engine has ever yet been given a systematic trial to determine these quantities. Curves 1 and 2 of the Straight Line engine are irregular, and too much so to reveal any definite law, taken by themselves, but, taken with the other evidence presented, may be considered as fully corroboratory of the conclusions deduced. Test No. 3 gives a very regular and satisfactory curve, and this accords perfectly with the others in exhibiting the law of variation

of friction with engine speed. The full line drawn through this group of observations is considered as fairly representative of the mean result of all tests on this engine, and is a straight line, the representative of the law previously discovered and stated. The curve for the 8 × 12 Automatic engine is anomalous, and differs from every other curve obtained, in falling with rising speed. It is evident that this engine differs, in some respect, from all ordinary engines in its law of variation of internal friction with engine

speed. The smoothness of the curve would indicate that this is a real attribute of this engine, and not a mere accident of the time or of the construction of the machine. It would be interesting to push the trials of this engine farther, and to ascertain what is the final outcome of this apparent anomaly at higher speeds, and also to learn where the lower limit of the curve comes into view. The Tandem Compound shows precisely the same general law as the other forms of engine, but it is subject to less variation than any other, the curve slowly rising, as the speed increases, throughout the whole range of experiment.

All these variations of engine friction have an important bearing upon the theory of the true commercial efficiency of engines. It is so important a matter that no correct or satisfactory theory of the steam engine can be constructed until the influence of this form of loss and waste can be determined and can be introduced into the general treatment of that subject. There thus remains for investigation the mathematical theory of efficiencies of the steam engine as affected by friction wastes, and the determination of the conditions of maximum total and commercial efficiency for every engine to which it may be attempted to apply that theory. The solution of the problems thus arising in the introduction of the more commonly employed engines has an extraordinary importance for the engineer, and especially for the builder and for the user. Neither can intelligently select and operate an engine in any given locality, or under any given set of external conditions, so as to secure highest efficiency, without first solving this class of problems in relation to that engine or class of engines. Rankine's graphical method, as modified by the writer, and as applied to modern engines in the manner shown in earlier papers presented to the American Society of Mechanical Engineers, supplied the most convenient and satisfactory method of effecting the solution of these problems.*

Fig. 23 similarly illustrates the variation of engine friction with variation of the point of cut-off and ratio of expansion. In all three cases taken, the variation of internal resistance of engine is visibly altered by the variation of the expansion, slowly but observably rising with diminishing expansion. The same engine, tested by the two pairs of observers, in 1887 and 1888, shows different absolute magnitudes of friction, the engine having had a year's work in the interval, but the law of variation is the same * Trans., Vol. II., p. 125; Vol. III., p. 245.

and the rate of variation is nearly equal in both cases, although the friction is seen to be more nearly constant in the first set of trials. In the third curve also, that in which the work on the 7 x 10 traction engine is illustrated, the same law and the same rate of variation shown by the first of these trials, 1887, are exhibited. All show plainly the fact that, other things equal, the friction of the engine varies slightly with change of ratio of expansion, the amount increasing as the point of cut-off is advanced and the engine is set to "follow" further. It must be kept in mind, however, that the ratio of friction of engine to total power of

engine is continually varying in the opposite direction, and it does not at all follow from these observations, as here graphically illustrated, that the shorter. cut-off and lower powers of engine are, on the whole, more economical than the higher. The true point of maximum economy and efficiency, all conditions being regarded, can only be ascertained by the application of the determined facts in the complete theory of the several efficiencies of the engines studied.

Fig. 24 is the graphical summary of the work done to ascertain the method and extent of variation of the friction of the engine with change of load, other conditions being, so far as possible, retained constant. The lowest curve on the plate is that obtained

from the work on the Jarvis engine, and is considerably lower than any other, absolutely and relatively. It is a straight line, is parallel to the axis of abscissæ, and indicates constant waste by friction, at all loads and powers. The next curve is that of the 8 × 12 Automatic engine, which is much more variable and less satisfactory as a measure of the true loss; but it gives a mean, as shown by the full line, very nearly representative of constant friction; the same is true of the 7 x 10 Traction engine, and of the 7 × 12 Straight Line engine. All give a mean which is practically independent of the power exerted by the engine. The widest range of work is that obtained with the compound condensing engine, and extends from zero up to nearly 100 H. P., the brake being the measure. This also gives some irregularity of result; but its mean is a constant at all powers, and is independent of the load on the engine, so far as can be detected in this series of observations. Finally, the compound tandem engine, a new engine, naturally gives a high measure, comparatively, of the internal loss by friction; but the law is seen to be nearly the same for variation of load, and its operation confirms the deductions previously drawn from all other work of this character which the writer has been able to offer. In both of the compound engines, however, there is some evidence of a tendency to reduce friction slightly as the power is increased, a change contrary in direction to that detected in other cases; but in neither set of examples is this variation great. (See Figs. 29 and 30.)

TABLE X.

THE JARVIS ENGINE, 7′′ × 7''.
Friction with speed and load variable.

No governor. Speed varied by the throttle. Steam pressure constant at 80 lbs. Trial No. 2.