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ards through a third liquid C, is intermediate between the drop-size of . through C and that of B through C; and the greater the proportion of
', there is in the mixture, the more nearly does the drop-size of the mix
ure approach to the drop-size of j, alone.
It is remarkable that supplementary drops are found in the cases just onsidered, just as in the case of water dropping through the same liquids. 3ut the supplementary drops of benzol and turpentol through water bear L much smaller ratio to the main drops than do those of water through ■enzol and turpentol to their main drops. Judging only from the equality n their rate of ascent through the measuring-tube, all these supplementary hops are very exactly of the same size. The supplementary drops were not further examined, but were always collected and measured with the main drops.
Viewed as a means of quantitative chemical analysis, the measurement of the drop-sizes of liquids which drop up through water is yet more sensitive than that of the drop-sizes of water falling downwards through the liquids. Thus, from Table XVII., the least proportional difference of drop-number, caused by an alteration in the proportion of the liquids, is between T and BT„, where a diminution of 33-33 per cent, in the turpentol and an addition of 33*33 per cent, of benzol causes a difference of 35*3 in the drop-number.
Difference of fB 3333
percentage.. (T 33-33
Difference ofl 35.3 2W 24.3 102.0
Or this stalagmometer shows the composition of the liquid to within 1 per cent. Further, if the mixture contain less than one-third of benzol, we could determine the proportion, on an average, to within 0-33 per cent.
It may be noticed with regard to SLL that the value of gt is of much less influence upon the drop-size than in the case SLG. It is generally sufficient in the former case that the average value of gt should be constant. This is especially the case where the drops are formed from a tube (as the end of a siphon), and not from a convex solid. The reason is obviously that in the former case the thickness of the residual film, upon which we have found the size to depend, is at all rates indefinitely great, while in the latter case it depends upon the rate of supply.
In order to compare the drop-size of A through B with that of B through A under quite similar conditions, the siphon A of fig. 10 was inverted and applied to the cup stalagmometer of fig. 7. The arrangement of the end is seen in fig. 11. In using this form of stalagmometer, the end of the delivery-siphon must be at first wiped dry, so that the water may not creep back along its outside, and so give rise to an irregular drop-base. Water was made to drop through A, fig. 11, at the same rate, fft=2", and through the same liquids as before, namely T, BT2, BT, BaT, B. Ttm same measuring-tube was used as in fig. 10, or Table XVII., and it filled to the same point. Correction was made for meniscus.
We may now compare Tables XVII. and XVIII., since the conditions of the experiments whence they are got are identical. The drop-sizes are inversely as the drop-numbers. Let us use the symbol X to denote the drop-size of the liquid X through medium Y, &c. Comparing, first, the size of a drop of X through medium Y with the size of a drop of Y through
medium X, or finding the values of y1", we have (putting W for water)
Bw 86-2 W
Hence in none of these cases is the drop-size of one liquid through another equal to the drop-size of the second through the first. We get the general law, that—
If the liquid X has a larger drop-size than the liquid Y in the liquid Z, then the liquid Z has a larger drop-size in X than it has in Y. Further,—
If a liquid X has a larger drop-size than a liquid Y in air, then the drop-size of X through Y is greater than the drop-size of Y through X. Again,—
If the drop-size ofXbe greater than the drop-size ofY, and the dropsize ofYbe greater than the drop-size of Z «n air, then the ratio between the drop-sizes of X in any mixture of Y and Z, and the drop-size of that rixtvre ofY and Z through X, is greatest when the ratio between Y and i is vnity.
From Tables XVII. and XVIII. we may gather an interesting fact, rhich illustrates other brandies of physics. The drop-numbers of turientol and benzol through water being relatively 286 and 102, and the Irop-numbers of water through benzol and turpentol being relatively 256 ind 86-2, we may construct the following Table, in which the theoretical lumbers are compared with the experimental ones. The theoretical num>ers are got as follows. Ex.:—
1037 + 2x287
In all cases, then, the theoretical drop-number is less than the experimental one; or the theoretical drop-size is greater than the experimental one. Mixture impairs cohesion. Generally, when two solids are mixed, the melting-point of the two is lower than the mean of the melting-points of its components; sometimes lower than that of either. When two liquids are mixed, the boiling-point of the mixture (the initial boiling-point) is lower than that of either. The drop-size, which is also a function of the cohesion, we find here in no case to be less than the drop-size of either of the constituents, but in all cases to be less than the theoretical mean. Mixture impairs cohesion.
Further, comparing the drop-sizes of Table XVII. with one another, or all with Bw, we get
In like manner, comparing the drop-sizes of Table XX. with one inother, or with WB, we have
WT 862 i y°J
W" 219 =2-541.
The main results with regard to drops may be collected into the following laws:—
Law 1.—The drop-size depends upon the rate of dropping. Generally, the quicker the succession of the drops, the greater is the drop; the slower the rate, the more strictly is this the case. This law depends upon the difference, at different rates, of the thickness of the film from which the drop falls.
Law 2.—The drop-size depends upon the nature and quantity of the solid which the dropping liquid holds in solution. If the liquid stands in no chemical relation to the solid, in general the drop-size diminishes a* the quantity of solid contained in the liquid increases. The cause of this seems to be that the stubborn cohesion of the liquid is diminished by the solid in solution. Where one or more combinations between the liquid and solid are possible, the drop-size depends upon indeterminate data.
Law 3.—The drop-size depends upon the chemical nature of the dropping liquid, and little or nothing upon its density. Of all liquids examined, water has the greatest, and acetic acid the least drop-size.
Law 4.—The drop-size depends upon the geometric relation between the solid and the liquid. If the solid be spherical, the largest drops fall from the largest spheres. Absolute difference in radii takes a greater effect upon drops formed from smaller than upon those formed from larger spheres. Of circular horizontal planes, within certain limits, the size of the drop varies directly with the size of the plane.
Law 5.—The drop-size depends upon the chemical nature of the solid from which the drop falls, and little or nothing upon its density. Of all le solids examined, antimony delivers the smallest, and tin the largest rops.
Law 6.—The drop-size depends upon temperature; generally, the higher be temperature the smaller the drop. With water, the effect of a change f temperature of 20° C. about 30° C. is very small.
Lata 7.—The nature or tension of the gaseous medium has little or no ffect upon drop-size.
Law 8.—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.
Law 9.—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 the drop-size 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 dropsize of C through B.
Lata 10.—If the drop-size of A through B be greater than the dropsize of A through C, then the drop-size of a fourth liquid, D, through B is also greater than the drop-size of D through C.
Law 11.—If a liquid, A, drop 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 drop-size through B and its drop-size through
C. Corr. And the greater the proportion of p in the mixture the more
nearly does the drop-size of A through the mixture approach to the drop
size of A through p alone.
Law 12.—The drop-size of any mixture of two liquids, A and B, dropping through a third liquid, C, is intermediate between the drop-size of A
through C and that of B through C; and the greater the proportion of p
in the mixture, the more nearly does the drop-size of the mixture approach
to the drop-size of ■„ alone, whether the dropping liquid be heavier or
lighter than the liquid medium.
Law 13.—If the liquid X has a larger drop-size than the liquid Y in the liquid Z, then the liquid Z has a larger drop-size in X than it has in Y.
Law 14.—If a liquid, X, has a larger drop-size than a liquid, Y, in air, then the drop-size of X through Y is larger than the drop-size of Y through X.
Law 15.—If the drop-size of X be greater than the drop-size of Y in air, and the drop-size of Y be greater than the drop-size of Z in air, then the ratio between the drop-sizes of X in any mixture of Y and Z, and the drop-size of that mixture of Y and Z through X, is greatest when the ratio between Y and Z is unity.