Log.
30 =.011857X. A + 2 Az (A)Two values in the table answering to given indices, F 9 are sufficient for finding A and AI; but on account of the irregularities of observation, it will be better to proceed as follows: Form the expressions of the seven quotients in the table corresponding to the indices 1, 2, 3-7, and take a mean of the whole; thus .010198 -=.011857 4 A + 8 In like manner, form the expressions of the four last quotients, and take a mean; thus, 23 .007842 =.011857 A + 61 By means of these two equations we get A =.0004545 and = 00001986, and by these values e Log.
30 of A and the values of and of c are com puted by the formula A, and inserted in columns 8 and 9. Thus to find c for temperature 130° and index 4 e Log.
30 we have t = 82° and 820 = .010158 whence ,og. = 0.8329 = 1 + .1671, then 1.1671 Log. 30 1.4771 Log. e 0.6442, e = 4.408. In this ,vay all the elasticities in col. 9. have been calculated, ind their agreement with the experimental quantities s very striking, so that the formula A may be con >idered as representing the elasticities as exactly as :ould be wished.
In reducing the formula to a proper form for use, NIr. Ivory proceeds thus, substituting the values of A and and arranging the terms according to the powers of x. Thus Log.
30 .= .011857.00046.143 x + .00000993 . 50 162 + t But x 20 20 wherefore by substituting, Logarithms of coefficients.
Log. = .0087466 t - - - - 3.9418393 30 .000015178 - - - 5.1812202 (B) + .000000024825 - - 8.3871228.
At 32°. f = 180° and c, comes out 0.185, very near 0.2, Dr. Ure's result. Hence the formula (13) is nearly exact for the range of Dr. Ure's experiments.
Mr. Ivory then proceeds to apply this formula to two experiments, at temperatures of and 419°, made by Mr. Southern and Mr. Clement. He finds that at it gives the elasticity 26.1 inches, vvhich is 24 inches above Mr. Southern's result; but at 419° the formula gives only 23.8 atmospheres in place of 35 atmospheres, as determined by Mr. Clement. formula therefore," says Mr. Ivory, "although it is very accurate for a long range of temperatures, finally digresses altogether from the truth." Mr. Ivory led to the important result that the quotient e Log. 30 decreases to a minimum, and then increases again, not only in the formula, but in nature. For example, in Clement's experiment, where 1 :=207, we have 35 207 = 007454, but in the table we find .007454 in the column of quotients opposite 310°; consequently, while the temperature increases from 310° to 419°, the quotient must have decreased to a minimum, and then increased again to its first mag nitude. Hence Mr. Ivory concludes that the mini mum takes place at or about 152° or 153° be yond the boiling point.
Mr. Ivory concludes by stating, that the quotient is represented by the square of the ordinate to the conjugate axis of a hyperbola, the square of the semi transverse axis being the minimum, for the expres e Log.
30sion B becomes 1_A B (n A and B being known numbers, and n the distance of the minimum from the boiling point.
The expansive power of steam had been hitherto examined and used only at moderate temperatures, till Mr. Oliver Evans of Philadelphia, and Mr. Jacob Perkins, conceived the idea that great advantage would be gained by using steam of a high expansive force. When I reflected," says Mr. Perkins, " on the almost infinite power that is sometimes displayed in the eruptions of Mount Vesuvius, throwing up incalculable masses of matter into the very clouds, I was induced to consider how this immense power could be generated. How is it that this power is so
wonderfully great? Is it not high elastic steam? The thought struck me that it must be owing to the water being confined by pressure, until it got sufficiently charged with heat to enable it to rend asunder what ever confined it, thereby driving every thing before it. If one wanted farther proof of the tremendous power of steam, we have only to inquire of many practical iron founders what it is which has some times caused the liquid iron to leave its mould, and pass off through the roof of the foundry, in a metal lic shower. The answer would be, that a small quan tity of water had accidentally found its way into the bottom of the mould; and it might also be added, that a thousand times that quantity thrown on its heated surface would be perfectly harmless." These considerations led Mr. Perkins to make a number of experiments on the elastic force of steam generated at very high temperatures, with the view of improving the high pressure engine. Ile has ap plied degrees of temperature so great, that the water in the boiler or gasometer was brought to a red heat. lie has not, we believe, completed any regular series of experiments on the elastic force of steam generated with such enormous heat; but he considers the obser vations which he has made as leading to the following while the temperature rb;CS in an arith metical ratio. the expansive force 2011 be that of an in creasing ratio, and the increments of fuel will be a de creasing ratio.
During these experiments, Mr. Perkins had occa sion to observe the very curious phenomenon that steam generated at such high temperatures produced no scalding effect. " I have frequently observed," says he, " that when the slop-cock of a high pressure boiler was opened, whether at the water or steam cocks, the temperature W as lowered in proportion to the height of the steam. In a recent experiment on high steam it occurred to me that the great force and rapidity of motion of the steam caused the atmos pheric air to be driven before it, evidently tending to produce a partial vacuum, to which the surrounding atmosphere would rush in and diminish its tempera ture. To test this theory, the following contrivance was resorted to: 1 took a vessel containing heated water of a temperature of 420 degrees of Fahrenheit; a tube eight inches in diameter. and four feet in length, and open at both ends, was suspended immediately over the stop-cocks, and in such a manner as to be raised or lowered at pleasure. This tube was raised eight inches above the stop-cock; the stop-cock, the area of which was one-fourth of an inch, was then opened, and the steam rushed out with great velocity into and through the tube. It was observed, that the steam condensed rapidly on the inside as well as the outside of it. The tube was lowered directly over the stop-cock, and when it came in contact with the vessel, it allowed very little air to find its way between it and the tube. The condensed steam in the tube immediately evaporated, and the tube soon became too hot for the touch of the hand; and when the ther mometer was inserted eight or ten inches into the upper end of the tube, it indicated 230 degrees of temperature. The tube was again raised to about the same height, and immediately the condensation commenced as before.