It is in conformity with time honoured custom, and in the performance of duty, that I offer a short address on the occasion of the opening of the Society's 109th Session.

I confess that I have little to say which can be expected to attract the notice of the Fellows, or to bear to be recorded in our proceedings; but I am glad to be able to state that alike as regards Fellowships, Finances, and the work of the past Session, the Society is in a prosperous condition.

If the positive integral powers of be taken, and the expansion of each be separated into two parts, rational and irrational, thus—

then the ratio of the rational portion to the coefficient of in the other portion is approximately equal to , the convergence being perfect when the power of the binomial is infinite. This is the simplest case of a theorem discovered by the late Dr Sang, and enunciated by him as the result of a process of induction in his paper “On the Extension of Brouncker's Method to the Comparison of several Magnitudes” (Proc. Roy. Soc. Edin., vol. xviii. p. 341, 1890–91).

The object of this enquiry was to ascertain and compare the electrical resistances of various kinds of urine, both in states of health and of disease.

The measurements were made by means of a Wheatstone's bridge, with alternating currents, and a telephone according to Kohlrausch's method.

The fluids were held in a U-shaped electrolysis tube (a drawing of which accompanies this paper), of an internal diameter of about 1·55 centimetres, and containing a delicate thermometer. Two disc shaped platinum electrodes, each with a diameter of 1·4 c'm., were arranged so as just to rest upon the surfaces of the urine, with a very thin film of the fluid upon their upper surfaces.

The problem occurs in a paper of Professor Tait's (“Glissettes of an Ellipse and of a Hyperbola,” Proc. Roy. Soc. Edin., xvii. pp. 2–4). An ellipse whose semi-axes are a and b is considered as moving so as always to be in contact with both axes of coordinates, and the glissette in question is the curve traced out during this motion by a point whose coordinates with respect to the axes of the ellipse are p and q. Professor Tait states, and it is readily seen, that if the current coordinates of the point be x and y, and θ be the variable angle made by one of the axes of the ellipse with the axis of x, we have the equations

and that to obtain the x-and-y equation of the glissette it remains to eliminate θ between these two equations.

The first instalment of this part of my paper deals mainly with the theory of the behaviour of mixtures of CO2 and N, for which some remarkable experimental results were given by Andrews about 1874. His full paper, so far as he had drawn it up for press, was published posthumously in the Phil. Trans, for 1886, and is reprinted in his Scientific Papers, No. L. One special reaaon for the introduction of this question at the present stage of my work was the desire to attempt a correction of Amagat's numbers, for the (very small) admixture of air with his CO2. The virial equation for a mixture is formed on the same general principle as that I employed for a single gas. There are, of course, more undetermined constants :—and, unfortunately, the data for their determination are barely adequate. The general results, however, agree in character with those described by Andrews :—the particular phenomenon which is most closely studied being the increase of volume, at constant pressure, when the gases (originally separated by the liquefaction of one) were allowed to diffuse into one another.

It is outside the scope of the present paper to enter into the geographical distribution generally of the Lesser Rorqual or Pike Whale (Balænoptera rostrata), and indeed there is no reason why I should do so, as it has so recently been considered by Professor Van Beneden, in his Histoire naturelle des Balénoptères. For a number of years it has been my custom to collect information regarding the Cetacea captured or stranded on the Scottish coasts, and when possible to obtain the animals or their skeletons. I have accumulated, therefore, a considerable body of information regarding the whales frequenting the Scottish seas, some of which I have already published. In the present communication it is my intention to record some facts regarding Balænoptera rostrata, and I may say that when a newspaper paragraph relates the capture of a whalebone whale, and, when measurements are given, if the length is under 30 feet, the animal is most probably the Lesser Rorqual.

All who watch the flight of hawks or kites are struck by the extraordinary power they have of sustaining themselves for a long time, sailing about in the air without flapping their wings or making any conspicuous effort whatever.

Most birds of prey, as distinguished from game, are able to do this, and thus hold commanding heights from which, to descry food. The expression “wind-sucker,” as used by Ben Jonson, refers to the kestrel, a kind of hawk unsuited for falconry ; the astonishing way in which it keeps itself poised in the air, facing the wind with beak outstretched, led to the name, which implies the only explanation of the phenomenon that the science of those days could furnish. Sea-birds are also very proficient.

In June of last year one of us gave before the Society a short account of certain preliminary experiments on the volume effects of magnetisation. These experiments had been made in Japan; and the results obtained evidently called for a more thorough investigation. The facilities of the Physical Laboratory of Edinburgh University were kindly placed at our disposal by Professor Tait. Five tubes of Swedish iron, all cut from the same original bar but made with different bores, were prepared for study in much the same manner as formerly. Many experimental difficulties encountered us; and only now have these been satisfactorily overcome. For it must be remembered that the effect to be observed is very minute, and can be measured only in one way, viz., by the motion of the meniscus along the narrow capillary tube which is in connection with the iron tube, the whole being filled with fluid. But such an arrangement is obviously a very delicate thermometer; and, as a matter of fact, we have seldom got the meniscus really steady. Generally it is moving at a rate which, though as inappreciable to the naked eye as the motion of an hour hand, is only too evident under the microscopic power necessary for the observation of the magnetic effect.

The problem consists in the elimination of θ from two equations which (after expressing cos2θ in terms of sin2θ) may be written

As only two of the equations can be used, the elimination will be effected by means of (2) and (3), using the relation cos2θ + sin2θ = 1, where necessary, to suppress the term of cos2.