For temperatures above the boiling point, the part of' the syphon under E is evidently superfluous, mere ly containing in its two legs a useless weight of equi poise mercury. Accordingly, for high heats, the ap paratus, Figs. 2 or 3 is employed, and the same method of' procedure is adopted. The apertures at 0, Fig. 3, admits the ball of the thermometer, which rests as usual on 1." The recurved part of the tube is filled with mercury, and then a little liquid is passed through it to the scaled end. Heat is now applied by an argand flame to the bottom of C, which is tilled with oil or water, and the temperature is kept steadily at 212° for some minutes. Then a few drops of quicksilver may require to be added to D" till L" and /" be in the same horizontal plane. The further conduct of the experiment differs in no respect from what has been already described. The liquid at C is progressively added over L" to restore the initial level or volume at /", by equipoising the progressive elasticity. The column above L" being measured, represents the succession of elastic forces. When this column is wished to extend very high, the verti cal tube requires to be placed for support in the groove of a long wooden prism.
The height of the column in some of the experi ments being scarcely twelve feet. it became necessary to employ a ladder to reach its top. It was found to be convenient in this case, after observing that the column of vapour had attained its primitive magni tude, to note down the temperature with the altitude of the column, then immediately to pour in a mea sured quantity of mercury, nearly equal to three ver tical inches, and to wait till the slow progress of the heating again brought the vapourinequllibrio with this new pressure, which at first had pushed the mercury within the plating ring at /". When the lower sur face of the mercury was again a tangent to this ring, the temperature and altitude were both instantly ob served. This mode of conducting the process will account for the experimental temperature being very often odd and fractional numbers. They are, there fore, presented to the public as they were recorded on the instant.
The thermometers were constructed by Creighton with his well known nicety; and the divisions were read off with a lens, so that one-sixteenth of a degree could be distinguished. After bestowing the utmost pains in repeating the experiments during a period of nearly two months, it Was found that the only way of removing the little discrepancies which crept in be tween contiguous measures, was to adopt the astro nomical plan of multiplying observations, and deduc ing truth from the mean. It is essential to heat with
extreme slowness and circumspection the vessels A, B, C. One repetition of the experiment occupies, on an average, seven hours." The next experiments on the elasticity of steam, were those of Mr. Philip Taylor, at temperatures from to 320°. The results which he obtained, are given in the following table.
Most of the philosophers who have investigated the elastic force of steam, have endeavoured to con struct empirical commix, for representing the rela tion between the temperatures and the elastic forces. It would be a waste of time to reprint and to explain these formula, as they are of little service when we possess the experimental results.
Our distinguished countryman, however, Mr. Ivory, has recently investigated a numerical formula, with the view of finding some property or law which may give us some general information respecting the elas ticities beyond the range of our experiments. For this purpose he makes Dr. Ure's experiments the ground work of the following table:— In the above table, col. 2, marked T denotes the temperatures beginning at 50°, and increasing by as far as Dr. Ure's table carries us. In col. 1. are the indices x, or the number of intervals of Hence we have for any temperature the correspond ing index.
— 50 20 The third column contains the elasticities e as found by Dr. Ure, and then follow in column fourth, the logarithms of the same elasticities estimated in parts of an atmosphere of 30 inches. Column fifth con tains the temperatures, reckoned from the boiling point, those below it being negative, and those above it positive. Column sixth is the quotient of column fourth divided by column fifth. These quotients are irregular, near because as — approaches to uni ty, its log. varying rapidly with any variation of e, the errors of observation have a great influence in this part of the table. It is remarkable that the num bers in this column continually decrease, and it would be interesting to determine if they would decrease to a fixed limit, or if they would decrease to a minimum and then increase again. Column seventh contains the differences in these quotients which are extremely irregular, and which, taken directly, seem to furnish no guide us in our present research. But as they decrease slowly, we may infer that the quotients may be expressed with tolerable accuracy by means of the first and second orders of differences. If we represent the first and second differences by A and we have the following general expression of the quo tient corresponding to the index x.