In a paper, entitled “On the Action of Carbonic Acid Water on Minerals and Kocks,” read before the Edinburgh Geological Society on the 18th February 1886, and subsequently published in their Transactions for that year (vol. v. part ii. p. 282), I gave some account of the simple experiments made with a view to elucidate the action of carbonated water on various minerals, which up to that period I had been able to carry through.

The law which is sometimes associated with the name of Talbot is generally stated thus:—Once complete fusion has been reached, no alteration in the intensity of the resultant impression produced by a series of flashes takes place, however short the time during which each flash acts may be, provided that the number of flashes in a given time and the length of each stimulation be always kept inversely proportional. Complete fusion of stimuli here is analogous to complete tetanus of muscle. And, as in the latter case, it has been discussed as to where the upper limit of frequency lies, or whether there be an upper limit, so in the former case are like questions in place. With the various answers which have been given in regard to muscle tetanus we are not here concerned; except that it may be noticed that the later investigators, where they have at all admitted the probability of a limit, have had a tendency to shorten the time between each stimulus which they regarded as the minimum.

One of the most interesting departments of embryology is that which treats of twin development, and the many forms of abnormality or monstrosity produced by the arrest or modification of its process.

When the first cleft of the ovum is incomplete at some part, and two organisms arise from its halves, arrested twin development in its widest sense occurs, and a form of double monstrosity results. That the condition is due to imperfect cleavage, and not to a fusion of two ova, is shown by the fact that the sex of the twins is invariably the same, and, as Ahlfeld has pointed out, that they are always united at identical parts. The individuals are rarely of equal size and perfection of structure, although there are several instances on record where such was the case; more commonly one of the organisms has its growth arrested at an early period of life, and clings as a parasite to the fully developed autosite. In such cases the parasite varies in size and form, existing sometimes as an almost complete organism, possessing not only external parts, but internal organs; at other times, it is represented by a limb or part of such, only (as in the case described by Handyside). This arrested development of the second organism (parasitism) is undoubtedly due to an incomplete blood supply passing to the second fœtus, a condition brought about either by placental changes, or changes within the body of the monster itself, at a very early period of intrauterine life.

In a recent paper on “Certain Theorems mainly connected with Alternants (II.),” the possible generalization of the series of theorems (I.)1 (II)1, (III)1, &c, is referred to in § 6. The object of the present communication is to endeavour to effect this generalization, considering for the present Integral functions only.

I understand that it devolves on me, as Chairman at this meeting, to cast a retrospective glance over the Session which has now come to a close, and, in connection therewith, to make a few observations of a kind likely to be of general interest to the Society. In endeavouring to discharge this duty, I have to acknowledge that our Assistant-Secretary, Mr Gordon, has made my task almost as easy as it could be made.