This scheme is verified by the experimental results obtained. Of lad liquids water forms the largest drops in falling through air, because in it the stubborn cohesion prevails to the greatest degree over the joint action of persistent cohesion and weight. In water mercury forms drops greater than in all other liquids, because in water (as a medium) stubborn cohesion and weight prevail to the greatest degree over persistent cohesion.

The case SLL may be inverted if the drop-forming liquid be specifically lighter than the medium liquid. Thus every case of SLL which we have examined in which a liquid, A, drops downwards through a liquid, B, has a counter case in which the liquid B drops upwards through the liquid A. ¦ In order to measure the size of such ascending drops, the stalagmometer (fig. 7) is modified in form. It is not found possible to cause the dropping liquid to adhere with sufficient completeness and uniformity to a solid sphere immersed in the denser medium, in the cases experimented on. The end of the siphon A was turned upwards, and served as the solid whence the liquid dropped, without the interposition of a sphere or other solid. The measuring-tube D was removed from the neck of the cup C, a stopper being inserted in its place. The cup C was filled with water, : and the measuring-tube D, being also filled with water, was inverted into it and supported by the holder H. The modified stalagmometer is seen in Plate V. fig. 10. Care was taken that the end of the siphon A should always be at the same depth beneath the surface of the water in C.

The drop-sizes of the liquids of Table XVI. were first examined by this stalagmometer.

The following Table XVII. shows the number of drops of the various liquids, dropping through water, required to fill the measuring-tube up to the given mark. The measuring-tube employed was different from that used in forming Table XVI. On this account, and because the delivering solid was quite different in shape, and gt only 2", no immediate comparison can be made between Tables XVII. and XVI. In Table XVII. correction is made for meniscus.

TABLE XVII.

1

We gather from this Table a law quite similar to that deduced from the measurement of the size of the downwards moving drops of water through these same liquids. It is as follows:

The drop-size of any mixture of two liquids, A and B, dropping up

* See Part I. Introduction.

wards 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

A

B there is in the mixture, the more nearly does the drop-size of the mix

A
B

ture approach to the drop-size of alone.

It is remarkable that supplementary drops are found in the cases just considered, just as in the case of water dropping through the same liquids. But the supplementary drops of benzol and turpentol through water bear a much smaller ratio to the main drops than do those of water through benzol and turpentol to their main drops. Judging only from the equality in their rate of ascent through the measuring-tube, all these supplementary drops 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.

1

Or this stalagmometer shows the composition of the liquid to within 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, gt=2′′, and through the same liquids as before, namely T, BT, BT, BT, B. The Fr same measuring-tube was used as in fig. 10, or Table XVII., and it was th 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 we have (putting W for water)

Xy

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 of X be greater than the drop-size of Y, and the dropsize 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.

From Tables XVII. and XVIII. we may gather an interesting fact, which illustrates other branches of physics. The drop-numbers of turpentol and benzol through water being relatively 286 and 102, and the drop-numbers of water through benzol and turpentol being relatively 256 and 86.2, we may construct the following Table, in which the theoretical numbers are compared with the experimental ones. The theoretical numbers are got as follows. Ex.:

one.

In all cases, then, the theoretical drop-number is less than the experimental one; or the theoretical drop-size is greater than the experimental 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 another, or with WB, we have

Lastly, on comparing these figures with those of Table XX., we get the remarkable law, which it would be difficult to express in words, that WB.TW WR. BTW WR. BTW WB. B2Tw .

WT. Bw

WBT2

=

BTW.

=1 nearly.

Bw

WB2T.BW

The main results with regard to drops may be collected into the following laws:

SLG.

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 as 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