CONCLUSIONS. I.—It appears from the preceding investigation that jets of steam show unmistakable change of appearance to the eye when steam varies less than one per cent. from the condition of saturation either in the direction of wetness or superheating. II.-It appears from the investigation following in Part II. that the instrumental error of portable condensing calorimeters does not theoretically interfere with the measurement of about one per cent. of variation in the heat of saturated steam. But in the use of such calorimeters there has always been found to exist an accidental variation or error considerably in excess of the theoretical instrumental error, even Regnault's magnificent work not being an exception in this respect.* Consequently if a jet of. steam flow from a boiler into the atmosphere under circumstances such that very little loss of heat occurs through radiation, etc., and the jet be transparent close to the orifice, or be even a grayish white color, the steam may be assumed to be so nearly dry that no portable condensing calorimeter will be capable of measuring the amount of water in steam. If the jet be strongly white, the amount of water may be roughly judged up to about 2%, but beyond this a calorimeter only can determine the exact amount of moisture. III. A common brass petcock may be used as an orifice, but it should, if possible, be set into the steam drum of the boiler and never be placed further away from the latter than 4 feet, and then only when the intermediate reservoir or pipe is well covered. PART II. GENERAL EXPRESSIONS FOR THE INSTRUMENTAL ERRORS OF CONDENS ING CALORIMETERS FOR TESTING THE QUALITY OF STEAM. I. Establishment of Formula for Percentage of Priming. Let W the weight of condensing water, including the calorific equivalent of the containing vessel or calorimeter. w the weight of steam condensed, the degree of dryness of which is desired to be measured. the temperature, Fahrenheit, of W before the condensation *See Table at End of Part II. 81 = enheit. * the mean specific heat of water between t, and zero, Fahr the temperature of W after the condensation of w. Sa = the mean specific heat of water between t, and zero, Fahrenheit. c = correction in degrees Fahrenheit to be added to t, to compensate for the losses due to radiation, conduction and evaporation from the calorimeter during the interval of an experiment. tz t, the temperature, Fahrenheit, at which water boils under the pressure at which the steam w is produced. 8, the mean specific heat of water between t, and zero, Fahrenheit. = H the heat in British thermal units reckoned from zero, Fahrenheit, which should be 'realized from the condensation of each pound of w, if the latter is perfectly dry or saturated steam, such as steam tables based on Regnault's researches represent. That is, H = 1092.7 +0.305 (ts — 32) + 32. h = the heat in British thermal units, reckoned from zero, Fahrenheit, which should be realized by the cooling of each pound of w, if the latter is entirely liquid water at the temperature t. That is, h = 1383. P = the percentage of w, which is liquid water or the per cent. of its weight, which by condensation will afford only h thermal units per pound. Then the thermal units which will be contained in the calorimeter after the entrance of the w pounds of steam are, P 100 × W × h + (w P 100 × w) H + W × t1 × 81. But by the observation of t, and determinations of c we have, the heat present in the calorimeter after condensation also equals (w + W) × (ta + c) 82; The value of P is commonly known as the "Percentage of Priming." The equivalent of this formula has been written in several shapes by various writers. The above arrangement is thought to represent most directly the physical relations involved; thus, if the expression W [(tsc) 8, t,8,] w [H- (t2 +8) 82] be represented by Q, then Qis the amount by which the heat belonging to the w pounds of steam condensed differs from the heat belonging to the same weight of steam, if it had been such steam as Regnault used in his experiments, which is the steam of standard "dryness." imparted to the condensing water by the w pounds of tested steam is less than w [H− (t2 +c) 82], or the heat which w pounds of Regnault's steam would be capable of imparting to the condensing water; hence, it is assumed that a weight of the tested steam must have contained liquid water. If Q is minus, then the tested steam imparts more heat to the condensing water than would w pounds of "Regnault's" steam, and consequently the tested steam is assumed to be superheated a number of degrees equal to Q divided by the specific heat of steam at constant pressure, or -Q 0.480' Formula (1) then gives a value of P which is minus, and which expresses the equivalent of the superheating in percentage units, which, if taken against the latent heat of a pound of Regnault's steam expressed in thermal units, gives the amount by which the tested steam was superheated above the temperature of Regnault's steam. Thus, if t, represent the temperature to which steam is superheated, then P(H-h) -Q = 0.480' II. Formula for Errors. (2) If, in the operation of making a priming test, each of the quantities entering into (1) be assumed subject to a certain error of obser vation, then the estimated value of P will be incorrect by an amount 4P. Let it be required to determine how much of 4P is due respectively to W, w, (t2 + c) 82, t181, H and h. We will represent by 4Pw, 4Pw, 4Pt2, 4Pt1, 4P and 4P the errors due directly to W, w, (t + c) 82, etc., respectively, so that it will follow that ΔΡ=ΔΡ + ΔΡ + ΔΡΙΑ + ΔΡ + ΔΡΑ + ΔΡΑ w Let the possible error of W be AW pounds H If in (1) we add to each quantity its error we shall have: P+4P= ( W + ( 100 {(∞ +4∞)[H+AH−(t2+C) 82—At2] − ( W+4 W )[(t2+c) 82 + At2−(t;8; × 4t;)] (w + A∞) [H + ▲H − (h + Ah)] (4) Subtracting Equation (1) from this, member by member, we ∞ (w + Aw) [H + 4H − (h + Ah)] We have 4P equal to the algebraic sum of the following quantities, which are each to be understood as having the above common denominator. The constant 100 is also omitted: |