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made decimal parts of such weight), the total weight, required in each liquid, will at once indicate its Specific Gravity *.
This Instrument, though in its simple form most admirably adapted to scientific purposes, was found incompatible with the dispatch required in business, particularly in the use of the smaller weights, and a Scale of Divisions was introduced to represent them. This apparently inconsiderable change also introduced the error which has been hitherto considered an insurmountable impediment to the perfection of such an Instrument; a familiar description of this error will now be attempted.
The Instrument, when furnished with the Scale of Divisions, to enable it to act through a limited range of Specific Gravities, being transferred from one liquid into another of greater Specific Gravity without its weight being increased, could not sink so low: its previous application thus became reversed; it no longer determined the Specific Gravities of the liquids under trial by comparative weights of the same bulk or measure of them, but by the comparative bulks of the same weight + of such liquids; and as the bulk immersed diminished, the Divisions of the Scale, the values of which are always certain proportions of this bulk, necessarily diminished with it, and therefore no two Divisions, if accurate, could be of equal length in any part of the range of the Scale.
Again, each successive range of Scale, being required to express the same aliquot part of the Specific Gravity 1000, the additions of weight, equivalent to such range, successively required to sink the Scale to its first point or zero, again became the difference in the weight of equal bulks of the liquids; and being equal to one another, these equal weights or differences became less in proportion to the succeeding ranges of Specific Gravity ¦ ; therefore no two Scales, or equal number of Divisions, could be of equal length in any part of the range of the Instrument §.
* Some of these Instruments being lately made to displace exactly 1000 troy grains of pure water, their accompanying Weights have the advantage of being grains also; a very slender wire is used to receive the index point, by means of which the Instrument is rendered susceptible to the 100th part of a grain, which represents an unit in the fifth decimal place of figures.
+ All floating bodies sink till they have displaced their own weight of the liquids, and rest in a state of equilibrium.
¦ As 30, the common difference in the Saccharometer, becomes a less proportion of 1030 and 1060, of 1060 and 1090, &c, than of 1000 and 1030.
§ This may be exemplified by immersing an Hydrometer, or any such Instrument (which floats in water at a point marked near the top of the Stem), into liquor of 1030 Specific Gravity, and marking upon the Stem the new point, which rests, in the surface of the liquor; the placing it into