In two papers read before this Society, I have very fully described the Diatomaceæ of the Glenshira Sand, which is very remarkable both for the large number of species found in it, which is certainly more than 320, and for the circumstances in which it must have been deposited. There can be no doubt, from the nature of the locality, which I have lately visited, that this bed was formed in the bottom of the Dhu Loch, a shallow fresh-water lake, at that time extending about two miles farther up the valley than it now does, and being at a higher level. In consequence of a rise in the level of the land, or a fall in that of the sea (from which—that is, from Loch Fine, the lower end of the lake is separated by a narrow and low barrier, through which the waters of the lake pass to Loch Fine), the lake has long ago been drained, till its upper end is nearly two miles from the point it must have reached when the bed of sand was formed. The present level of the lake is considerably lower than it was then; the precise difference I had no means of ascertaining, but I believe it is about 30 feet.

Notwithstanding the progress made of late years in animal chemistry in connection with comparative anatomy, I am not aware of any observations that have yet been published on the urinary secretion of fishes. The neglect of this inquiry probably has arisen from several circumstances,—the nature of the element inhabited, the peculiarities of the urinary organs, the difficulty of collecting the matter voided, and its having no well-marked distinctive qualities obvious to the senses.

For some years, as leisure and opportunities offered, I have given attention to the subject, and in the paper which now I have the honour to submit to the Society, I beg to communicate the observations I have made. Few and imperfect as these are, they are given mainly with the hope of attracting notice to the inquiry and of inducing others more favourably situated to engage in its prosecution.

It has been long known that contractile tissue presents itself in the human body in two forms, one composed of fibres of considerable magnitude, and therefore readily visible under a low magnifying power, and marked very characteristically with transverse lines at short intervals, the other consisting of fibres much more minute, of exceedingly soft and delicate aspect, and destitute of transverse striæ. The former variety constitutes the muscles of the limbs, and of all parts whose movements are under the dominion of the will; while the latter forms the contractile element of organs, such as the intestines, which are placed beyond the control of volition. There are, however, some exceptions to this general rule, the principal of which is the heart, whose fibres are a variety of the striped kind.

To those who study the progress of exact science, the common spinning-top is a symbol of the labours and the perplexities of men who had successfully threaded the mazes of the planetary motions. The mathematicians of the last age, searching through nature for problems worthy of their analysis, found in this toy of their youth, ample occupation for their highest mathematical powers.

No illustration of astronomical precession can be devised more perfect than that presented by a properly balanced top, but yet the motion of rotation has intricacies far exceeding those of the theory of precession.

Owing to the great length of time over which the investigation of the products of the destructive distillation of animal substances has stretched, and various circumstances which it is unnecessary to detail, the inquiry has been pursued in a somewhat fragmentary manner, and with less continuity than might have been desired. The difficulties attending many of the experiments, and the occasional exhaustion of materials prepared by laborious processes, extending in many instances over considerable periods, have occasioned long intervals in the regular course of the inquiry which it became necessary to occupy with the examination of such matters as could be taken up at the moment. In this way a number of facts required to complete the history of the bases already described have gradually been accumulated, some of the products of their decomposition examined, and the pyrrol so frequently adverted to in the previous parts of this paper has been subjected to a full investigation. The details of these experiments form the subject of the present communication.

1. The method for the solution of questions in the theory of probabilities applied in this paper, is that which was developed by the author in a treatise entitled, “An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities.” The practical object of the paper is to deduce from that method certain conclusions relating to the combination of testimonies or judgments. Beside this, however, it will have a speculative reference to some more general questions connected with the theory of probabilities; and especially to the following question, viz.: To what extent the different modes in which the human mind proceeds, in the estimation of probability, may be considered as mutually confirming each other,—as manifestations of a central unity of thought amid the diversity of the forms in which that unity is developed.