the several liquids examined. The expansions being expressed by formulæ of the form V=1+at+bt2 + ct3 in which t denotes the temperature, and a, b, c are constants to be determined by observation for each particular liquid,—the true coefficients for each temperature are calculated by the formula It will be seen from this table (1) that for all the above liquids, both the mean and true coefficients of expansion increase with the temperature; (2) that for temperatures above 0° the true coefficient is greater than the mean, whereas below 0° it is less; (3) that the true coefficient increases more rapidly than the mean. In the following table, the volume of the liquids at their boiling point is taken for unity, and the changes of volume are given for all the liquids at equal distances from their boiling points. At the head of each column is given the boiling point of the liquid, together with the barometric pressure at the time of observation.-The results detailed in this table are of especial importance in connection with the equivalent volumes of the several liquids; since, according to Kopp and Schröder, the equivalent volumes of liquids should be compared at temperatures equally distant from their boiling points. Number of degrees Wood-spirit Alcohol below boiling B. P. 66.3° point. B. P. 59-5° B. P. 78.3° B. P. 131-80 B. P. 74-14° B. P. 102-10 (bar. 759mm), | (bar. 758mm). (bar.751-26mm)|(bar. 761·2mm). (bar. 766·5mm), (bar. 743·9mm). boiling B. P. 59-5° point. B. P. 78.3° B. P. 131-80 Acetic Butyrate of B. P. 102-10 of degrees below boiling Butyric Iodide of Iodide of Bromide of B. P. 70° B. P. 43.80 B. P. 13° B. P. 40.7° B. P. 1190 point. (bar.747-50mm (bar. 751-7mm). (bar. 750mm). (bar. 759mm). (bar. 757mm). Ether B. P. 11° (bar. 758mm). Number of degrees below boiling point. Chloride of Bromide of Chloride of Bromide of Bichloride Bichloride (bar.761-88mm) (bar. 756-9mm). (bar. 760·1mm). (bar. 760·1mm). (bar. 753·1mm).|(bar. 762-3mm). 0-917091 0.938579 0.945978 0.926407 0.952951 0.935553 0.944836 0.920327 0.948163 0.929760 0.939635 0.924067 0.934713 0.938680 0.918466 0.929664 0.924710 0.911907 0.921710 0.896944 0.929340 0.907530 0.919844 0.901715 0.912454 0.885427 0.920142 0-896918 0.910309 B. P. 175:30 B. P. 63° B. P. 80 B. P. 175-80 B. P. 78-34° B. P. 133-81° B. P. 63° 0.952975 0-937128 0.945611 0.944399 0-942637 B. P. 160-3° 60 65 0-944052 0-926248 0-935504 0.934406 0-931959 0-929562 0-926717 70 0.935288 0.915707 0.925638 0-924652 0-921537 It will be seen from these tables: I. That a nearly equal contraction from the boiling point downwards is exhibited by: (1). Fusel-oil, woodspirit and alcohol; (2). Bromide of ethyl and broinide of methyl; (3). Iodide of methyl and iodide of ethyl; (4). Acetic ether and acetic methyl-ether; (5). Butyric ether and butyric methyl-ether. II. That this equal contraction from the boiling point downwards does not extend to all groups of liquids containing a common element united with different isomorphous elements (e. g. chloride of phosphorus and chloride of arsenic), but appears to be confined to the ethyl and methyl series. III. That in each group of liquids the difference of contraction increases constantly in the same direction, in proportion as the temperature falls below the boiling point. IV. This difference of contraction attains in some cases a very considerable magnitude; e. g. in the group consisting of the bromide and chloride of silicium it amounts to half the total expansion of one of these liquids. V. In each group, the liquid which has the lowest boiling point expands and contracts the most. This observation must not however be extended to liquids belonging to different groups. Kopp has also published an elaborate series of researches on the expansion of liquids. (Pogg. 72, 1 and 223; abstr. Ann. Chem. Pharm. 64, 212.) The following are the results obtained with regard to the expansion of water, the volume at 0° being taken for unity. |