The instrument is provided with a sliding rule, with scales corresponding to the several weights, which indicate the specific gravity corresponding to the several divisions of the hydrometer scale compared with water at 55° F. The slider upon the rule serves to adjust the scale for different temperatures, and then indicates the strength of the spirit in percentages over or under proof. The slider is also provided with scales, marked respectively Dicas and Clarke, which serve to show the readings which would have been obtained had the instruments of those makers been employed. The line on the scale marked "concentration" indicates the diminution in volume consequent upon reducing the sample to proof strength (if it is _over proof_, O.P.) or upon reducing proof spirit to the strength of the sample (if it is _under proof_, U.P.). By applying the several weights in succession in addition to No. 4 the instrument can be employed for liquids heavier than water; and graduations on the other three sides of the stem, together with an additional slide rule, adapt the instrument for the determination of the strength of worts. Atkins subsequently modified the instrument (_Nicholson's Journal_, 8vo, iii. 50) by constructing the different weights of different shapes, viz. circular, square, triangular and pentagonal, instead of numbering them 1, 2, 3 and 4 respectively, a figure of the weight being stamped on the sliding rule opposite to every letter in the series to which it belongs, thus diminishing the probability of mistakes. He also replaced the letters on the stem by the corresponding specific gravities referred to water as unity. Further information concerning these instruments and the state of hydrometry in 1803 will be found in Atkins's pamphlet _On the Relation between the Specific Gravities and the Strength of Spirituous Liquors_ (1803); or _Phil. Mag._ xvi. 26-33, 205-212, 305-312; xvii. 204-210 and 329-341. In Gay-Lussac's alcoholometer the scale is divided into 100 parts corresponding to the presence of 1, 2, ... % by volume of alcohol at 15° C., the highest division of the scale corresponding to the purest alcohol he could obtain (density .7947) and the lowest division corresponding to pure water. A table provides the necessary corrections for other temperatures. Tralles's hydrometer differs from Gay-Lussac's only in being graduated at 4° C. instead of 15° C., and taking alcohol of density .7939 at 15.5° C. for pure alcohol instead of .7947 as taken by Gay-Lussac (Keene's _Handbook of Hydrometry_). In Beck's hydrometer the zero of the scale corresponds to density 1.000 and the division 30 to density .850, and equal divisions on the scale are continued as far as is required in both directions. [Illustration: FIG. 8.--Sike's Hydrometer.]