into the law connecting temperature with the pressure of steam. The commission consisted of the illustrious members of the Academy, Baron de Prony, Arago, Girard, and Dulong; and the results of their investigation, finished in 1829, are given in the tenth volume of the Memoirs of the Academy of Sciences, printed in 1831. These experiments, conducted principally by the MM. Arago and

Dulong, were on a scale of magnitude and expense suited to the munificence of the French government and the resources of the Academy. The precautions adopted to ensure minute accuracy, entitle them to confidence, no less

that it is impossible to obtain a glass tube of considerable length and magnitude which shall have a tolerably cylindrical interior; and that there are a number of practical difficulties, which render it impossible to obtain even such a tube as that of a common thermometer, which shall possess the uniformity necessary to a good instrument. To make the proper allowance for this inevitable imperfection, the academicians easily might have adopted the same method as that used in the case of thermometer tubes, by determining the volume of successive small portions of its interior; but even this would have furnished a very partial remedy for the evil, because it had not been ascertained that the space occupied by the air in the manometer would diminish in bulk exactly in the proportion of the increase of compressing force, or of the corresponding increase in the height of the equivalent column of mercury. problems were therefore to be resolved at once, the elimination of the error of the tube, and the determination of the elasticity of air under high pressures. Both of them were satisfactorily accomplished, by the following laborious research.

Two

As a preliminary measure, it was resolved to graduate the manometer, and determine the law of the elastic force of air under high pressures, by direct comparison with a column of mercury, from 75 to 80 feet in height. Such an experiment required a suitable locale and a stupendous apparatus. Among the buildings of the Royal College of Henri Quatre, there may be observed an old square tower, sole relic of the ancient church of Sainte Genevieve: there exist still in the interior three vaulted floors, pierced in the centre, and affording the very supports that were required for the erection of this stupendous mercurial gauge. In the

strument for measuring with precision the pressure of the fluid in the boiler, was observed to give very erroneous indications, and the necessity of a more delicate apparatus was demonstrated. The improved index of pressure, made use of in the experiments, is shown in fig. 18. For measuring the great pressures to be used, a tube of mercury, 80 feet high, would have been requisite; but there was used, as a substitute for it, a glass tube z z, closed at the upper end, filled with dry atmospheric air, and having a length of only five feet seven inches, and an internal diameter of of an inch, and of a thickness nearly equal to its diameter. It was so arranged as to furnish a convenient manometer, capable of giving the same indications, by the contraction of the contained air, as would have been given in similar circumstances, by a column of mercury of the height due to the diminished volume of the air. The graduation of this manometer, however, presented new difficulties.

These difficulties were successfully encountered by the skill and ardour of the academicians. Every one knows

that it is impossible to obtain a glass tube of considerable length and magnitude which shall have a tolerably cylindrical interior; and that there are a number of practical difficulties, which render it impossible to obtain even such a tube as that of a common thermometer, which shall possess the uniformity necessary to a good instrument. To make the proper allowance for this inevitable imperfection, the academicians easily might have adopted the same method as that used in the case of thermometer tubes, by determining the volume of successive small portions of its interior; but even this would have furnished a very partial remedy for the evil, because it had not been ascertained that the space occupied by the air in the manometer would diminish in bulk exactly in the proportion of the increase of compressing force, or of the corresponding increase in the height of the equivalent column of mercury. Two problems were therefore to be resolved at once, the elimination of the error of the tube, and the determination of the elasticity of air under high pressures. Both of them were satisfactorily accomplished, by the following laborious research.

As a preliminary measure, it was resolved to graduate the manometer, and determine the law of the elastic force of air under high pressures, by direct comparison with a column of mercury, from 75 to 80 feet in height. Such an experiment required a suitable locale and a stupendous apparatus. Among the buildings of the Royal College of Henri Quatre, there may be observed an old square tower, sole relic of the ancient church of Sainte Genevieve: there exist still in the interior three vaulted floors, pierced in the centre, and affording the very supports that were required for the erection of this stupendous mercurial gauge. In the

centre of this opening there was raised a squared tree of the required height, and to this it was determined to attach the glass tube of 80 feet in height. To form a single glass tube of so great a length was impossible: its own weight, when constructed, under the pressure of the mercury, would have endangered its existence. The glass column was built of separate portions, united in mastic, with great care, in viroles of steel. Each portion of tube was suspended in the air by an exact counterpoise, acting over pulleys fixed to the tree; and the whole of the parts were so united in equilibrio, that each sustained only its own weight, and the pressure of the mercury due to the height of the superior portion of the column. A homogeneous metallic scale was attached, and its divisions read by a vernier, as in the common barometer.

The manometer to be graduated, and this column of mercury, were both connected by tubes with a strong cylindrical vase ƒ, holding about 100 lbs. of mercury. When thus placed in communication, a column of water was forced into the vase above the mercury by a hydraulic pump, and the pressure thus produced raised the metal with equal force up into the glass-tube column on the one hand, and into the manometric tube on the other. The point to which the air was compressed was read off by a vernier, and the corresponding height of the mercury having been determined, it was manifest that the same degree of compression of the less instrument would ever after serve as the index of an equivalent column of mercury. In this manner the whole tube was graduated by careful experiment. The result of this graduation was satisfactory and very instructive. In forming the scale of the manometer, no room was left for errors of practical execution; and the

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