in the stroke than about, as the angular advance necessary to give any earlier cut-off would involve a too early exhaust and compression.

3. From the cut-off, C, to the release, D, is the expansion curve. Assuming the applicability of the Mariotte law to expanding steam, the shape of the expansion curve, CE, should be such that, if the distance from any point in it to the clearance line, H H, taken on a line parallel with the atmospheric line, be multiplied by the distance from the same point to the vacuum line measured vertically, the product will be the same for all points in the curve. Hence, if at the commencement of the curve, the two measurements are multiplied together, and the product divided by the distance from the clearance line to any other point, the quotient will be the distance of that point from the vacuum line, or the pressure at that point, if the pressure scale is used for the measure

ments.

4. The release at D will take place earlier or later, according to the amount of lap, both steam and exhaust, that is introduced. The steam-lap affects it indirectly, as, the greater it is, the greater the angular advance necessary to maintain the proper lead. Lap on the exhaust side affects it directly without change in the angular advance, by opening the port so much later, and consequently closing it so much earlier. The requirements of perfect working are, that it shall be early enough to release the piston of all undue back pressure before much of the return stroke is made, and late enough not to materially diminish the power of the engine. The conformation of diagram No. 1, page 291, shows about as early an exhaust as is admissible, because little or nothing would be gained by a later one, as the steam is not thoroughly exhausted until the piston has moved a short distance on its return stroke; and, while a later release would add a little to the average forward pressure, it would also increase the back pressure. Besides, a later release would involve either a later cut-off or an earlier compression; and, although the general practice is to place all these events later than is shown on the diagram, such practice is not calculated

to realize the best possible steam economy with that class of engines.

5. The back-pressure line, EF, should coincide with the atmosphere, or nearly so, in non-condensing engines and with the pressure shown by the vacuum-gauge in condensing engines. When it is in excess in either case, it indicates insufficient capacity in the exhaust-ports or pipes, or both.

6. The compression curve, F G, owes its form to the same laws that govern the expansion curve, and its degree of conformity to theory may be tested by the same methods. The only differences between the two are in the quantities of steam evolved in their production, and the order of their formation; the ending of one corresponding to the beginning of the other. As to the amount required to satisfy the best conditions, some difference of opinion exists. It is ascertained that a certain amount is advantageous, as a means of arresting the momentum of the reciprocating parts, while changing the direction of the force on the crank-pin in a more gentle and quiet manner, than would be done by the admission of steam as an opposing force. If the compression, or, more properly speaking, the cushion has fulfilled its functions, the induction will find the parts already prepared for the shock, and prevent a jar or thump. The maximum pressure reached by the cushion should never be greater than the average initial pressure; but within this limit considerable latitude exists, as, while it diminishes the power of the engine, it lessens the consumption of steam. The less the exhaust-lap, the earlier the exhaust will take place, and the later the compression, and vice versâ.

7. The lead line, G B, need not conform to any arbitrary standard. It satisfies the eye of the engineer best when it is vertical, or nearly so; but it may lean slightly inwards, indicating deficiency of lead, or outwards, indicating excess, without affecting the economy of the engine, and in most cases without sensibly affecting the smoothness of its running. In many cases the commencement of the lead line proper cannot be exactly located; but engines always run best when the compression and lead lines join

each other with an easy curve. When a single slide-valve is used, both the steam- and exhaust-lap must be provided for in its construction, and cannot be subsequently changed without a change of proportion. But since it is not the absolute amount of lap, but its amount relatively to the travel of the valve, which determines its influence, it follows that, by reducing the travel, the lap both steam and exhaust will be virtually increased, and vice versâ. Any change of travel must be accompanied by such change of angular advance as will maintain the proper lead. The adjustment of the cut-off by the link-motion of the locomotive is an instance of such change of travel and angular advance.

In the foregoing description all the capital letters refer to diagram No. 1, on page 291.

When two slide-valves are used, each performing the functions of induction and exhaust at its own end of the cylinder, the steamlap may be increased by setting them farther apart, and diminished by contracting their connection; but in such cases steam-lap is obtained at the expense of the exhaust-lap, and vice versâ. Having learned from an engine embodying correct construction and performance the general features which should characterize a diagram, the engineer will have no difficulty in recognizing defects as well as deviations from diagram No. 1, on page 291. These conditions should be understood before the slide-valve, throttling engine diagram can be intelligently criticised.

Diagrams taken from Automatic Cut-Off Engines.

The points of difference between diagrams from automatic cut-off engines and those from slide-valve engines will be mainly found in the steam lines, the points of cut-off, and the expansion curve. When the automatic cut-off engine is worked in accordance with the theory of its operation, the steam is never throttled for the purpose of regulating the speed, but is admitted freely to the valves, the speed being regulated solely by means of variations in the point of cut-off. Hence, the steam line should indicate a

pressure equal to that in the boiler, whatever the load may be, and would undoubtedly do so, if the proportions were good and the valve-gear in perfect order. The necessary difference, then, between the throttling and automatic cut-off engine diagrams, may be thus stated. In the former, the height of the steam line varies with the load, the length remaining the same; in the latter, the length of the steam line varies with the load and pressure, the height remaining always approximately that of the boiler pressure.

The theoretical diagram. From what has been said in the foregoing paragraphs, it is clear that a theoretical diagram may be constructed, representing perfect performance on the automatic cut-off principle, which cannot be done in the other case, as the height and conformation of the steam line depends on conditions too numerous and complex for analysis. Thus, with a given boiler-pressure for a steam line, a straight horizontal line may be drawn, corresponding with that pressure, and, from a given point of cut-off, an expansion curve may be drawn having the properties already described, and reaching to the end of the stroke. If the remaining terminal pressure is greater or less than the counterpressure, a vertical line extending upwards or downwards to the height required by the counter-pressure will represent a perfect exhaust line. Then, for the return stroke, a line coincident with the atmosphere or a perfect vacuum, according as the engine is non-condensing or condensing, will represent the counter-pressure, and a vertical line up to the beginning of the steam line will represent the admission line and complete the figure.

If a compression curve is desired, it may be drawn through the assumed or actual point of exhaust-closure on the counter-pressure line, but such a curve cannot originate from a perfect vacuum. Hence, when the diagram is from a condensing engine, and the actual compression curve is to be tested by a theoretical one, the latter must be based on the actual counter-pressure present at the closure of the port.

This theoretical diagram being for the present assumed to be