the two proportions last mentioned will be reverted to seriatim. Returning to the requisite dimensions for the example given, they will be found to be thus:

Let A= width of port supply.

Boutside lap.

Cinside lap.

Dwidth of bar.

Ewidth of exhaust space in valve.
F= width of exhaust port in cylinder.
Ghalf travel of the valve.

E=2·5×1·5+1·5+2·5+[1—125]=8·625

F-8.625-[1-125×2]=
G=2·5+1·5=.

. 6.875

4.0

The above calculations, and the results, represent the proportions of the valve and ports in Figs. 1 and 2. It may, perhaps, be well to add, that the formula given will be correct for any proportion, whether the valve is intended to cut off at one-quarter, three-eighths, one-half, fiveeights, three-fourths, or seven-eighths of the

stroke. Also the exhaust may bear any proportion to the supply, remembering, of course, to use the ratio required, rather than the one given at present.

In Fig. 2, the valve, as before stated, is at full stroke. It will be seen also that the end of the valve overlaps or travels beyond the supply port (exhausting). This overlap will be found, in all cases, to equal the outside lap, minus that of the inside. Therefore, when the valve has closed the supply port, the exhaust will be open in width, equal to the outside lap minus inside lap.

It needs scarcely be added, that when no inside lap is given, the outside lap regulates the excess of time (beyond that for the supply) for exhausting. In the example now alluded to, the areas (from the supply ports) both for exhaust and supply, are equal; due, of course, to the slide travelling the entire width of the port. Now, to lessen the stroke of the valve would be to reduce the area for the entrée of the steam, while that for the exhaust would not be affected, i.e., should the reduction of the half-stroke of the valve not exceed the overlap on the exhaust side in Fig. 2. To retain the area for the entrée of steam-but increase that for the exhaust more in proportion than in the diagrams Figs. 1 and 2, but not to

exceed or reduce the stroke of the valve-the width of all the ports must be increased in proportion, hence the origin of the "exhaust relief valve."

For the purpose of future comparison and illustration, it will be better to give the proportions and formula for this valve. Now, presuming an engine of the same power as the last example, and ratio of area for the supply steam to be equal, also the stroke of the valve-but allowing the area of the port to exceed that of the opening (caused by the stroke of valve)—the following result is obtained, viz. :-The exhaust side of the piston is less susceptible to the action of the steam, generally known as back pressure or "cushioning;" the explanation of this will be further alluded to hereafter. The following formula or data will now be in requisition before proceeding further :

Width of port width of supply opening caused by valve × 1·5.

Width of exhaust opening caused by the valve

width of port × 1.5.

Width of exhaust space in valve

width of

port1.5+half travel of the valve+width of

bar minus inside lap.

Width of exhaust port in cylinder:

width of

bars minus inside laps deducted from the exhaust space in valve.

Before making use of these rules, it will be

requisite (to prove their veracity,) to explain their origin. To begin with the rule for the width of the port, it will be seen that a constant

number is given. Now, it must be strictly understood that this sum can be lessened or increased according to the discretion of the calculator, the number given being compiled from the average of general practice.

The second rule bears strict reference to the distance of the inside of the bar to that of the valve when at full stroke, as at Fig. 2, hence the increase of area or width of the exhaust port to that of the supply. The width of the exhaust space in valve is produced by a formula, as in the first example; also the last rule now given is the same in composition. In Fig. 3 will be seen a diagram of a valve and ports arranged for the exhaust relief principle. The valve is entirely covering one supply port, or cutting off, while the exhaust side is partially open; due, of course, to the arrangement before alluded to. In Fig. 4 the valve is shown at full stroke. Now, on comparing the widths of the ports (for the exhaust) in Figs. 2 and 4, the relative areas can be readily understood (the scale being the same throughout). It is, therefore, obvious that, while the valve is opening the port, for a given width as in Fig. 4, that for the exhaust is increased, the ratio being due to the discretion of the designer. Having thus briefly described the action of the valves