glycerine forms the medium through which mercury drops. In this case, when gt=5", there are always two supplementary drops of mercury formed. It is impossible to determine whether they both have their origin at the same moment and from the same drop. The probability, however, is that they have not, but that one is first separated from the main drop, and the second from the first; for there is always a great disparity between the sizes of the two supplementary drops, whereas, if they were both formed at the same time and for the same reason, we should be justified in expecting greater equality. The drops soon separate in falling, in consequence of the difference of their surfaces. The relative sizes of the main and sup. plementary drops in the case of mercury falling from copper through glycerine were determined as follows:-A number of porcelain cups (fig. 9) were arranged at the bottom of a shallow dish full of glycerine; when the rate of dropping was uniform at gt=4", the dish was shifted horizontally so that every drop with its two supplements was caught in a separate cup. The globules of mercury in each cup were removed by a little scoop of copper foil. Ten of each kind were collected. After washing and drying, they were weighed, with the following result : TABLE XIV.-Mercury. gt=4". T=21°3 C. Radius of sphere = 12.8 millims. grms. 6.3447 0.1242 .... do. do. 0.0229 .... 10 principal drops weighed do. 10 first supplementary drops weighed 10 complete drops weighed........ In all cases of SLL the supplementary drop or drops were collected and weighed or measured with the main drop. In Table XV.— Column 1 shows the medium through which the mercury dropped. Column 3. The weight of the drops. The weight of every batch of drops is given, in order that the approximation between the figures for each liquid may be compared with that between the separate liquids. In two cases only, marked by an asterisk, are the numbers probably erroneous. They are not reckoned in taking the mean. Column 4. Mean weight of single drop, from column 3. Column 5. Specific gravity of medium. Column 6 shows the weight of the drop of mercury in the liquid. Since the falling of the drop is determined in part by its weight, and since the weight depends not only upon the size of the drop, but also upon the density of the medium in which it is formed, it is interesting to see how the 2 N VOL. XIII. size of the drop is affected by the diminution in its weight caused by the density of the medium. then W1=required weight of drop of mercury in liquid, A=specific gravity of liquid, B-specific gravity of mercury; The liquid media are arranged according to the order of magnitude of the numbers of column 4. The salient points of Table XV. are chiefly these : 1. The drop-size of a liquid which drops under like conditions through various media does not depend wholly upon the density of the medium and consequent variation in the weight, in the medium, of the dropping liquid. Thus glycerine, whose density is above that of all the other liquids examined, does not, as a medium, cause the mercurial drop to assume either its minimum or maximum size. 2. The liquids in Table XV. are in the same order as in Table VII. In other words, if there be two liquids, A and B, which drop under like conditions through air, and the drop-size of the one, A, be greater than that of the other, B; then if a third liquid, C, be made to drop through A and through B, the drop-size of C through A is greater than the drop-size of C through B. 3. Further, on comparing Tables XIII. and XV. it appears that, whether water or mercury drops through turpentol and benzol, the drop through benzol is greater than the drop through turpentol. This we shall afterwards find confirmed in other instances into the law, If the drop-size of A through B be greater than the drop-size of A through C, then the dropsize of D through B is also greater than the drop-size of D through C. It is further observed that, while mercury exhibits its largest drop when falling through air, water assumes its smallest drop-size under this condition. This method of the examination of liquids by drop-size in the case SLL, which brings so prominently forward a comparatively slight difference between similar liquids, may be used, not only to detect commercial adulterations of one liquid by another, but perhaps to distinguish between those remarkably-related isomeric liquid bodies (the number of which is quickly increasing) between whose terms the difference has until lately escaped detection. Of these bodies perhaps the first most remarkable instance was furnished by the two amylic alcohols; but the greatest number at present known is amongst the hydrocarbons. We may take an example illustrating the use of the stalagmometer in approximately measuring the proportion, in a mixture, of its two chemically and physically similar, but not isomeric constituents. Suppose we had a liquid which we knew to consist wholly of a mixture of benzol and turpentol, and we wished to find the proportion in which these two ingredients were present. We could scarcely approach to an as answer by any of the means hitherto employed. The specific gravities of! the two liquids are so close (864, 863) that the density of the mixture would give us no substantial aid. Though there is a considerable difference (80° C.) in their boiling-points, no one who is familiar with the difficulties of fractional distillation would place any reliance upon a quantita tive separation based upon volatility. Their refractive indices are nearly the same*. Their vapour-densities, 2.77, 4.76, though comparatively different, are not absolutely very wide apart. They are active and passive towards most of the same chemical reagents, and interfere with one another's reactions. If we have recourse to chemical analysis (C12 He, C20 H16), a very small experimental error would point to a great difference in the proportion of the two. 12 16 To find how far the stalagmometer (Plate V. fig. 7) is applicable in this case, it was filled with five liquids in succession: 1st, with benzol ..... =B. 2nd, with two volumes benzol and one of turpentol = BT. =T. The time-growth being brought in each case to 5", the number of drops of water required to fill a given volume was counted, allowance being made for the meniscus. Hence a difference of 16.6 per cent. in one of the constituents corresponds to an observed difference, under the most unfavourable conditions, of three drops. In other words, the stalagmometer is sensitive to an alteration of about 6 per cent. By increasing the capacity of the recipient, it is clear that the drop-numbers, and therefore their differences, might be increased at pleasure. Thus by counting the number of drops necessary to fill a volume six times the size, we could tell to within one per cent. how much turpentol and how much benzol were present. But it is perhaps in the cases of the still more proximate identity of isomeric bodies mentioned above that the stalagmometer may be used rather *The refractive index of turpentol is 1.476; that of benzol does not appear to have been measured; but that it is almost identical with that of turpentol is seen on mixing the two. In those cases in which I propose chiefly to use the stalagmometer, namely with isomeric liquids, the method of refraction is useless, because isomeric liquids seem always to have the same refractive indices. as a stalagmoscope, to render evident rather than to measure a difference - of drop-size. From Table XVI. we gather the general law concerning three liquids, = two of which are insoluble in the third. If a liquid, A, drop downwards - under like conditions in succession through two liquids, B and C, then its drop-size through any mixture of B and C is intermediate between its e drop-size through B and its drop-size through C; and the greater the proportion of C in the mixture, the more nearly does the drop-size of A through the mixture approach to the drop-size of A through alone. B B We have already examined the influences on the drop-size in the case SLG of the density of the dropping liquid, and of its persistent and stubborn cohesions respectively. Increase in the former two tends to diminish the drop-size; increase in the last to increase it. Let us examine in like manner the influence of the similar properties of the medium. 1. The density of the medium.-Increase in the density of the medium is equivalent to diminution in the density of the dropping liquid, and must therefore be followed by a tendency to increase in the drop-size. 2. Stubborn cohesion of medium.-The resistance to displacement, or stubborn cohesion of the medium, tends to keep back the drop in its place, and makes it necessary for a larger quantity of the dropping liquid to accumulate; that is, it increases the drop-size. 3. Retentive cohesion of medium.-The same force of persistent or retentive cohesion which causes a drop of a liquid to take the spherical form, would also cause the liquid to give or tend to give a spherical form to an irregularly-shaped volume of a solid, liquid, gas, or vacuum in it. Thus gas-bubbles in liquids have an approximately spherical form, not by reason of the cohesion of the parts of the gas, but by the persistent cohesion of the liquid medium which moulds the gas into that form by which the cohesion of the liquid is most gratified. Hence increase in the retentive or persistent cohesion of the medium tends to diminish the drop-size of the dropping liquid. In all cases of SLL we may represent the direction of the influence of the determinants by the following scheme, in which the sign + denotes a tendency to increase, the sign one to diminish the drop-size:— |