(c) Should the line d m, instead of being at right-angles to the atmospheric line, be slanted with the top inclined to the right as from 7 to m, it would show there is excessive lead given to the steam valve.

(d) Had the upper right hand corner been slanted off or rounded, as shown by the dotted line fg, the defect would have been that the steam-valve opened too late, caused by valves having too little lead.

(e) When the exhaust corner is cut off, as shown by the dotted line h i, it shows that the exhaust-valve opens too soon.

(f) But if the exhaust corner had been in the form shown by the dotted line kl, the exhaust-valve would have opened too late, and after it did commence to open, would open with too slow a velocity, preventing the free escape of steam, or the exhaust passages would have been too small, which would produce a similar effect to the valve opening too slowly.

(g) Should the steam line, instead of being parallel to the atmospheric line, fall in as shown by the dotted line m n, it shows that the throttle-valve is partially closed, or the steam passages too small, preventing the full flow of steam into the cylinder. It will be seen that the pressure is not maintained uniformly for any part of the stroke, by reason of a diminished supply of steam.

297. The manner of laying out a true Hyperbolic Curve.-In the case of an expansive engine the theoretical curve of expansion will be an hyperbola. We will show a method of laying out the curve that will be found useful in connection with the diagrams. In fig. 16, AB is the atmospheric line, and CD is the perfect vacuum line; CE is the receiving line, EF the steam line, and at F the steam is cut off, and the pencil describes the hyperbola F a b c d, called the expansion line. We can lay this out merely by applying Mariotte's law. Divide the whole length of the

stroke CD into any number of equal parts, and observe how many of those parts the steam follows. In the case under consideration: suppose the initial pressure of steam is 60 pounds, and the steam follows two of the spaces into which we have divided the stroke. Then, when the steam reaches the third space, its volume will be times what it was originally, and its pressure will, therefore, be 3 of 60 or 40 pounds. Similarly, as at the fourth division

the volume is doubled, the pressure will be of 60, or 30 pounds. At the fifth division the volume is 2 times its original bulk, and the pressure is of 60 or 24 pounds, and so on. When all the points are found, describe the curve Fabcd. EF abcd DC is, then, the theoretical diagram taken from an engine carrying 45 pounds of steam per gauge, and following of the stroke.

An experienced engineer can tell at a glance whether an engine is in good working order from its diagram; but, nevertheless, in most cases it would be well to draw the true curve, in order to ascertain how much the actual one differs from it, for by this means we can ascertain when under way, whether the valves or piston leaks. In drawing the theoretical curve on a diagram taken from an expansive engine, it must be remembered that all the steam in the clearance also expands. This clearance, then, must be reduced to an equivalent length of cylinder, and added to the end of the stroke. In the practical case the curve will usually fall a little below the theoretical curve. If it is very much below, it is caused by a leak, either in the exhaust valve or around the piston. If the actual curve is above the theoretical, it will be on account of a leak in the steam valve, whereby steam is admitted to the cylinder after the valve is closed. Our practical diagram is EFghklmef.

Fig. 19.

Leaky Slides.-This is an illustration of an indicator figure taken from an engine with leaky slides. The line below the diagram is the line of perfect vacuum, and the dotted line shows the figure that ought to be made if the slide valves were tight. Should the steam valves leak while everything else remains tight, the termination of the expansion line will be too high.

298. How to discriminate between errors due to the slide-valve and these due to the eccentric.-In discriminating between an error due to the slide-valve and one due to the eccentric, remember that the effect of shifting the eccentric is to move all the points of opening or of closing the ports round the diagram opposite to that in which the eccentric has been shifted. The effect of an alteration in the position of the slide-valve, or of any of the edges of the slide-valve is, as a rule, to move the points affected by the alteration along the diagram in the same direction in which the valve or valve edge has been altered. When the valve does not open to admit steam until the crank has passed the centre, the point of admission is an exception to this rule. The points are all in pairs, each point of opening has a corresponding point of shutting. If one point is wrong, find whether the corresponding point on the other side of the diagram is also wrong, and whether the two points require to be shifted round upon the diagram, or whether they require to be moved along the diagram in the same direction, and state the alteration required.

299. Effects produced on an indicator diagram by shortening and lengthening slide-rod.

Figs. 20 and 21 show a full speed diagram with lap, and one without lap on the slides.

Fig. 20.

B

A

In the diagram, Fig. 20, it is shown that the steam is carried uniformly to the end of the stroke; but in Fig. 21 it will be seen that it is cut off when the piston has some distance to travel, which is caused by the lap on the valve. In the former case the valve only just covered its ports, therefore, it is only shut at the end of its stroke; but in the latter, by means of the lap, the port is closed sooner, and steam is admitted to the opposite side of the piston before the completion of its stroke.

Fig. 21.

A

Observe that if the cushioning corner of an indicator diagram is very square, it may be attributed to too little lap being on the exhaust side of the slide-valve.

The following diagrams, Figs. 22 and 23, illustrate the effect produced by shortening the slide-rod.

TOP STROKE.-(Shortening the rod.)

Fig. 22.

B

C

D

The effects on the Top Stroke (Fig. 22) are that the steam enters sooner, A; the cut-off is later, B; the exhaust is later, C; and the slide is closed sooner, D; in other words, the defects shown by the diagram are that the steam line, A B, is too long, or spread out, and the exhaust line, CD, is contracted.

On the Bottom Stroke the effect produced is exactly the opposite, for we find the steam is late in entering, A. The steam is cut off quicker, B. The port is open to the exhaust sooner, C; while the closing is later.

While the effect produced by lengthening the slide-valve rod is precisely the opposite of what has just been explained.

By this we find that on the Top Stroke the steam is late in entering the cylinder, A (Fig. 24), the valve not opening sufficiently early.

The slide-valve has, it will be seen, cut off the supply at an earlier stage, B.

The exhaust is also sooner, C, while at the termination of the stroke the slide is longer in closing, D. In other words, the defects of the (Tor) diagram with the slide-rod too long are, the steam line is contracted or too short, and the exhaust line is too long.

BOTTOM STROKE.-(Lengthening the rod).

Fig. 25.

B

D

On the bottom stroke the steam enters sooner, A; the cut-off is later, B; the exhaust is later, C; but the valve at the end of the stroke is closed sooner, D. (See fig. 25.)

300. Illustration of the effect produced by altering the position of the eccentric.-Advancing the eccentric round the shaft causes the eccentric to put the slide into all its positions of admission, cut off, exhaust, cushioning, &c., a little earlier than formerly, while the contrary effect is produced by moving it backwards.

For example. In a diagram taken after advancing the eccentric (Fig. 26) where the cushioning is early, D; the cut-off is early, B; and the exhaust is sooner, C. We have a diagram something similar to that given when the slide-rod is too short, because all the movements of the slides are too early, but the corners will be sharp and irregular instead of round. There is a distinction between this case and the cases where the eccentric-rod is too long or too short. In the case under consideration the same fault would exist in the diagrams taken from the top and bottom of the cylinder; but when the slide-rod is in fault, the opposite defects would exist at top and bottom (see Figs. 23, 24, 25, and 26).