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steam considerably earlier, to let the exhaust go a little earlier, and also to give a little more compression.

We will next consider how, retaining these proportions of slide valve and ports, it would be possible by changes in the dimensions, and in the lead of the eccentric, to cause the cut off to take place more quickly. I will again imagine that the steam port a begins to be uncovered exactly when the crank is at the left-hand end of its stroke, but that the slide valve is to be driven by an eccentric of so small a throw that it will no longer cause the slide valve to travel far enough to the right, to open the steam passage the whole way, and that we are about to content ourselves with opening it only 414 of its width. These conditions could be satisfied by a radius of throw of the eccentric, which, if the width of the passage be called unity, should be the root of 2 (1.414); and to enable such an eccentric to put the slide valve into the position of being just ready to open when the crank was on its centre, the centre o of that eccentric must have a lead of 45 degs., as is shown in fig. 37. With this arrangement, by the time that the crank has travelled 45 degs.— that is, by the time that the piston has made 3-20ths, in round numbers, of its whole stroke-the slide valve will have made its extreme travel to the right, or will have opened the port a 414 of its width, and by the time that the crank has travelled a further 45 degs., or, in other words, by the time that the piston has made half its stroke, the centre o of the eccentric will be immediately over the point from which it started, and therefore will have closed the slide valve (see fig. 38), cutting off the steam at half-stroke. A further 45 degs. of the crank will bring the slide valve to the centre, at which position the compression on the right-hand side of the piston, and the exhaust from the left-hand side of the

piston will commence, and at this time the piston would have travelled about 17-20ths of its stroke. The diagram resulting from this arrangement is shown by fig. 39.

You will see that whatever may be the angular ' lead’ and the throw' of the eccentric, the position of its centre, at the time when the crank is at the left-hand end of its stroke, must be somewhere on the line y, as that line is so much to the right hand of the central position of the throw or travel of the eccentric as is equal to the lap of the slide valve-the lap in this case being assumed to be the width of one passage-and that this amount of travel from the central position must be made before the

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FIG. 39. Imaginary indicator diagram cutting off one-half.

slide valve can be just in the act of opening. Therefore, it is clear that if some means were provided by which the centre of the eccentric could be shifted at will, along the line x y, from to any point up to the centre line, the proportion of the stroke during which steam is admitted could be lessened at will, until by the time the centre o had reached the horizontal line, the admission of steam would cease, as there would be no opening of the slide what

ever.

You will remember I called your attention to the obvious fact, that if the centre of the eccentric were placed above the shaft instead of below it, while the crank was assumed to be at the left hand, the engines

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would go in the reverse direction. If, therefore, the movement of the centre could be continued along the line xy above the centre line towards y, then we should obtain the reversal of the direction of motion of the engine; and, according to the position that the pin occupied in the line a y above the horizontal line, so would be the rate of expansion in the backward direction, corresponding to the rates of expansion in the forward direction when the centre was at a similar position but was below the line.

Having thus prepared the way, I now come to the link motion'-a contrivance by which it is possible, while the engine is running, to produce on a slide valve precisely the same effects as could be obtained by the shifting of the centre that I have indicated.

I have thought it would make this subject more clear if I were to produce before you a large elementary model of the link motion, and in order that I should not be encumbered, in that model, with considerations arising from the curvature of the link, I have made the cylinder (the slide valve of which this model is to work) capable of being moved up and down in reference to the link, rather than make the link capable of being moved in reference to the cylinder, for this latter movement would have involved the curvature of the link. I need hardly say this is not the construction in practice. See figs. A to I in fig. 39A.

With a link motion, two eccentrics are employedone having its centre suitably placed for the least expansion when in forward gear, the other having its centre suitably placed for the least expansion in back gear, and I will adhere for this purpose of least expansion to the proportions given by the 30 degs. of advance of the centre of the eccentric, that is to say, each eccentric could cut

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NOTE. In all the figs. of diagrams (figs. G to H) the eccentric rods are assumed to be of indefinite length.

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