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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$From the densities the corresponding volumes, relatively to those ocfi pied at the temperature of 60° Fahr., were then found by the formula-]^ ‘ (C) V = v' ; )■ 1 in which v is the volume at 60°, d the density at 60°, d the volume)^ any given temperature, and d' the density at the same temperature, ’ Table VITI gives the results of the calculations just described, togel \yith the densities and volumes from 92 to 100 per cent.: for the expk tion of which, see § 5. ^ § 5. Table VIII comprises densities at every degree of tempera from 20° to 100°, inclusive, and for every per cent, of alcohol from 100. The per cents., from 1 to 92, at the various temperatures, were c puted from the data of Gilpin and Blagden, as already explained. T1 from 92 to 100 were obtained by means of Biot’s interpolating formulaj y = a bx cx'^ (D) in which y is the required density corresponding to any given tem_ ture X; and a, b, c are coefficients computed from the densities for e fifth degree of temperature, and for liquors of the respective strengf 87, 93, and 99 per cent. The densities of 87 per cent, we obtained from the data of Gilpin Blagden. Those of 93 per cent, were found by reduction from the t sides of 92.6 given in table III, above. For the exteqsion from 93 to 100 per cent, we have the experime 51 results of Gay Lussac, Delezemies, Tralles, Muncke, and myself, as 'ii forth in chapters I and II of iny fourth report, (Sen. Doc.'No. 50,: !• Congress, 1st session.) ■ Thcise of other observers were not employed .d reasons assigned in that report. The results of the observations b » reduced to a common scale, the density 0.79846 of 99 per cent. < lal hoi, at the temperature of 60° Fahr., as determined by myself, was fc loii to be identical with that obtained by Tralles for the same per cent, le temperature. This density we therefore assumed for that temperai rrai In order to obtain the densities of 99 per cent, alcohol at the different lal peratures, we found that the mean difference of the densities corresp ii ing to 55° and 60°, for all per cents, from 87 to 93, was 0.00236; w fiiiii difference decreased by the constant second difference 0 00002 for e 5^; 6° below 60°, and increased bjr the same above 60°, As this Btp( was true for per cents, between 87 and 93, it was pr*ovisionally assu ;of to be true for those from 93 to 100 per cent., and accordingly the den; for 99 per cent, in the table IX were computed. ' 4c( From the numbers of this table we obtained by formula D the inf lated results of table X. It remained to verify the interpolated densities of table X, by com i;.. sons with the observations of Gay Lussac, Delezennes, Tralles, Mui l^i and myself. iSj tij 6. From the data given on page 477 of Sen. Doc. No. 50,30th C( ijit 1st session, we deduced the comparison given in table XI betweei 5ir, observed results of Muncke for 100 per cent, alcohol and those of t|,j VIII obtained by interpolation. try, Similarly, the researches of M, Gay Lussac (see Sen. Doc. Nc fro„ 30th Cong., 1st session, page 481) furnish the basis of table XII. ^ Between the data of Tralles (Sen. Doc, No. 50, page 456) and the$