Let L equal the length of the line A1, B1, 0 equal the angle Ө 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.

0°

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.

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 A1, its original position. During this movement the wheel will revolve through the same angle that it did in moving from A, to A,, 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. 0× 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

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

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.

The illustration shows this counter provided with an arrangement for re-setting all figures to zero. For this purpose each wheel is mounted on a carrier or short lever, which swivels on a pivot screwed into the base of the counter. After removing the cover of the counter and releasing the catch, the wheels can be all disengaged and set to zero.

HARDING COUNTER

Fig. 183 is an external elevation and fig. 184 shows the counting mechanism.

The figures are engraved upon a number of wheels, mounted. on a separate shaft. When each wheel has completed a revolution two small projections engage with the corresponding small toothed wheels, causing the latter to turn the next wheel

through one-tenth of a revolution. The small wheels also serve to lock the large wheel in position after each movement.

The end of the secondary shaft carries a lever, the end of which rests loosely on the main shaft, thereby holding the large wheels in engagement. Upon raising this lever the wheels may be disengaged and set to zero.

The actuating mechanism resembles in principle that employed in the counter shown at fig. 182, and this counter is also available for reciprocating and rotary motions in both directions.

TACHOMETER, OR SPEED INDICATOR

Fig. 185 is an external elevation of a simple form of tacho

The apparatus can be fixed in any required position for slackening the nut shown in the illustration; it can be turned round completely in the support.

The pulley may be driven in either direction, when the actual speed of driving shaft is calculated from the ratio of the diameter of the driving pulley to that on the indicator.

This instrument is often fixed or coupled to a shaft, so as to constantly record the speed of it.

TACHOMETER

This type of tachometer shown in figs. 186 and 187, which is intended for use by hand, constitutes a modification of the larger instrument shown at figs. 183 and 184.

It is very light and portable, and will indicate the speeds of rotating shafts with the same degree of accuracy as the larger instruments.

This tachometer is employed by holding it with a slight pressure of the hand against the end of the rotating shaft so that the steel bit provided on the end of the apparatus enters the centre mark of the shaft. The instrument will then indicate directly and continuously the precise speed of rotation of the shaft.