In an introductory section of the paper, a sketch is given of the literature of the subject, and reference is made to the labours of Jameson, Macculloch, Berger, Boue, Oyenhausen, Von Dechen, Necker, Zirkel, Judd, and other observers. The author then mentions the progress of his own investigations, which were begun some thirty years ago, and of which the first published part appeared in the Transactions of the Society for 1861. A journey into Western America in 1879 gave him new insight into the problems presented by the youngest volcanic rocks of Britain. Since that time he has devoted every available interval to the prosecution of this research, and he now offers the completed results to the Society, which encouraged him by printing his earliest communication on the subject.

Of all the processes for computing to great precision this most important ratio, that by means of the series for the arc in terms of its tangent is the most rapid. Seemingly short, however, it is truly a very long process; to reach its beginning we must know the laws of differentials and integrals, must be familiar with the higher algehra, and with the advanced branches of trigonometry; must know how to divide an arc whose tangent is an aliquot part of the radius, into smaller arcs whose tangents have the same character; and while studying these chapters in mathematical science we shall have often used our knowledge of this very ratio of which we are in search. The real utility of this formula lies in its enabling us to extend the approximation to a great number of decimal places. Even although the labour be not overwhelming, we can hardly regard as other than useless, the toil of computing and verifying the value of π to upwards of five hundred places.

The art of figuring the lenses of a telescopic objective consists in correcting the spherical aberration by successive trials, until approximately aplanatic curves are obtained.

It is a matter of some difficulty even to demonstrate that the blood is an alkaline fluid. The reason is that its red colour masks the reaction. The plasma itself is, however, practically colourless, and by allowing it to mingle with red litmus solution, after its corpuscles have been strained away, a blue tint may be observed. This was effected by Liebreich, who moistened dry neutral plates of plaster of Paris with litmus solution.

Of late this subject has become of considerable practical interest in medicine, especially in connection with the use of voltaic currents for the treatment of uterine fibroids and other pelvic disorders.

In this memoir details are given which prove the true renal functions of the Malpighian tubules in the Libellulidæ.

A considerable amount of work has been performed in investigating the nature of the nodular outgrowths upon the roots of various plants. One of the earliest observations in this direction was by Naegeli in 1842, who found that the swellings upon the roots of Iris were caused by a parasitic fungus.

Dana, in his Report on the Crustacea of the North Atlantic Exploring Expedition, described a number of genera founded on larvae of various Crustacea. Of these genera Calyptopis, Furcilia and Cyrtopia were shown by Claus in 1863 to represent three stages in the development of the Euphausiidas. Metschnikoff, in 1869, described a still earlier stage under the name of Metanauplius; and in 1871 the same investigator was enabled to show that the young Euphausiidse are hatched as true Nauplii, having a rounded body and three pairs of swimming appendages.

Whilst examining my “tow-nettings” from the West Coast, I have met with a peculiar Decapod larva, which, so far as I know, is unlike anything previously described. In general appearance it is very like semi-adult forms of Lawifer, having an elongated “neck,” at the tip of which the eyes and antennae are carried. My specimens were obtained from two localities—1st, about half a dozen at about the same stage, from tow-nettings taken in Machrie Bay (west shore of Arran), 17th September 1886; and 2nd, about 20 specimens, some further advanced than those of the previous gathering, which were collected at a depth of 8 to 10 fathoms in the Sound of Mull, 24th August 1887. These were associated with various larval stages of Porcellana, Galathea, and other Decapods.

A grant was made by the British Medical Association, on the recommendation of the Scientific Grants Committee of the Association, towards the expenses of a research, a part of which appears in this communication.

Laplace, assuming molecular force to be insensible at distances greater than a small quantity a, finds the resultant molecular force on a unit particle at a distance x within the (plane) surface. This being called X, the internal pressure is

where p is the density of the liquid. But this is evidently the work required to take unit volume of the liquid (particle by particle) from the interior to the surface. And it is easily seen that to carry it from the surface beyond the range of the molecular forces requires just as much more work:—for the density of the surface-film is treated as equal to that of the rest of the liquid.

During labour the membranes and placenta become separated and expelled, but while the expulsion of these takes place after the child is born, the entire separation does not occur at any one period. During the first stage of labour the membranes in the lower portion of the uterus, in the part termed the lower uterine segment, become detached. The placenta, if placed partly in this segment, a condition known as placenta prsevia, becomes also separated. The rest of the membranes and placenta do not become separated until after childbirth, and this is followed by their expulsion as a whole.