A report of the computation of tables, to be used with the hydrometer recently adopted for use in the United States custom-houses / made under the superintendence of A.D. Bache, by R.S. McCulloh.

Alexander Dallas Bache

Date:: 1851

Credit: A report of the computation of tables, to be used with the hydrometer recently adopted for use in the United States custom-houses / made under the superintendence of A.D. Bache, by R.S. McCulloh. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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$jorresp'mding density of the mixture, and d the specific gravity, 0.825, it60°Fahr. of the alcohol used by Gilpin and Blagden, water being |nity at that temperature. The results thus obtained were multiplied by the coefficient 0.026, to •feduce them to the standard adopted by Tralles; according to which, Gil- )in’s alcohol of 0.825 contains 92.6 per cent., and the specific gravity of Ibsolute alcohol is 0.7930, at 60° Fahr., the maximum density of water jeing unity. These results differed inconsiderably from those obtained |y reducing the per cents, by volume calculated by Gilpin and Blagden p the same standard, as will be observed by examination of table II. § 3. Having thus found the per cents, by volume, according to the standard of'I'rallesj the next step was to reduce the corresponding densi- '.es at the different temperatures to the scale of the maximum density of ^ater assumed as unity. These densities were then corrected for errors ;f mixture, weighing, &c., by the method of curves combined with that f least squares, resulting in very slight changes in the fifth place of deci- Lials, in no instance varying more than 0.00U04 from the original num- 'tic. (See curve diagrams Nos. II to V, annexed.) Using the corrected t !coud differences found by the curves, the densities were extended from I)° to 20°, and from 80° to 100° Fahr. We also attempted to correct for errors of temperature, (see curve i sagram lNo. YI;) but such similarity appeared in the fluctuations of the hirves, that it was deemed advisable not to make any alteration in this 'Spect, particularly as the final results would not be materially affected, is probable that the analogy observed in the curves arises from neglect the experimenters to make barometric observations when taking the • 'ecific gravities, or from some other constant source of error. The densities of water given by Gilpin and Blagden for temperatures i tween 30° and 80° Fahr. were likewise reduced, corrected for second i fferences, and extended from 30° to 20° by adopting Despretz’s data, ; ;d from 80° to 100° by means of second differences. (See table IV.) series of uneven or fractional per cents, from 0 to 92 6, and their cor- ••ponding densities for every fifth degree of temperature from 20° to 0° Fahr., were thus obtained. (See table III.) ^ 4. From the fundamental data contained in the last two tables we 131) obtained by interpolation every intermediate integral per cent, cor- , ponding to the density at each degree of temperature between the limits .20° and 100° Fahr. For this purpose various interpolating formulas retried, and it was found that the results obtained by carrying the iroximation to second differences were nearly identical to the fifth place iecimals with those given by simple proportion, as shown in table V. »Ve therefore computed by proportion all the densities corresponding even per cents, between 1 and 92, inclusive, for each degree of tem- r ature between 20° and 100°, using for this purpose the formula— X — x' x — x' familiar equation of a straight line passing through the points .r', t/ ■ ^'■) ]/'■) so arranged as to give the value of any density y, when any cent. X, intermediate to .v/, a/', is given. 'The calculations of the last ?i of the second member were performed by logarithms, to facilitate y = ’/ 4- iv” — V') ($