strokes, and, both together, an impulse for each stroke, or two for each revolution. This places it on a par in this respect with a single-crank steam-engine, and the governing features are good for any service. In the largest sizes it is made still better, however, by having two cranks and rods, with two pairs of cylinders, the cranks being set at ninety degrees with each other, by which method four impulses per revolution are secured. Engines of the single-crank type are made in powers ranging from 200 to 2000 horse-power, and of the double-crank type from 400 to 4000 horsepower. Since very high temperatures are produced in all gasengines during combustion, sometimes as high as 2800 or 3000 degrees Fahrenheit, which is above the melting-point of cast iron, water circulation in all parts exposed to the heat is necessary, and in the double-acting engines this cooling of the enclosed pistons presents some difficult features in design.

The Diesel oil-engine is built in vertical form, with either two or three cylinders and sets of moving parts, and in general appearance resembles a marine steam-engine. Each cylinder is single. acting, giving one impulse in two revolutions, so that the engine as a whole gives either one or one and one-half impulses per revolution, which insures good governing features. The maximum temperature in the cylinder is not far from 1400 degrees Fahrenheit, which is that resulting from the preliminary compression, since the admission of fuel oil is so regulated that it burns during expansion without rise in temperature. The engine is built at present in sizes ranging from 75 to 225 horse-power, but may be readily doubled up on the same shaft and so double the range of power.

As efficient converters of heat into mechanical energy these engines may well be studied in comparison with the steam-engine, since it is with the latter that they come into competition. In this comparison a compound condensing steam-engine will be taken as the type representing the class in large manufacturing plants and for power-station service. A good type of steam-boiler will utilize from 70 to 75 per cent. of the heat in the fuel, as equipped and operated in first-class establishments. The engine of the kind in question will utilize from 14 to 15 per cent. of the heat coming to it in the steam in general service, or 10 to 11.2 per cent. of the total heat value of the fuel burned. The bulk of the remainder of the heat is carried away in the cooling water in the condenser and up the flue from the boilers. The gas- and oil-engines, on the other hand, work with a thermal efficiency of from 17 to 25 per cent., with possibilities of still better results.

As desirable forms of prime movers in commercial plants the gas- and oil-engines must be subjected to complete analysis that shall include all conditions of first cost, depreciation, repairs, and labor, as well as fuel cost. This we will now proceed to do with our typical cotton-mill.

A single gas-engine of 1800 horse-power, to use natural gas, may be purchased for about $43 per horse-power; foundations will cost about $7; making the total cost of the engine, erected, $50 per horsepower, or $90,000. This is somewhat less than the average first cost of a water-power plant, but the difference is not likely to be enough to influence appreciably the total investment in the mill. Depreciation may be taken at four per cent. and repairs three per cent. on $90,000, giving $6300 annually. Labor for attendance, one man, at $750 per year. Gas consumption will be about ten cubic feet per horse power per hour, or 54,000,000 cubic feet per year of 3000 hours. With gas at 25 cents per 1000 cubic feet, the fuel bill will be $13,500, and hence the total annual cost of power, $20,550. This, when compared with the preceding calculations, giving $22,500 for water power and $38,000 for steam power, shows well for the gasengine. When installed with a suction producer, using coal for fuel, conditions will be different. Actual figures for cost of producers of this capacity are not available, but $10 per horse-power will be a safe figure, which, with $2000 added to the cost of the engine to provide for the slightly increased size necessary when used with the suction producer, makes the total cost of the appara. tus $110,000. It will be assumed that Arkansas anthracite coal will be used, at $6 per ton, and that the rate of fuel consumption will be 1.25 pounds of coal per horse-power per hour, which is a liberal figure. This gives 3375 tons of coal burned per year, at a cost of $20,250. Depreciation and repairs will be increased to seven per cent. of $110,000, or $7700, and labor increased by two men, at $150 each per year, making total labor $1650 per year. This makes the total cost of power $29,600 per year, or $7100 more than the cost of water power. This excess is, however, but forty-five per cent. of that occurring with the use of steam, and is $760 less than that with water power with electrical transmission and motor drive. As already noted, however, the power cost with the latter system may be reduced under favorable conditions; so it may fairly be stated that costs are about the same for the hydro-electric system and the gas-engine with suction producer.

The first cost of the gas equipment is $50,000 less, however; so that there would be a difference in dividends in its favor of over

0.5 of one per cent., while there would be a difference of less than one per cent. between it and directly applied water power in New England. Freight differences on raw materials would probably more than counterbalance this difference, so that the cotton-mill in Kansas will be on the same plane with the New England mill as betwen power cost and freight, while with natural gas at 25 cents per 1000 cubic feet it will be better off on power alone by 0.2 of one per cent. in dividends.

It is almost useless to make calculations for power costs from crude petroleum as a fuel. The price is subject to great fluctuation, and if it should be adopted to any very considerable extent in manufacturing plants it is extremely doubtful if the supply would be adequate, in view of the great demand for the lighter distillates, and in any case the price would greatly increase. Under present conditions in Kansas it offers great advantages as a substitute for coal, especially when used in the oil-engine.

In point of economy in fuel consumption there can be no doubt as to the superiority of the gas- and oil-engines over the steam-engine. This does not mean that the latter is to be at once relegated to the junk heap, however. At the present stage in the development of the internal-combustion engine, its small financial advantage, as shown in the preceding calculations, is often offset by the practical usefulness of steam in auxiliary service, to say nothing of the advantage accruing from the familiarity of operating engineers with the older type.

As it has taken a century and a quarter to develop the steam-engine since it first assumed its practical form in the hands of Watt; so must more time be given to perfect this later type of prime mover which first appeared in really successful operation in 1876. The gas-engine is now passing through a transitional period, while it is coming into prominence as a real factor in the larger business interests of the world. The new form of Westinghouse engine already described shows the manner in which the type is progressing, following instinctively the path of progress marked by the steamengine, but standing as a more economical machine. It is moving far more rapidly than did the steam machine, and even now, as the latest and most improved steam motor, the turbine, is being perfected and successfully established as a positive step in advance, prominent European scientists and at least one of the prominent engine-building companies of this country are working on the gasturbine, which we may expect to see making its appearance in the

near future as the latest and most refined result of scientific engine designing of the age.

The commercial development of Kansas of which we speak belongs to the future, perhaps not far distant. The present narrow margin in favor of the gas-engine will be made larger as time goes on, principally by a reduction in the fixed charges for depreciation and repairs, resulting from standardized forms and lower first cost, since the present prices for the engine are abnormally high. Operating engineers are gradually becoming acquainted with it, which in itself will insure increased favor, and there can be no doubt but that in this form of motor Kansas, and other similarly situated states, will find the source of power that will serve in the permanent advancement of the manufacturing interests.

NOTE ON CERTAIN FORMULAS FOR THE DESIGN OF REENFORCED CONCRETE BEAMS.

IN

By A. K. HUBBARD, Lawrence,

N chapter II of the book on Reenforced Concrete, by A. W. Buel and C. S. Hill, some formulas and deductions are given which are incorrect. It is the object of this paper to point out the mistakes in these formulas and deductions, and to illustrate the errors involved by numerical examples.

Before proceeding to a consideration of the formulas, it will be well to notice the assumptions on which the formulas are based. It is not proposed to enter into any discussion concerning the correctness of these assumptions:

1. The strain of any fiber is directly proportional to the distance of that fiber from the neutral axis of the beam.

2. The stress in any fiber is proportional to its distance from the neutral axis.

3. Any variation of stress or strain near the reenforcement is neglected.

Referring to figure 1, the author uses the following notation:

M = bending moment in inch-pounds.

1= length of beam in inches, center to center of supports.

h= depth of beam in inches, out to out concrete.

b= breadth of beam in inches.

A = total area of cross-section of beam = hb.

A.= area of steel reenforcement in tension.

A1area of steel reenforcement in compression.

AcA-(A,+A1)= area of concrete.

x=distance from neutral axis to outer compression fiber of concrete. y= distance from neutral axis to outer tension fiber of concrete. u=distance from neutral axis to outer compression fiber of steel. z= distance from neutral axis to outer tension fiber of steel.

t=distance from neutral axis to center of steel sections in compression. v=distance from neutral axis to center of steel sections in tension. y=z+d; x=u+d1; h=x+y; h1=u+z; ht+v; y=v+dı; x = t + di1.