VOL. I.XXXII.] PHILOSOPHICAL TRANSACTIONS. 271 



fully as much accuracy as can be required; of their preference in other respects, 

 the practical officers who are to use them will probably be found the best judges. 

 That which can be managed with the greatest facility and quickness, which af- 

 fords the least opportunity of making blunders, which is least liable to be out of 

 order, and shows most immediately if it be so, will unquestionably prove the 

 most satisfactory in practice. Hydrometers having a thermometer inclosed-within 

 them must be condemned, as not ascertaining the temperature with the requisite 

 precision. An attempt to supersede the use of the thermometer, by employing 

 for the hydrometer, a substance which " has the same degree of expansion as 

 the mean of the compounds," is very inconsistent with the kind of accuracy 

 sought by these experiments. 



As an allowance is made, in our table of specific gravities, for the expansion 

 and contraction of the glass weighing-bottle, this must be taken into the ac- 

 count, with every areometer, whenever much exactness is desired. 



I am still of opinion, that the best way of laying the duty, would be directly 

 on the quantity of alcohol contained in any composition ; and though this might 

 require too great a change in the present system of laws, yet as the same prin- 

 ciple may be applied in estimating the strength, and taking stock, I will just 

 mention in what manner the computation can be most readily made. From the 

 numbers in this supplementary report a table must be constructed, on the top 

 of which shall stand every degree of heat from 40, or 30, to 80, and at the side 

 every specific gravity from .825 to ] .000, if it be thought necessary, or as much 

 less as will answer the purpose. The places of this table are to be filled up, by 

 computing, from the original tables, the quantity by measure of alcohol and 

 water corresponding to each specific gravity and degree of heat; and then divid- 

 ing the quantity of alcohol by the whole quantity of the mixture; thus a decimal 

 multiplier will be obtained, which must be put in the compartment of the table 

 formed by the intersection of the columns of that particular heat and specific 

 gravity. When the table is completed in this manner, we have only to multiply 

 the contents of any cask, as found on gauging it, by the decimal number given 

 in the table for the heat and specific gravity of the liquor, and the product will 

 be the quantity of pure alcohol it contains. Hence it must be evident, that no 

 objection can lie to this method on account of difficulty; if however it be thought 

 more eligible, for different reasons, to adopt the proportion of alcohol per cent., 

 the relation of strength to the point of proof, or any other method, the numbers 

 in this report will equally apply to all, with the proper variation in the table to 

 be employed. 



As to the calculation necessary for constructing the table of decimal multipliers, 

 what has been already said with respect to the reduction of the harmonic num- 

 bers applies also to it. The labour of the whole will not be very great, and it is 



