liquid will always be of the same size, if it is formed of the same liquid substance and falls from a solid of the same substance, size, and shape, provided that the temperature remain the same, and the growth-time be constant.

The size of the drops may be most conveniently determined by weighing a noted number of them. We are concerned rather with the relative than with the absolute sizes of the drops. The sizes of drops formed of the same liquid are proportional to their weights; of different liquids, to those weights divided by the specific gravities of the liquids.

In the first series of experiments the apparatus, fig. 1, was employed. The globe A, full of the liquid under experiment, is inverted into the cylinder B, containing the same. The mouth of A is supported just in

contact with the surface of the liquid in B, by means of the tripod stand D. A and B are carried on a table, which may be raised or lowered at pleasure. A siphon, E, leads from the reservoir B, and is firmly held by the clamp F. The longer limb of E, from which the liquid flows, is

turned up at the end, and touches a plug of cotton wool at G. sphere H, from which the dropping takes place, is hung by three thi wires from the ring of a retort-stand. The upper half of the sphere clothed in cotton wool, which reaches up to the plug at G. The whol arrangement is placed upon a separate table from that which supports thei balance, so as to avoid the vibration caused by opening and shutting the balance case. The drops which fall from H enter the funnel L, whose lower end is somewhat bent, so that the drops are thrown out of the ver tical, and all upward splashing avoided. The rapidity of the flow through the siphon, and consequent dropping from H, is regulated by raising or lowering the table C. The vessel A acts as a regulator for keeping the level of the liquid in B at a constant height.

The first series of experiments was made with the double object of determining how far the rapidity of dropping influenced the size of the drops, and to establish the uniformity of the size of the drops which drop at equal intervals of time.

In these experiments cocoa-nut oil was taken as the liquid, an ivory sphere as the solid, and atmospheric air as the gas. The ivory sphere was washed in hydrochloric acid, so as to deaden its surface. Immediately before and after each batch of drops, the same number of drops were counted, and their time of falling compared with the time which elapsed in the actual experiment. In no case, however, was there a difference between the two of a single second, so that gt may be considered in each case to be exactly given.

Preliminary experiments having shown that the size of a drop is greatly affected by the rate at which the dropping takes place, that is, by the time occupied by the drop in its formation, the following experiments were performed to establish the connexion between the two.

It may be here remarked that with some liquids, of which cocoa-nut oil

is one, a continuous stream of liquid by no means implies a faster delivery of it than may be achieved by a succession of drops. On the contrary, just as by walking more rapid progress may be made than by running, so may dropping deliver more liquid than passes in a stream. A uniformly rapid series of drops may be converted into a stream, and reconverted into drops under certain restrictions, at pleasure, without altering the quantity of liquid delivered. We shall return to this point.

From this Table is constructed the following Table III., which shows gt in seconds and the corresponding drop-weights in grammes, the latter values being the mean of the results in Table II. gt is got by dividing the time-lapses of Table II. by the number of drops.

Hence it appears that, within the above limits, on the whole, the weight or size of a drop diminishes as its growth-time increases. Further, it seems that between the rates gt=433 and gt=567 a minimum occurs, that is, instead of there being a continuous diminution in the weight as the growthtime increases, there is at first a diminution, then an increase, and finally a continuous diminution, so that drops of the rate gt=500 have sensibly the same size as those of the rate gt='633.

In order to establish more precisely the position of this minimum and . the general relation between rate and size, the observations must be both more minute and more extended. For this purpose a fresh sample of oil was taken, and the time-intervals extended from 25" per 60 drops to 240′′ per 20 drops; as before, four experiments were made at each time-interval. The mean results are given in Table.IV.*, in which the values of gt are obtained by dividing the time-intervals by the number of drops. The mean weights of the single drops are got as in Table III. The weights of oil passing in one second are found by dividing the terms of column 2 by those of column 1, which correspond to them.

TABLE IV.-Cocoa-nut oil (specific gravity =0.9195).

* A Table exhibiting the details is given in the MS., which is preserved for reference in the Archives.

It was found impossible to arrest an exact number of drops when the rate was faster than 60 drops in 25". A few rather discordant results, got at the rate of 60 drops in 20", gave a mean of 0·09264 grm. as the weight of a single drop; this tends to show that at this high rate the drops were considerably larger than at any lower rate.

Towards the end of the Table, at the slower rates, the error of time becomes so exaggerated (the least alteration in the adjustment of the instrument makes so sensible a change in the entire time-lapse) that it is nearly impossible to avoid an error of about 0"-5 in the whole time of several minutes. Although the time-error thus becomes palpable, it nevertheless remains, relatively to the whole time-lapse, as immaterially small as the inappreciable errors of the swifter rates of dropping. The numbers of Table IV. present us with several interesting and important facts.

From gt=333 to gt= 433 there is diminution.

The most prominent fact is that, on the whole, the drops undergo a continuous diminution in weight or size as gt increases. To such an extent is this the case, that the most rapidly falling drops of the above Table are nearly twice as heavy as the most slowly falling ones. The cause of this is probably to be sought for in the circumstance that when the flowing to the solid is more slow, the latter is covered with a thinner film of liquid, so that, as the drop parts, the solid reclaims by adhesion more of the root of the drop than is the case when the adhesion of the solid to the liquid can satisfy itself from the thicker film which surrounds the drop in the case of a more rapid flow. The influence of rate is seen to extend even to the exceedingly slow rate of gt=12".

This connexion between rate and weight (or quantity) should not be lost sight of by prescribers and dispensers of medicine. A pharmacist who administers 100 drops of a liquid drug at the rate of three drops per second, may give half as much again, as one who measures the same number at the rate of one drop in two seconds, and so on.

For our present purpose the effect of rate upon the size of a drop is of great moment, because it proves that there is no such thing as a drop of normal size. At no degree of slowness of dropping do drops assume a size unaffected by even a slight change in the rate of their sequence. Hence, whenever a comparison has to be made between the sizes of different drops, we shall have to eliminate this source of difference by taking drops which follow at exactly the same rate.

About the rate at which the diminution of size takes place for equal increments of gt, the Table gives us little information beyond the fact that,