other. The string of both may be taken together on the same strip, and if the scale is twice the number of ordinates, the length of the string will give the mean pressure at once without multiplying. When taking such a continuous string for two diagrams, the termination of the first should be marked with a pencil, so that the two may be compared.

When diagrams are met with, in which the expansion curve crosses the counter-pressure line, the string should be taken from the beginning up to the point where the lines cross, and after that in a reverse direction on the strip, so as to cancel the part of the string already made. When the terminal end is reached, what remains of the string first made will give the mean effective pressure (M. E. P.) in the usual way; or the total mean impelling and counter-pressure above vacuum may be found separately, and their difference ascertained.

To Space the Ordinates.

Draw vertical lines touching the ends of diagram No. 1, A B E I, and apply a rule across them in a more or less oblique direction, till some division on the rule, as 1, 2, 1, §, or 1, will divide the distance between the points where the rule crosses the lines, the desired number of two or three times the number of times. Thus the line HCI, in diagram No. 1, is 33 inches long, and contains the division 60 times; consequently, 331⁄2 pointed off at each end, and for the other spaces, will correctly divide the diagram for 20 ordinates. With a little greater obliquity the distance would be 4 inches, when end spaces, and for the rest.

inches would be right for the

To Calculate the Indicated Horse-Power (I. H. P.).

Multiply the speed of the piston in feet per minute by the area. of the piston in square inches, and divide the product by 33,000. The result will be the H. P. for each pound of M. E. P., or the

H. P. value of each pound. See table on page 290. Then multiply the M. E. P. by this value. This method is preferable to multiplying by the M. E. P. before dividing, as, when several diagrams from the same engine representing varying loads are to be calculated, the value when once obtained will answer for all, the speed being practically the same in each case. The area of the pistonrod is generally ignored in such calculations, though it will diminish the area of one side of the piston about '.

Theoretical Economy.

If the steam used by an engine was known to be saturated, and at the same time free from any excess of water, and if it both entered and left the engine in that condition, it would be easy to calculate from the diagram the amount of water which the engine would use in a given time, supposing it to be practically free from leakage. Under such conditions the expansion and compression curves would conform rigidly to exact theory, and the total piston displacement for one stroke, divided by the volume of terminal pressure, and the displacement up to any point in the curve divided by the volume of the pressure at that point, would give the same result wherever the point was taken, which result would be the number of cubic inches of water used during that stroke. Unfortunately, the nature of steam is such that no exact calculations of water consumption can be made. Even if its exact condition as it enters the engine is known, as it may be by the calorimeter test, its capacity for receiving and parting with heat is so great that its condition changes immediately upon entering the cylinder, so that, after deducting the water of supersaturation, known to be present before it enters the cylinder, the diagram will still fail to account for all of the remainder. Nevertheless such calculations are frequently made, and as a means of ascertaining the relative economy of different engines, and of different loads, pressures, and adjustments in the same engine, they possess great value, since, whatever uncertainty may exist as to the unin

dicated consumption, it may, so far as the engine is concerned, be assumed to be the same in each of the cases under comparison.

When it is desired to approximate as nearly as possible to the actual consumption by calculation, a certain amount must be added to the theoretical result. This amount varies from 10 to 50 per cent., according as the conditions are more or less favorable; but when they are so unfavorable as to require an addition of 50 per cent., they are obviously so bad as to call for repairs and changes, rather than elaborate calculations. When the conditions are generally good, a careful examination of them will make it possible to fix the margin of uncertainty within tolerably narrow limits. A large engine, with well-jacketed cylinder and tight-fitting valves and piston, will generally require at least 10 per cent. addition, independent of the percentage of unevaporated spray, which may exist in the steam with which it is supplied, and this, unless the boiler is so set as to superheat the steam, will require from 10 to 25 per cent. more. In fact, the margin of uncertainty due to the boiler is much greater than that due to the engine, as not only will differently constructed boilers vary greatly in the amount of unevaporated water given off, but great difference will be found to exist with the same boiler, according to the height the water is carried, the rapidity with which it is evaporated, the amount of impurities present in the feed-water, or which have accumulated in the boiler, and many other conditions. Thus a rapidly fired generator, containing a large area of heating surface in proportion to the amount of water and little steam room and superheating surface, may, and often will, give off nearly or quite as much unevaporated water as is contained in the steam. The only fair way to test the performance of an engine is to test the steam as it enters it, both as to moisture and heat. It should also be borne in mind that, according to Trowbridge's tables, the difference between the economy of engines of over ten cubic feet capacity of cylinder and those under one cubic foot, is about 12 fer cent. in favor of the larger size.

How to Calculate Theoretical Rate of Water Consumption.

The total displacement per stroke in cubic inches divided by the volume of the steam at release pressure, and the quotient multiplied by the number of strokes per hour, will give the total cubic inches used per hour. This, divided by 27-648, the number of cubic inches of water per pound, will give the total number of pounds used per hour, which, if divided by the I. H. P., will give the result in pounds per I. H. P. per hour. This is the usual method; but, when the rate only is desired, a shorter process may be adopted, based on the fact that, from a given diagram, the result would be the same, whether the calculations are based on the actual size of the engine, or some other size is assumed, say a smaller size; as, although the total consumption would be changed, the divisor would also be proportionately changed.

Suppose the engine to be of such displacement as to develop one horse-power with one pound pressure, and that it is driven by that pressure of water instead of steam. It being but one horsepower, its total consumption per hour and per horse-power per hour will be the same. Being driven by water, its displacement will be its water consumption, which will be obtained as follows: A horse-power is 33,000 lbs. lifted one foot high per minute, or 33,000 × 601,980,000 lbs. per hour, or 1,980,000×12=22,760,000 lbs. lifted one inch per hour, which would be the displacement of such an engine in cubic inches, and consequently its consumption in cubic inches of water when driven by water. Then, taking 27.648 cubic inches of water per lb., we have 22,760,000 ÷ 27-648 859,375 as its rate of consumption in lbs. of water per H. P. per hour. Then, if the pressure were greater than one lb., the amount used would be as many times less than the above, as the pressure was greater than one lb.; and also, if it were driven by steam instead of by water, the amount used would be as much less, as the volume of steam at the terminal pressure was greater than an equal weight of water. It follows that if we divide

=

859,375 by the product of the mean effective pressure, and the volume of the total terminal pressure of the diagram under analysis, the quotient will be the desired rate, whatever the size and speed of the engine. The use of this constant number renders the operation more easy and short, and, except in the case of the compound engine, entirely independent of all data except those furnished by the diagram itself, the scale of indicator being known,

The terminal pressure for this and subsequent rules is found, when the exhaust takes place before the end of the stroke is reached, by continuing the expansion curve to the end of the stroke. In other words, it is not what the pressure may be at the moment of release, but what it would have been if it had not been released until the end of the stroke.

How to apply the rule to diagrams taken from compound engines when the strokes of the two cylinders are equal. Multiply the M. E. P. of the low-pressure cylinder diagram by the area of its piston, and divide the product by the area of the piston of the high-pressure cylinder. The quotient will be the pressure, which, acting on the low-pressure piston, will be equivalent in energy to that acting on the high-pressure piston. Then add this quotient to the M. E. P. of the high-pressure cylinder, and with its mean pressure so augmented treat it in all respects as an ordinary diagram. Or the process may be reversed, i. e., the diagram from the low-pressure cylinder, with its M. E. P. augmented by the quotient of the product of the area and M. E. P. of the horsepower cylinder divided by the area of the low-pressure cylinder, may be treated as an ordinary diagram; but the result by this method will be less than by the first.

When the two cylinders have different strokes as well as different piston areas, multiply together the M. E. P. piston area, and stroke of the high-pressure cylinder, and divide the product by the product of the piston area of the low-pressure cylinder multiplied by its stroke. The quotient will be the amount to augment the M. E. P. of the horse-power cylinder before treating it as a simple diagram.