off the steam at three-fourths of the stroke of the piston. Now, if the eccentric rod of one of these eccentrics be attached to the top end of a long bar ay', and the rod of the other eccentric be attached to the bottom end of that bar, the top and bottom ends of that bar will have the same relative position to the right and to the left as the centres of the two eccentrics have, that is, as the line xy, uniting those points, has (although the bar may not be parallel to the line a y, because it is much longer than that line). If, therefore, the slide rod be attached to any point in this bar, the rod will have precisely the same motion as if it were driven by a crank pin placed in the same relative position in the line x y that the point of attachment is placed in, in the bar a' y'. For example, if it be placed at the top end of the bar, it will have the exact motion which would be given by the eccentric which is in connection with the top end; if at the bottom end of the bar, then it would have the exact motion which would be given by the eccentric in connection with that end; if at the middle of the bar, then it would have the motion that would be given to the centre of the line xy, which, you will remember under the circumstances stated, is one which would just, not open the steam passage at all.

We will now put the model into operation, and show that when the crank is, say, at its left hand (see diagram 39A, fig. A), the link will be vertical, and therefore the moving of the slide stalk up and down this link will have no effect whatever in changing the position of the slide valve. Similarly, when the crank is turned half round so as to bring the crank to the right-hand end, the link will again be vertical, and again there will be no effect by altering the point where the slide stalk engages with the link. But let us next put the crank to an angle of 60 degs.

in the backward direction (fig. B). The backward eccentric x is now at its full throw, and if the slide stalk be connected with the lower end of the link x', the left-hand steam passage will be open to its fullest extent.

If we now cause the crank to travel a further 60 degrees (see fig. C), or a total of 120, equal to three-fourths of the stroke of the piston, it will be found that the backward eccentric is immediately above the position which it occupied at the commencement of the stroke, and that thus the slide valve has closed the port, and expansion has commenced. Restoring the crank to zero, let the slide stalk be raised until it is connected to the link at a point m', say midway between its lower end, a', and its centre (see fig. D), a point which, when set out upon the line x y, and connected by a radial line to the centre of the crank shaft, would be found (see l m in fig. D) to give the equivalent of an eccentric having a lead of about 49 degrees instead of the 30, and a throw of rather less than twothirds of that of the actual eccentrics; at this point of attachment to the link the extreme motion of the slidevalve, which will be only sufficient to open the steam passage about one-third, will be found to occur when the crank has travelled the difference between the 49 degrees of lead and 90 degrees, that is to say, when the crank has travelled 41 degrees (see fig. E), equivalent to approximately 4th of the stroke of the piston; and when the crank has made a further 41 degrees, or 82 in all (see fig. F), equal to about 43 per cent. of the stroke of the piston, the imaginary centre of the diminished and advanced eccentric we are considering, will be immediately above the position in which it was when the crank was at the commencement of its stroke (see fig. D), and the slide valve will be reclosed, and expansion will begin.

I need not occupy further time by tracing the effects of shifting the point of attachment to other parts of the length of the link below its centre, as it will suffice to say that the period of cutting off the steam may be hastened until it be made infinitely short; calling attention, however, to the fact that this hastening is accompanied by a continual diminution of the width of the opening to admit the steam to the cylinder. Similarly I need not occupy your time by showing on the model that if the point of attachment be anywhere above the centre of the link, the engine will revolve in the reverse, or forward direction, and that the expansion will follow the same rules as it obeyed when the engine was assumed to be running in back gear.

We have now considered the action of the model on the assumption that the ports are made to open to the steam exactly as the crank is on the centre, but in practice the ports are always open to the steam before the crank is on a centre-as already mentioned when speaking of the single eccentric that is to say, the line x y is put still further from the centre of the crank. I believe I can change the model and can show its effect in working.

For this purpose I will give a further lead of 5 degrees to each eccentric, making a total of 35 degrees (see fig. G): this will have the effect of moving the line ay and with it the slide, so as to open the passage to the steam rather more than one-seventh of its width when the crank is on its centre: if now the attachment of the slide stalk to the link be made at its lower end, the extreme opening of the steam passage will of course be effected when the crank has travelled only 55 degrees, as p (instead of the 60 degrees), that is to say, when the