shown in Fig. 144, since water is many times as efficient as air or furnace gases in