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  The determination of the density of a liquid by weighing a plummet in air, and in the standard and experimental liquids, has been put into a very convenient laboratory form by means of the apparatus known as a Westphal balance (fig. 8). It consists of a steelyard mounted on a fulcrum; one arm carries at its extremity a heavy bob and pointer, the latter moving along a scale affixed to the stand and serving to indicate when the beam is in its standard position. The other arm is graduated in ten divisions and carries riders—bent pieces of wire of determined weights—and at its extremity a hook from which the glass plummet is suspended. To complete the apparatus there is a glass jar which serves to hold the liquid experimented with. The apparatus is so designed that when the plummet is suspended in air, the index of the beam is at the zero of the scale; if this be not so, then it is adjusted by a levelling screw. The plummet is now placed in distilled water at 15°, and the beam brought to equilibrium by means of a rider, which we shall call 1, hung on a hook; other riders are provided, th and th respectively of 1. To determine the density of any liquid it is only necessary to suspend the plummet in the liquid, and to bring the beam to its normal position by means of the riders; the relative density is read off directly from the riders.

3. Methods depending on the free suspension of the solid in a liquid of the same density have been especially studied by Retgers and Gossner in view of their applicability to density determinations of crystals. Two typical forms are in use; in one a liquid is prepared in which the crystal freely swims, the density of the liquid being ascertained by the pycnometer or other methods; in the other a liquid of variable density, the so-called “diffusion column,” is prepared, and observation is made of the level at which the particle comes to rest. The first type is in commonest use; since both necessitate the use of dense liquids, a summary of the media of most value, with their essential properties, will be given.

Acetylene tetrabromide, C2H2Br4, which is very conveniently prepared by passing acetylene into cooled bromine, has a density of 3.001 at 6° C. It is highly convenient, since it is colourless, odourless, very stable and easily mobile. It may be diluted with benzene or toluene.

Methylene iodide, CH2I2, has a density of 3.33, and may be diluted with benzene. Introduced by Brauns in 1886, it was recommended by Retgers. Its advantages rest on its high density and mobility; its main disadvantages are its liability to decomposition, the originally colourless liquid becoming dark owing to the separation of iodine, and its high coefficient of expansion. Its density may be raised to 3.65 by dissolving iodoform and iodine in it.

Thoulet’s solution, an aqueous solution of potassium and mercuric iodides (potassium iodo-mercurate), introduced by Thoulet and subsequently investigated by V. Goldschmidt, has a density of 3.196 at 22.9°. It is almost colourless and has a small coefficient of expansion; its hygroscopic properties, its viscous character, and its action on the skin, however, militate against its use. A. Duboin (Compt. rend., 1905, p. 141) has investigated the solutions of mercuric iodide in other alkaline iodides; sodium iodo-mercurate solution has a density of 3.46 at 26°, and gives with an excess of water a dense precipitate of mercuric iodide, which dissolves without decomposition in alcohol; lithium iodo-mercurate solution has a density of 3.28 at 25.6°; and ammonium iodo-mercurate solution a density of 2.98 at 26°.

Rohrbach’s solution, an aqueous solution of barium and mercuric iodides, introduced by Carl Rohrbach, has a density of 3.588.

Klein’s solution, an aqueous solution of cadmium borotungstate, 2Cd(OH)2·B2O3·9WO3·16H2O, introduced by D. Klein, has a density up to 3.28. The salt melts in its water of crystallization at 75°, and the liquid thus obtained goes up to a density of 3.6. Silver-thallium nitrate, TlAg(NO3)2, introduced by Retgers, melts at 75° to form a clear liquid of density 4.8; it may be diluted with water.

The method of using these liquids is in all cases the same; a particle is dropped in; if it floats a diluent is added and the mixture well stirred. This is continued until the particle freely swims, and then the density of the mixture is determined by the ordinary methods (see ).

In the “diffusion column” method, a liquid column uniformly varying in density from about 3.3 to 1 is prepared by pouring a little methylene iodide into a long test tube and adding five times as much benzene. The tube is tightly corked to prevent evaporation, and allowed to stand for some hours. The density of the column at any level is determined by means of the areometrical beads proposed by Alexander Wilson (1714–1786), professor of astronomy at Glasgow University. These are hollow glass beads of variable density; they may be prepared by melting off pieces of very thin capillary tubing, and determining the density in each case by the method just previously described. To use the column, the experimental fragment is introduced, when it takes up a definite position. By successive trials two beads, of known density, say d1, d2, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube. If the bead of density d1 be at the distance l1 above the crystal, and that of d2 at l2 below, it is obvious that if the density of the column varies uniformly, then the density of the test crystal is (d1l2 + d2l1)/(l1 + l2).

Acting on a principle quite different from any previously discussed is the capillary hydrometer or staktometer of Brewster, which is based upon the difference in the surface tension and density of pure water, and of mixtures of alcohol and water in varying proportions.

If a drop of water be allowed to form at the extremity of a fine tube, it will go on increasing until its weight overcomes the surface tension by which it clings to the tube, and then it will fall. Hence any impurity which diminishes the surface tension of the water will diminish the size of the drop (unless the density is proportionately diminished). According to Quincke, the surface tension of pure water in contact with air at 20° C. is 81 dynes per linear centimetre, while that of alcohol is only 25.5 dynes; and a small percentage of alcohol produces much more than a proportional decrease in the surface tension when added to pure water. The capillary hydrometer consists simply of a small pipette with a bulb in the middle of the stem, the pipette terminating in a very fine capillary point. The instrument being filled with distilled water, the number of drops required to empty the bulb and portions of the stem between two marks m and n (fig. 9) on the latter is carefully counted, and the experiments repeated at different temperatures. The pipette having been carefully dried, the process is repeated with pure alcohol or with proof spirits, and the strength of any admixture of water and spirits is determined from the corresponding number of drops, but the formula generally given is not based upon sound data. Sir David Brewster found with one of these instruments that the number of drops of pure water was 734, while of proof spirit, sp. gr. 920, the number was 2117.

—Density and density determinations are discussed in all works on practical physics; reference may be made to B. Stewart and W. W. Haldane Gee, Practical Physics, vol. i. (1901); Kohlrausch, Practical Physics; Ostwald, Physico-Chemical Measurements. The density of gases is treated in M. W. Travers, The Experimental Study of Gases (1901); and vapour density determinations in Lassar-Cohn’s Arbeitsmethoden für organisch-chemische Laboratorien (1901), and Manual of Organic Chemistry (1896), and in H. Biltz, Practical Methods for determining Molecular Weights (1899).

 DENTATUS, MANIUS CURIUS, Roman general, conqueror of the Samnites and Pyrrhus, king of Epirus, was born of humble parents, and was possibly of Sabine origin. He is said to have been called Dentatus because he was born with his teeth already grown (Pliny, Nat. Hist. vii. 15). Except that he was tribune of the people, nothing certain is known of him until his first consulship in 290 when, in conjunction with his colleague P. Cornelius Rufinus, he gained a decisive victory over the Samnites, which put an end to a war that had lasted fifty years. He also reduced the revolted Sabines to submission; a large portion of their territory was distributed among the Roman citizens, and the most important towns received the citizenship without the right of voting for magistrates (civitas sine suffragio). With the proceeds of the spoils of the war Dentatus cut an artificial channel to carry off the waters of Lake Velinus, so as to drain the valley of Reate. In 275, after Pyrrhus had returned from Sicily to Italy, Dentatus (again consul) took the field against him. The decisive engagement took place near Beneventum in the Campi Arusini, and resulted in the total defeat of Pyrrhus. Dentatus celebrated a magnificent triumph, in which for the first time a number of captured elephants were exhibited. Dentatus was consul for the third time in 274, when he finally crushed the Lucanians and Samnites, and censor in 272. In the latter capacity he began to build an aqueduct to carry the waters of the Anio into the city, but died (270) before its completion. Dentatus was looked upon as a model of old Roman simplicity and frugality. According to the well-known anecdote, when the Samnites sent ambassadors with costly presents to induce him to exercise his influence on their behalf in the senate, they found