The tabulated values of n, in the preceding, were computed from a well-known steam table with Vega's logarithms and are essentially the averages from 100 to 70 per cent., inclusive, as found by Zeuner. It is seen that as a decreases, n decreases. For 100, 90, and 80 per cent. qualities at the several pressures n decreases; for 60 per cent. and below it increases. At 70 per cent., n is practically constant. When the curves are plotted, as in Fig. 9, a crossing of each other is noticed. This cannot be said of carbon di-sulphide, ace

tone, ether, or carbon tetrachlorides. Ammonia and some of the other vapors have not been considered on account of lack of experimental data for specific heats of the liquids. Alcohol was omitted because of the fact that dissociation takes place during evaporation.

The hyperbola, which is used quite largely as a curve for comparison with the expansion curve on an indicator diagram, would not be traced by the indicator pencil, true

by unity.

adiabatic expansion taking place, until the quality was reduced to 31 or 32 per cent.; practically two-thirds of the weight of steam having condensed.

The lower parts of the preceding five tables give instantaneous values of n. The variation between these values and the average values above are quite noticeable.

In Figs. 4, 5, 6 and 7, the sets of large curves at the left are the adiabatics and those at the right, marked B, are their evolutes. Referring to the central diagrams, those curves which diverge upwards, C, give instantaneous exponent values for the different pressures along the several adiabatics, so marked from initial qualities. The other sets of curves, D, to the same axes, show the instantaneous values of n for any given pressure, across the several adiabatics. Since these diagrams have three sets of variables, solids may be formed which will give the instantaneous value of n for any given pressure and dryness fraction. The photograph, Fig. 8, is that of the five solids so obtained. Beginning at the top and reading to the right are those of steam, carbon disulphide, ether, acetone and carbon tetrachloride. Their similarity of figure is quite noticeable. If horizontal planes be passed through the surfaces, the lines of intersection are the curves D and C in the plates just described. Planes giving curves marked D, are those made by the XY planes passed through the surface, as shown in Fig. 3.

It was hoped that some general expression might be obtained which would give the exponents for adiabatic expansion for any vapor at any pressure with any given. quality modification. It is seen that the curves D, Figs. 4, 5, 6 and 7, are not coincident, hence any expression that might be obtained would be too cumbersome to be of any practical use. Fig. 9 shows that the average values of " do not form coincident curves. In the following Fig. 10,where their logarithmic values are plotted, it is seen that while the curves are not coincident they form almost straight lines to 60 per cent. quality; that is, any given curve representing the varying exponential values at a given pressure, is almost logarithmic. That being the case,

n = (x/c)"