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. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. the first. If we repeat the same manipulation a suitable number of times, we shall ultimately obtain the cylinder of the greatest height which our apparatus permits. I have in this manner obtained a perfectly cylindrical mass 7 cen- timeters in diameter, and about 14 centimeters in height, (Fig. 23.) To allow of the cylinder of this considerable height being perfect, it is requisite that per- fect equality be established between the densiti

. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. the first. If we repeat the same manipulation a suitable number of times, we shall ultimately obtain the cylinder of the greatest height which our apparatus permits. I have in this manner obtained a perfectly cylindrical mass 7 cen- timeters in diameter, and about 14 centimeters in height, (Fig. 23.) To allow of the cylinder of this considerable height being perfect, it is requisite that per- fect equality be established between the densiti Stock Photo
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Library Book Collection / Alamy Stock Photo

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RM5JDC

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7.1 MB (291.8 KB Compressed download)

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1129 x 2212 px | 19.1 x 37.5 cm | 7.5 x 14.7 inches | 150dpi

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. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. the first. If we repeat the same manipulation a suitable number of times, we shall ultimately obtain the cylinder of the greatest height which our apparatus permits. I have in this manner obtained a perfectly cylindrical mass 7 cen- timeters in diameter, and about 14 centimeters in height, (Fig. 23.) To allow of the cylinder of this considerable height being perfect, it is requisite that per- fect equality be established between the densities of the oil and the alcoholic liquid. As a very slight diflFerence in either direction tends to make the mass ascend or descend, the latter assumes, to a more or less marked extent, one of the two forms represented in Fig. 24. Even when the cylindric form has been obtained by the proper addition of alcohol of 16°, or absolute alcohol, as occa- sion may require, (§ 24 of the preceding memoir,) slight changes in tempera- ture are sufficient to alter and reproduce one of the above two forms. 39. Let us now examine the results of these experiments in a theoretical point of view. First, it is evident that a cylindrical surface satisfies the general condition of equilibrium of liquid figures, because the curvatures in it are the same at every point. Moreover, such a surface being convex in every direction except in that of the meridional line, where there is no curvature, the pressure corresponding to it ought to be greater than that corresponding to a plane sur- face. The same conclusions are deducible from the general formulte (2) and (3) of paragraphs 4 and 5. In fact, as we have already stated in paragraph 37, one of the quantities R and R' is the radius of curvature of the meridional line, and the other is the portion of the normal to this line included between the point under consideration and the axis of revolution. Now, in the case of the cylinder, the meridional line bei

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