Before we leave this subject, on which a vast deal more might be said, there are one or two points which we must not omit to consider. Let us note, in the first place, that the appearance which our plane diagrams suggest of inequality of the several cells is apt to be deceptive; for the differences of magnitude apparent in one plane may well be, and probably generally are, balanced by equal and opposite differences in another. Secondly, let us remark that the rule which we are considering refers only {383} to angles, and to the number, not to the length of the intermediate partitions; it is to a great extent by variations in the length of these that the magnitudes of the cells may be equalised, or otherwise balanced, and the whole system brought into equilibrium. Lastly, there is a curious point to consider, in regard to the number of actual contacts, in the various cases, between cell and cell. If we inspect the diagrams in Fig. 169 (which represent three out of our thirteen possible arrangements of eight cells) we shall see that, in the case of type _b_, two cells are each in contact with two others, two cells with three others, and four cells each with four other cells. In type _a_ four cells are each in contact with two, two with four, and two with five. In type _f_, two are in contact with two, four with three, and one with no less than seven. In all cases the [Illustration: Fig. 169.] number of contacts is twenty-six in all; or, in other words, there are thirteen internal partitions, besides the eight peripheral walls. For it is easy to see that, in all cases of _n_ cells with a common external boundary, the number of internal partitions is 2_n_ − 3; or the number of what we call the internal or interfacial contacts is 2(2_n_ − 3). But it would appear that the most stable arrangements are those in which the total number of contacts is most evenly divided, and the least stable are those in which some one cell has, as in type _f_, a predominant number of contacts. In a well-known series of experiments, Roux has shewn how, by means of oil-drops, various arrangements, or aggregations, of cells can be simulated; and in Fig. 170 I shew a number of Roux’s figures, and have ascribed them to what seem to be their appropriate “types” among those which we have just been considering; but {384} it will be observed that in these figures of Roux’s the drops are not always in complete contact, a little air-bubble often keeping them apart at their apical junctions, so that we see the configuration towards which the system is _tending_ rather than that which it has fully attained[397]. The type which we have called _f_ was found by Roux to be unstable, the large (or apparently large) drop _a″_ quickly passing into the centre of the system, and here taking up a position of equilibrium in which, as usual, three cells meet throughout in a point, at equal angles, and in which, in this case, all the cells have an equal number of “interfacial” contacts.