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the exhaust steam would not be cleared from the cylinder until some portion of the return stroke was made; and the other, that there would not be any cushioning' by the steam, to assist in bringing the reciprocating parts of the engine quietly to rest at the end of each stroke. This latter is a very important point in connection with the smooth working of quick-running engines.

Now, if you will imagine that the slide and eccentric remain as they are in this diagram (fig. 30), but that the angle between the crank and the eccentric is altered, so that (when the crank is, say, at the left-hand end) the eccentric, instead of having its centre o in a vertical line below the centre of the crank, should have its centre to the right hand of that line, to the desired extent, the result, as you will see, would be this-that when the crank was on its centre, the steam passage would already be somewhat open, the exhaust passage at the other end would be somewhat open, and the exhaust passage at the left-hand end would have been closed some time before; thus the exhaust steam from the right-hand end of the piston would have had an opportunity of escaping before the termination of the stroke, while the continuance of the exhaust from the left-hand end would be stopped, and the boiler steam would be admitted in opposition to the motion of the piston, thereby cushioning' it to rest. This advance of the eccentric in relation to the crank is technically known as 'lead,' and you will see that, by itself, it gives some slight amount of expansion, because it cuts the steam off before the end of the stroke is quite reached. But even in the worst steam engines, valves proportioned as I have here, for the sake of illustration shown are never used: they are always made with 'lap' as well as with lead.' The diagram, figure 34, shows a slide valve thus constructed, with a suitable eccentric.

connected to it. The common proportions in use at the present time are here taken. The slide valve is made so that when in its middle position it not only covers the steam passages, but overlaps them by their own width at each end. With these dimensions it is obviously necessary that the travel of the slide (if the passages are to open fully to the steam-which they very commonly do not) must equal four times the width of the passage; and in order that the passage may begin to open just as the crank is on its centre (for that is the condition of things I will first consider), the centre o of the eccentric must be so far in advance of the 'without-lead' position as to have already made one-half its travel, that is, it must be advanced 30 degs. The diagram (fig. 34) shows the ports as before, with the crank at the left-hand end, the centre of the eccentric underneath, but 30 degs. in advance of the centre line, and the slide valve moved to the right-hand, so as just to admit the steam to the port a, to press upon the left-hand side of the piston, while the exhaust cavity of the slide valve is already uncovered the full width of the outlet b, thereby giving free egress for the exhaust steam before the termination of the stroke. By the time the crank has moved 60 degs., or the piston has made one-fourth of its stroke (always leaving the variations due to the angles of connecting rods and eccentric rods out of consideration, and treating those rods as though they were of infinite length), the centre o of the eccentric will have arrived at its extreme travel to the right hand, as will also the slide valve; at that time the steam port a will be fully open as in fig. 35, and the exhaust port b will also still be fully open, for the exhaust cavity in the slide valve will have travelled the width of the port beyond it. When the crank has moved a further 60 degs. (equal to three-fourths of the stroke of the

piston), the centre o of the eccentric will be immediately above its former position in fig. 34, and will have drawn the slide valve back, so as to just close the steam port a; from this period the steam will commence expanding in the cylinder. The exhaust b, however, will at this point still be wide open, but will gradually close as the eccentric continues its travel, and will be entirely closed when a further 30 degs. of motion has been made, for this will bring the centre o in a vertical line immediately above the crank shaft, and will therefore put the slide valve in its middle position. From this point there will be exercised compression of the steam contained in the cylinder on the

FIG. 36. Imaginary indicator diagram cutting off at three-fourths.

right-hand side of the piston. At this time also the exhaust will commence from the port a, at the left-hand end of the cylinder; but the crank will now have made a total movement of 150 degs., and the piston will, therefore, have traversed about 15-16ths of its stroke. With such an arrangement the indicator will no longer afford a square card, but a card of the form shown on the diagram figure 36. I will now ask you to imagine that this form of construction may be still further improved by giving the slide valve some lead,' so that the steam passage may be opened preparatory to the arrival of the piston at the end of its stroke; the results of this will be to cut off the

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