number of ordinates is made the same, or one-half, one-third, or one-fourth as many as there are pounds per inch in the scale of the diagram, the calculation is, if anything, simpler than the old process, since the sum of the ordinates, as measured on the strip of paper in inches, is the mean effective pressure at once, when the number of ordinates equals the scale, and in other cases it bears the same relation to it that the number of ordinates does to the scale. Ten ordinates may be used, however, for such scales as are divisible by 10.

Suppose the scale to be 60, and the number of ordinates 10, and that the sum of their lengths is 7 inches. According to the former process, 17 x 6042 lbs.; by the latter method, supposing the number of ordinates to be of the scale, the process is } simply 6x7=42; that is, the mean effective pressure would be six times the sum of the length of the ordinates, if the scale is six times their number.

Suppose the scale to be 40 lbs per inch, one-half of that number, or 20 ordinates, as shown in the above diagram, are used; and suppose the sum of their lengths is found by the process of measurement above given to be 15.3 inches, then twice that number will be the mean effective pressure in pounds per square inch, or 15.3x230-6 lbs. Suppose the cylinder of an engine is 20

inches in diameter, 40 inch stroke, running at a speed of 75 revolutions, or 500 feet per minute; the area of such a piston would

be 314-16 square inches; hence,

314.16 × 500

33000

4.727 horse-power

for each pound of mean effective pressure. The latter being 30.6, then 3064727 145,656, the indicated horse-power.

What Indicator Diagrams Show, and How they Show it.

The object of indicator diagrams is to show the pressure acting on the piston of the engine to which it is applied at all points, and also at what part of the stroke any change of pressure takes place.

Indicator diagrams supply the means by which to calculate the mean effective pressure acting on the piston, which, together with the known area and speed of the piston, furnishes the factors from which to calculate the power of engines.

Indicator diagrams show the steam-pressure by the height to which the pencil traces the line on the paper measured from the atmospheric or vacuum line.

When the line representing the back-pressure in the diagrams of high-pressure engines shows more than one pound above atmosphere, or, in low-pressure engines, two or three pounds more than the vacuum-gauge shows in the condenser, the diagram indicates undue back-pressure, and that there is evidently something wrong.

The diagram shows whether the valves of a steam-engine are properly set or not, because, if there is too little lead, it will lean towards the exhaust. If the exhaust takes place too early, the point, D, in diagram No. 1, page 291, will be further from the end, I; whereas, if the exhaust closes too early, and, as a consequence, there is too much cushion or "compression," it will be shown by the great distance of the point F from E.

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A diagram shows whether the piston and valves are leaky or not; though it is often difficult to decide to which the leakage may be due, as the one neutralizes the other. But if the piston alone leaks, the effect will be a more rapid fall of the pressure during

expansion than theory requires, and the back-pressure will be greater than if the piston was tight. If the slide-valve leaks, the effect on the diagram will depend on the point at which the leakage occurs. It may leak at the ends, so as to keep on admitting steam after it covers the port; or it may leak at the bridges, and allow the steam to escape in advance of the exhaust. In the first case, the expansion line would fall less, and in the latter case more, than theory requires.

A diagram shows whether the steam is throttled or not by the expansion curve falling below the boiler-pressure when the throttlevalve is wide open.

A diagram shows the effect of small ports and small steam connections by the steam-line starting below boiler-pressure, and falling before the closing of the cut-off. A pipe-diagram is the only reliable means of determining such defects.

A diagram shows the effect of exhaust-lead, by the exhaust taking place before the end of the stroke is reached, as in nearly all the diagrams shown.

A diagram shows that the indicator is out of order, or whether there is lost motion between the piston and the pencil lever, by indicating more back-pressure than actually exists.

A diagram shows the point of cut-off, which may be termed the point of contrary flexure, that is, the point where the steamline, B C, (explanatory diagram) changes its direction from a straight line to a curve.

A diagram shows the state of the vacuum in the condenser, and whether too much or too little injection-water is used or not; but in this case it is less reliable than the vacuum-gauge. Too much injection-water can only be shown on the diagrams, by taking one first with the proper quantity, and another with the increased quantity, and calculating the power of each. If the extra power, required to pump out the extra water against the atmospheric pressure, more than counterbalanced the gain from the better vacuum, the conclusion would be that too much injection-water was used.

The Planimeter.*

The planimeter, though not a recent invention, is almost unknown among engineers on this continent. This arises from the fact that, after its invention by Amsler, certain Swiss and German engineers got control

never been manufactured in this country, or even offered for sale, until quite recently. Its functions are to measure indicator diagrams, irregular flues, steam passages, and all difficult or intricate figures. It gives at once the area of a figure, without any second measurement being required, as the reading shown on the

10

index counter gives the accurate area in square inches of the diagram over which it had been passed.

To use the instrument, fasten the figure to be measured on a smooth board, and insert the point, A, in the board at any convenient location; then make a mark on the diagram, as at D; next fix the movable point, B, at the place selected for starting; then turn the index-roller, C, round until O, on its periphery, corresponds with the O on the fixed vernier; then move it round * See page 656.

the figure to the right, or in the direction of the hands of a watch. After it passes round the entire figure, note how many whole numbers and subdivisions have passed the O on the vernier. The whole numbers will indicate the square inches, and the subdivisions tenths of square inches. If the O on the vernier falls between two subdivisions marked on the roller, read the number of square inches and tenths; then look on the vernier from 0 to 10, and find a mark which coincides with one on the rollers; the number of such mark, counting from O, will be the hundredths or second decimal place.

Thus suppose that, in the figure measured, six subdivisions and part of another one have passed, and that the fourth mark on the vernier coincides with a mark on the roller, the area of the figure will be either 364, 1364, or 23.64 square inches, according to whether the roller has made less than one, more than one, and less than two, or between two and three revolutions. The eye can readily decide as to the number of revolutions the roller has made, as it would be impossible to make a mistake of ten square inches in estimating the area of a figure within the capacity of the instrument. If the figure measured is an indicator diagram, it will nearly always be of less area than ten square inches, or at most only a trifle more, as the utmost capacity of the indicator is 5 by 2 inches, or 15 square inches; and they are very seldom worked beyond 4 by 2 inches.

To find the mean effective pressure of a diagram from its area: Multiply the area by the scale, and divide the product by the length of the diagram in inches. Or divide the area by the length of the diagram, and multiply the quotient by the scale. product is the mean effective pressure.

The

Example. Suppose the area is found as above to be 3.64 square inches, the scale 40, and the length of the diagram is 37 (3-875) inches; 3.64 × 40 ÷ 3·875: 37.65 lbs., or 364 3.875 x 40=

37.65 lbs.

It will be seen that the labor of calculation will be facilitated, , in taking the diagrams, care is taken to make them even inches