These temperatures were raised from about 460° to 600°, by increasing the weight of water about sixteen times, indicating that considerable quantities of water, thrown upon heated metal, will be most rapidly vaporized when the metal is at least 200° below a red heat. 5th. While a red heat, visible in daylight, given to a metal, even when very thick, and supplied by heat from a glowing charcoal fire, does not prevent water, when thrown in considerable quantities, from cooling it down so as to vaporize the water very rapidly, it is much above the temperature at which the water thrown upon the metal will be most rapidly evaporated. Thus one ounce of water was vaporized in thirteen seconds, at about 550°, in a wrought iron bowl one-fourth of an inch thick, and required 115 seconds to vaporize in a cast iron bowl one-half an inch thick, at a red heat. Four ounces in the latter bowl vaporized in about 300 seconds, the bowl being red hot when it was introduced; and two ounces vaporized in thirty-four seconds at 600° Fah. 6th. The temperature of greatest vaporization, with a given thickness of metal, is lower in copper than in iron, the repulsive force being developed at a lower temperature. With equal thicknesses of iron and copper, the vaporizing power of the latter metal, at its maximum, was, with the oil bath, one-third greater than that of the former, and with the tin bath the power of copper .07 of an inch thick, was equal nearly, to that of iron, one-fourth of an inch thick, each being taken at its maximum of vaporization, for the different quantities of fluid employed. As the maxima for the iron are higher than those for the copper the advantage will be still greater in favor of copper when the two metals are at equal temperatures. 7th. The general effect of roughness of surface is to raise the temperature at which the maximum vaporization occurs, and to diminish the time of vaporization of a given quantity of water at an assumed temperature below the maximum. 8th. Though it has been shown that water thrown upon red hot metal is adequate to produce explosive steam, even when it does not cool the metal down to the temperature of most rapid vaporization, it is not the less true that metal more than two hundred degrees below a red heat, in the dark, is in the condition to produce even a more rapid vaporization of water thrown upon it, than when red hot. We thus acquire a certainty of this remarkable fact, that a boiler may be in a more dangerous condition; (that is, in a condition more fit to produce suddenly highly elastic steam,) when below a red heat, from water thrown upon the metal, than even when the danger shows itself by the luminousness of the metal. Although, as we have seen, explosion may be produced at a red heat. We are by all this plainly directed to the necessity for keeping up the supply of water in a boiler. A keen interest is excited as to the means of ascertaining this level. The necessity for methods of showing when the metal of the boiler becomes hot, before it has reached the point when it be comes dangerously so, is clearly proved. All these important practical matters the reader will find treated of, in the report from which I have drawn the materials of these essays. But to return to the theory of Mr. Perkins. We have followed up two of his positions, and have now arrived at the third. "The third and less frequent kind, [of explosion] although most terrific, is undoubtedly caused by an explosive mixture having been formed in the boiler." This "third kind" I propose to examine by the same light which has enabled us to separate truth from error in the first and second. Physical Science. D. Communication of a formula for facilitating the reduction of observations of the solar eclipse of May 15th, 1836. By S. C. WALKer. TO THE COMMITTEE ON PUBLICATIONS. GENTLEMEN: The formulæ communicated by me in the April number of the Journal, were intended for announcing the time of the principal phases VOL. XVIII.-No. 2.-AUGUST, 1836. 9 parts of the boiler. The problem is in some sort indeterminate. This has been pointed out in the report of the committee on explosions, and experiments have been devised by using different modes of applying heat, to give an idea of the true state of the case.' * They began by showing the early development of a repulsion in the heated metal, tending to diminish the vaporization of water, taking place when the quantity of water is too small to cool down the metal, at a lower temperature in copper than in iron, in a clean surface of metal than in one which is oxidated. This repulsion, preventing the effect of the increased difference of temperature in the metal, and the water to be vaporized produces a maximum in the vaporizing power of the metal. The vaporizing power of different metals at their maximum is different, being greater in copper than in iron, nearly in the ratio of the conducting powers of the metals. An important practical conclusion where the heat of the metal is kept up, as the temperature of greatest vaporization lies below that of our high pressure engines.† By increasing the water, from drops to as great a quantity as the bowls, used in the experiments, would contain, and varying the circumstances by communicating heat to the metal through oil, and through tin, the Committee proceeded to examine the question now before us. While the quantities of water were small, great regularity appeared in the results, permitting a calculation of the temperature of greatest vaporization from results below that temperature. The general conclusions are stated briefly thus:§ 1st. The vaporizing power of copper, when supplied with heat, by a bad conductor or circulator, such as oil, increases with great regularity as the temperature increases, up to a certain point, the water being supposed thrown upon the copper surface, in small quantities. Copper flues, heated by air passing through them, would be in this condition if left bare of water, and then suddenly wet. This holds with copper onesixteenth of an inch thick, without indication that a limit will be attained by a much more considerable thickness. The temperature at which the metal will have the greatest vaporizing power, is about 570° Fah., or about 230° below redness, according to Daniell. The law of vaporization of small quantities of water, by a given thickness of copper, is represented with singular closeness by an ellipse, of which the temperatures represent the abscissæ, and the times of vaporization the difference between a constant quantity and the ordinates. 2d. The same power in thin iron, .04 inch thick, increased regularly, and was at a maximum, probably, at 510°. With thicker metal the power increases more rapidly at the lower temperatures, and varies very little, comparatively, above 380°, with thicknesses exceeding one-eighth, and less than one-fourth of an inch; attain. ing a maximum at about 507° Fah., when the quantities are small; rising to 550°, and much above, as the quantity of water is increased relatively to the surface of the metal which is exposed. Quadrupling the quantity of water, the entire amount being still small, nearly tripled the time of vaporization at the maximum. 3d. When copper of one-sixteenth of an inch in thickness, was supplied with heat by melted tin, a worse conductor, and having a lower specific heat than copper itself, the time of vaporization, in a spherical bowl, of quantities varying from one-sixteenth to one-half of the entire capacity of the bowl, increased but three-fold, and the temperature of greatest evaporation was raised by 56°, or from 470° to 526°. When the bowl had half of the portion which was exposed to heat filled, the weight of the water was about one and one-tenth of that of the metal. 4th. The times of vaporization of different quantities of water, varying from oneeighth of an ounce to two ounces, in an iron bowl one-fourth of an inch thick, and sup plied with heat by the tin bath, were sensibly, as the square roots of the quantities, at the temperatures of maximum vaporization for each quantity. * Jour. Frank. Inst. vol. XVII. p. 152. † Ibid. See p. p. 150, 151. These temperatures were raised from about 460° to 600°, by increasing the weight of water about sixteen times, indicating that considerable quantities of water, thrown upon heated metal, will be most rapidly vaporized when the metal is at least 200° below a red heat. 5th. While a red heat, visible in daylight, given to a metal, even when very thick, and supplied by heat from a glowing charcoal fire, does not prevent water, when thrown in considerable quantities, from cooling it down so as to vaporize the water very rapidly, it is much above the temperature at which the water thrown upon the metal will be most rapidly evaporated. Thus one ounce of water was vaporized in thirteen seconds, at about 550°, in a wrought iron bowl one-fourth of an inch thick, and required 115 seconds to vaporize in a cast iron bowl one-half an inch thick, at a red heat. Four ounces in the latter bowl vaporized in about 300 seconds, the bowl being red hot when it was introduced; and two ounces vaporized in thirty-four seconds at 600° Fah. 6th. The temperature of greatest vaporization, with a given thickness of metal, is lower in copper than in iron, the repulsive force being developed at a lower temperature. With equal thicknesses of iron and copper, the vaporizing power of the latter metal, at its maximum, was, with the oil bath, one-third greater than that of the former, and with the tin bath the power of copper .07 of an inch thick, was equal nearly, to that of iron, one-fourth of an inch thick, each being taken at its maximum of vaporization, for the different quantities of fluid employed. As the maxima for the iron are higher than those for the copper the advantage will be still greater in favor of copper when the two metals are at equal temperatures. 7th. The general effect of roughness of surface is to raise the temperature at which the maximum vaporization occurs, and to diminish the time of vaporization of a given quantity of water at an assumed temperature below the maximum. 8th. Though it has been shown that water thrown upon red hot metal is adequate to produce explosive steam, even when it does not cool the metal down to the temperature of most rapid vaporization, it is not the less true that metal more than two hundred degrees below a red heat, in the dark, is in the condition to produce even a more rapid vaporization of water thrown upon it, than when red hot. We thus acquire a certainty of this remarkable fact, that a boiler may be in a more dangerous condition; (that is, in a condition more fit to produce suddenly highly elastic steam,) when below a red heat, from water thrown upon the metal, than even when the danger shows itself by the luminousness of the metal. Although, as we have seen, explosion may be produced at a red heat. We are by all this plainly directed to the necessity for keeping up the supply of water in a boiler. A keen interest is excited as to the means of ascertaining this level. The necessity for methods of showing when the metal of the boiler becomes hot, before it has reached the point when it be comes dangerously so, is clearly proved. All these important practical matters the reader will find treated of, in the report from which I have drawn the materials of these essays. "The third and less But to return to the theory of Mr. Perkins. We have followed up two of his positions, and have now arrived at the third. frequent kind, [of explosion] although most terrific, is undoubtedly caused. by an explosive mixture having been formed in the boiler." This "third kind" I propose to examine by the same light which has enabled us to separate truth from error in the first and second. Physical Science. D. Communication of a formula for facilitating the reduction of observations of the solar eclipse of May 15th, 1836. By S. C. WALker. TO THE COMMITTEE ON PUBLICATIONS. GENTLEMEN: The formulæ communicated by me in the April number of the Journal, were intended for announcing the time of the principal phases VOL. XVIII.-No. 2.-AUGUST, 1836. 9 of the solar eclipse of May 15. By applying a correction derived from observations made under a known meridian, they may be used for determining the longitude of places at which it was observed, when not too far distant from Philadelphia, for which place alone, they are strictly correct. The error of the middle time of the eclipse, as deduced from the formula, amounts to one second of time for New York and Albany, to two seconds for Baltimore and Washington, and to eight seconds for Boston and the University. of Virginia. By applying to the middle time by the formula, a correction depending upon the first and second powers of the difference of longitude from Philadelphia, results may be obtained, in which the greatest variation from a rigorous computation for the above places, will in no instance exceed 0.6 sec., and in which the average discrepancy will not exceed 0.4 sec. In the former communication it was omitted to mention that 7, denotes the geocentric latitude of the place for which the computation is made. Retaining the same notation and constants as before, we have for the resulting longitude of the place of observation from Greenwich, +East-West λ = · A+B+C Where, } A=x' + x + {M—M' } — [8.8557] { D— D' } 2 B = [4.9781] {5 h. Om 40s. + A- [7.1701] {5h. Om. 40s. +A C = − } {A+B—~'} In these equations a' Assumed longitude from Greenwich, in seconds of time. M = Local mean time of middle, observed. Duration, observed, D'= do. computed, computed by formula. X A correction for the errors of the tables. The unknown quantity x, is the mean of the times at beginning and end, in which the moon by its apparent motion, traverses a space equal to the tabular error on its true orbit, projected upon its apparent orbit. No material error will arise from assuming x, as constant for the limits to which this formula extends. Of the extent to which it may be used, an opinion may be formed from the following table, in which the middle time M' + B derived from it, is compared with the rigorous computations for several places in the American Almanac. The determination of x, requires observations under known meridians. This eclipse having been visible at European observatories, the value of x, will admit of accurate computation. If we assume the longitude of Independence Hall, Philadelphia, at 5h. Om. 40s. west from Greenwich, we shall have, after correcting for the small differences of longitude of several places of observation in Philadelphia, the following values of x, By the observations of R. M. Patterson, M. D. x= - 11.15 sec. As an application of the formula, let it be required to deduce the longitude of the Capitol at Washington, from the observations of F. R. Hassler, Esq. Latitude 38° 52′ 54." Beginning observed 6h. 53m. 58s. End at 9h. 20m. 8s., A. M. Mean time. Computation of the longitude of the Capitol. 1st. Approximation. 2d Approximation. Similar computations from John Gummere's observations, give the longitude of Haverford School. |