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on one side, the axis of the wheel being parallel to a line drawn from the hardened pin to the tracing point. This arm is used on a board having a metal square, C, B, fixed at the left-hand side, with a grooved plate, 1, below it, for the hardened pin to slide in. On the right-hand side of the board is a straight-edge, K, fastened to a slide, which may be moved towards or from the grooved plate, in order to accommodate different lengths of diagrams. Alongside of the grooved plate, a strip of specially prepared paper is fixed for the graduated wheel to run in.

In using the diagram averager, an indicator diagram is first placed under the clamps C and K in such a position that the atmospheric line is parallel with the lower edge B of the square C B, while the extreme left-hand end of the diagram nearly touches the perpendicular edge, C. The sliding clamp K is then moved to the left until its inner edge almost touches the right end of the diagram. Fig. 180 shows the correct position of the diagram and clamps, i.e., the diagram must be so placed that the centre of the tracer D, when touching the clamps, will come directly over the centre line.

The arm of the instrument is next placed on the board, with the pin at the lower end, resting in the groove, I, and the weight W applied to the top of the pin, to keep it in the groove. A slight indentation is then made in the paper at E, with the tracer D, when it is touching the clamp K, and preferably on the line of the diagram. This serves as a starting-point. The graduated wheel is then turned so that its zero is opposite the zero on the vernier, taking care that the tracer D does not move till the wheel is set.

Next move the tracer D carefully over the line of the diagram, moving to the left along the exhaust line, and to the right along the admission and expansion lines, until the starting-point E is reached (the wheel then shows the area of the diagram, but no account need be taken of this in ascertaining the average pressure), then move the tracer upwards, keeping it against the edge of the clamp K until the wheel returns to zero, and make another indentation in the paper. This is indicated at A. The distance between the two indentations equals the average height of card, and if measured by the scale corresponding to

the diagram will show the average pressure, either in pounds per square inch or in kilogrammes per square centimetre, according to the spring and scale employed.

The theory of this instrument is very simple.

Referring to fig. 181 the lines A, A,, A,, A., and A1, roughly represent an indicator diagram, and the line A,, B, represents

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the arm of the instrument in its initial position, A, representing the tracing point. Assume that this arm is moved downwards to the position A, B,, then the area moved over the line is the space A,, B1, Bo, A。, which is exactly equal to the rectangle A, A,, A, A, as it is on the same base and between the same parallels.

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Let L equal the length of the line A,, B1, 0 equal the angle between this line and the vertical traversed, then the area moved over by the line A,, B, is equal to L 8 in. x H. The axis of the measuring wheel, W, being parallel to the line A,, B1, this wheel will rotate in precisely the same manner as if its axis coincided with that line, and it will be so represented in this explanation.

When the arm is moved to A, B,, the wheel W is moved to W. Resolving this movement into its components, there is first, H cos. (represented by N W1), and this component being parallel to the axis of the wheel, cannot cause rotation. The second being H sin. 0 (represented by W1 N), which is in the direction of rotation of the wheel, will cause the wheel to turn round on the paper over which it runs, through a length of its circumference equal to this; but, as shown before, the area moved over by the arm was L sin. 0× H, and therefore this area is also equal to L x the rotation of the wheel.

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Next move the tracing point A to A-during this movement the wheel will revolve through a certain angle which need not be considered (as will be seen later); then move the tracing point from A, up to A; the motion now is parallel to the axis of the wheel, and the wheel will not revolve. Finally, move the tracing point from A to A,, its original position. During this movement the wheel will revolve through the same angle that it did in moving from A to Α, but in the opposite direction, which motions cancel each other. Therefore the final rotation of the wheel at A is proportional to H sin. ; and, as already shown, the area A A, A, A, is equal to L sin. x H; therefore the rotation of the wheel is proportional to the area enclosed by the line which the tracing point moves over. It will be readily seen from the above that only vertical components of its movement leave any permanent record on the wheel, the horizontal components cancelling each other when the tracing point is brought back to its starting-point.

Next take the whole of the diagram, including the curved side A, A. Approximately this diagram is equal in area to the sum of the rectangles shown, and will be exactly equal to this if the rectangles are narrow enough. Now from the explana

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tion above it will be readily seen that the area of each of these rectangles could be obtained separately and, as the movement along the line A A, does not affect the wheel, if the starting-point was at A and each rectangle moved over in turn without removing the tracing point from the paper, the wheel would mechanically add the areas of these rectangles together, and the result would be the area when the tracer was returned to the startingpoint A. It will also be readily seen that as in the horizontal movements of the pointer over the lines of the rectangle cancel each other, the result will be the same if the tracing point is simply moved over the boundary lines of the diagram.

If this explanation has been carefully followed, it will readily be seen why the instrument gives the average height of a diagram when the tracer is moved upwards against the movable clamp after completing the circuit; for as the tracer is moved upwards until the wheel returns to zero, the arm will pass over a parallelogram the area of which is equal to the area shown on the wheel, or the area of the diagram measured. And as shown, this parallelogram is on the same base and between the same parallels as the rectangles found by drawing horizontal lines from clamp to clamp through the two indentations made by the pointer; therefore this rectangle is equal in area to the diagram, and as it is of the same length, its height must be the average height of the diagram.

By means of the averager a skilful operator can measure fifty diagrams per hour.

CHAPTER XXXI

SPEED COUNTERS

ALTHOUGH the speed of an engine may be taken by counting the revolutions made in a known time, this method is only of use for approximate work; therefore it is necessary to use a counter which can be worked from the crank or side shaft of an engine, and which will record the exact number of revolutions made in any given time. A very simple form of such a counter is shown at fig. 182, which is available for reciprocating and rotary motion in both directions.

The lever H is connected for counting reciprocating movements; the angular throw of this lever must not be less than 60°. For counting revolutions the lever H must be removed, and the rod or spindle Z is inserted into the opening at the back of the instrument. The counter will then register revolutions of the spindle Z.

The counting mechanisms consists essentially of a short oscillatory lever which is actuated by means of the lever H or rod Z and is provided with two projections engaging alternately with the teeth of a ratchet wheel, so as to turn the wheel through one tenth of a revolution in the same direction for each revolution of the spindle Z or stroke of the lever H. The spindle of the

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ratchet wheel carries a disc provided with a pin and corresponding recess, which serve to propel the next wheel through onetenth of a revolution for each revolution of this wheel; and, similarly, each succeeding wheel turns the next following onetenth of a revolution after having completed a whole revolution. Each wheel has a dial with ten figures, of which only one is visible at a time; consequently the figure next to the lever indicates units, the second tens, the third hundreds, and so on. When all dials show 9 the next stroke or revolution changes them all to zero, and the counter starts afresh.

The counting is perfectly reliable, even at very high speeds, because each wheel is locked in position by the edge of the next disc engaging the space between the two succeeding teeth.

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