These results for superheated steam are very satisfactory, with one exception, and for saturated vapor are not quite as good as those in Table I. Mr. E. R. Dawson computed the pressures from each of the three following formulas for temperatures from 212° F. to 365° F. (Graduation Thesis, 1888, Stevens Institute of Technology): A comparison of the results thus obtained with those in steam tables caused a rejection of formula (C), and a preference for formula (B). A further discussion of the subject led to the adoption of the following formula: τ 136.88 P = 0.6734 v - 0.16 . . (D) in which p is the pressure in pounds per square inch, and v the volume of a pound in cubic feet. The following are the results of computations from formula (D): This agreement is practically exact. The computed and tabular pressures agree more nearly than those in different steam tables. Applying this formula (D) to superheated steam, I find the following results: This agreement, though fair, is not as close as is desirable for steam. We have, thus far, found no formula that represents both saturated and superheated steam as accurately as Zeuner's, but we have not yet exhausted the availability of Rankine's formula. It is certain that by using three, or more, terms of the equation, results may be found having any required degree of accuracy. Wüllner, in his Lehre von der Wärme, p. 668, gives a formula of Herwig's on the density of saturated vapors, which is in which v, is the volume in cubic meters of one kilogram of saturated vapor at the absolute temperature 7, P1, the tension of the vapor in millimeters of mercury at that temperature; while pand represent the pressure and volume that the vapor would have at that temperature if it obeyed Mariotte's law; hence pv = RT where R is a constant. Substituting above, and dropping the subscripts, we have where A includes all the constant elements of the equation. I have tested this equation by the use of the most modern steam tables, by determining the value of A, which is and if the formula is exact, the values thus found for 4 should be The difference between the largest of these and the smallest is very nearly 1 of the value of the largest and aside from the value given for v = 90.31, the error is about 5 per cent. of the largest. The formula then is not nearly so accurate as other formulas in use, and for steain pr} = a constant is more desirable. Equation (c) Zenner reduced to the following: pv = 0.0049287 — 0.187815√/P, in which the constants were determined for T, = 273° C. = 491°.4 F. absolute, and the mechanical equivalent of heat 428. Modern values of 492.66 F., and J = 432.1, would change these someT = what, and also produce a change in the numbers of the following table. The third column in the following table, and the fourth column in the table for superheated steam, were computed from the preceding formula: |