I find that during the past Session forty-one papers have been road. Of these, ten belong to the department of Physics, five to Mathematics, one to Chemistry, two to Geology, seven to Biology, one to Botany, four to Anatomy, three to Physiology, four to Meteorology, four to Astronomy.

Since the commencement of the past Session, eighteen Fellows have been added to our numbers. Of these, one is a Professor of Philosophy, two are University Lecturers, and six are Doctors of Medicine.

The instrument is delineated in the accompanying drawing. It consists of two thin and flat pieces, AIFD and BHO, of metal or other material. Those pieces are closely connected together hy a cylindrical pin inserted perpendicularly to their flat surfaces through a cylindrical hole at C in each of them, which it fits, and round which they can turn.

The problem of the trisection of an angle, analytically considered, depends on the solution of a cubic equation, say 4x3−3x−cos a = 0, which is in general irreducible, and therefore not soluble by means of quadratic radicals. It follows that the trisection of an angle cannot be effected by means of the ruler and compass alone. This, in fact if not in theory, appears to have been known to the early Greek geometers, and they proposed the use of various curves, the continuous mechanical construction of which must, of course, be postulated, for the solution of the problem. The Quadratrix and the Spiral of Archimedes, both transcendental curves, may be mentioned. It was early discovered that the conic sections could be used for the purpose, and in modern times various solutions have been suggested involving their use.

If, instead of causing the point B of the trisector to move along an arm of the angle, we cause P, the intersection of the two edges, to move along an arm, and find the locus of the point B, we get another curve associated with the instrument.

Many investigations have been made as to the destruction of red blood corpuscles in the spleen, and there can be little doubt that this occurs. If the hæmoglobin set free is also destroyed in the spleen, iron in some form will be liberated. The presence of iron in the spleen has already been shown by various observers, but the exact nature of the substances with which it is combined is still a matter of doubt.The object of this investigation was, if possible, to trace the stages in the decomposition of hæmoglobin as shown by the existence of intermediate compounds, and to ascertain the chemical nature of such compounds.

The idea has long been floating around in thoughtful minds that all the different varieties of matter in the world are formed out of one primordial substance or stuff, and that the different qualities they exhibit are caused by a mere difference of number, arrangement, and motion of the primordial units forming the atoms of our so-called elementary substances. For instance, the atom of oxygen would contain sixteen times as many of these units as the atom of hydrogen, which would account for the difference of their atomic weights; and besides, the motions of the units forming each atom would be different for the different atoms, thus accounting for their other different qualities. Nitrogen would contain fourteen times as many of these units, carbon twelve times, and so on according to their atomic weights.

In a series of papers dating from 1897, resumés of winch are given in the Bulletin international de I'académie des Sciences de Cracovie, Professor Browicz gives the results of observations on the liver cells, both in the normal state and in a pathologically altered condition, and draws from these observations certain important deductions. The most prominent fact which is recorded is the appearance (under normal conditions in the liver of the newborn child, and under pathological conditions in the adult human liver; under normal conditions, and after the intravenous injection of hæmoglobin some hours prior to death, in the liver of the dog) of erythrocytes, singly and in groups, and of free hæmoglobin and hæmoglobin crystals, as well as brown pigment, in the form both of granules and crystalline clumps, within the hepatic cells, both in the nucleus and in the cytoplasm. After affirming the undoubted existence of intracellular biliary passages communicating with intercellular bile ducts,—which intracellular passages he regards, not as accidental and temporary vacuoles, but as preformed channels within the cells, — Professor Browicz states that his observations, especially the presence within the liver cells of erythrocytes, demonstrate that the cells must be in communication with the hepatic capillaries.

In this system vectors are regarded as translators only. A special operator, R, transforms them into rotors. A second application of the operator retransforms rotors into translators. The system is essentially Hamilton's, with the removal of the restriction that vectors shall act as translators in addition, and as rotors in multiplication.

There has recently been discovered at the Royal Observatory, Cape Town, an interesting star of the Algol type of variation, thus making in all ten such stars at present known in the southern sky.

During recent years the great attention which has been paid to the study of reversible chemical actions has led to a desire for some method of specially indicating in the equations the reversibility of these actions. This is generally done by replacing the sign of equality by two parallel and oppositely-directed arrows; the use of this symbol in such cases does not only imply the reversibility of the action, it has the same value as the sign of equality in an ordinary equation. Unfortunately, there are several drawbacks to the use of this symbol: as generally printed, it is rather clumsy in appearance; the arrows, being widely separated, do not suggest the sign of equality which they replace; and further, in conjunction with formulæ, arrows are frequently employed, especially in organic chemistry, to indicate merely the stages and methods by which a substance can be produced from some other substance as starting-point. In such cases, as no attention is paid to the bye products, there is nothing of the nature of an equation involved. Numerous examples are to be seen in Richter's Organisehe Chemie, and amongst them cases in which oppositely-directed arrows, resembling the symbol employed for the equations for reversible actions, are used to indicate that each of the two substances concerned may serve as starting point for the preparation of the other, without involving equality on the two sides of the symbols. Such a double use of a symbol is highly objectionable.

In a paper already communicated to the Society by one of us attention was drawn to the fact that, in presence of a soluble silver salt, ammonium persulphate is decomposed with formation of nitric acid as well as sulphuric acid. The action had at that time been studied only in a roughly quantitative way, and it was therefore thought that a more exact study of the velocity of the reaction, and of the influence exerted by other salts present in solution, might prove of interest, and also throw light on the course which the reaction follows.

This investigation deals with the shielding which exists within hollow iron cylinders when placed in a uniform transverse magnetic field. This transverse field divided by the internal magnetic field is defined as the shielding ratio. For the thin iron cylinders experimented with, it appears from various mathematical contributions to the subject that the shielding ratio minus unity may for present purposes be taken to be proportional to certain geometrical data and to the permeability (the permeability being large). By means of a rotating inductor within the shield, connected with a ballistic galvanometer, experimental determinations of the shielding ratio are made under various conditions of magnetisation; and an endeavour is also made to show how far and under what conditions these results approximate to theoretical formulas which assume the permeability to be uniform all round the shield, and the absence of retentivity and coercive force in the iron. Two iron shields were experimented with, the hysteretic constants (η) being ·0015 and ·0028 respectively.

The method for specifying stress and strain hitherto followed by all writers on elasticity has the great disadvantage that it essentially requires the strain to be infinitely small. As a notational method it has the inconvenience that the specifying elements are of two essentially different kinds (in the notation of Thomson and Tait e, f, g, simple elongations; a, b, c, shearings). Both these faults are avoided if we take the six lengths of the six edges of a tetrahedron of the solid, or, what amounts to the same, though less simple, the three pairs of face-diagonals of a hexahedron, as the specifying elements. This I have thought of for the last thirty years, but not till a few weeks ago have I seen how to make it conveniently practicable, especially for application to the generalised dynamics of a crystal.

(1) Having formed from n things all possible sets of r, we may subject each of the Cn,r sets to the test of fulfilling one or more conditions, and so obtain a reduced number possessing a special characterisation. The present note deals with a few instances of this in which the reduced number is of the same algebraical form as the full number, that is to say, is a combinatorial Ca,b.

(1) In a paper in the Proceedings of the London Mathematical Society, vol. xxxiii. p. 229, Professor Elliott has occasion to consider the equation

which, it is stated, presents difficulties when a direct algebraical solution is attempted, but is seen indirectly to be

according as p is odd or even.

Before beginning the account of the present state of the Plague Research Laboratory, it may be interesting to glance rapidly at the history of Mr W. M. Haffkine, C.I.E., its originator and present Directorin-Chief.

That the absence of dissolved oxygen from water is fatal to fish is well shown by an observation of Wilh. Thörner (Forschungsberichte über Lebensmittel, 1897, 4, 172), on the condition of the water of the Hase at Osnabrück, where a great destruction of fish had occurred. Besides a complete absence of free oxygen in the water, nothing hurtful to fish could be detected.

It is not improbable that determinants in which the number of a row is distinguished by differentiation with respect to a definite variable, and in which the number of a column is distinguished by a particular function set for differentiation, may have appeared long before the time of Cauchy and Jacobi, the likelihood probably being the greater the fewer the number of functions and variables involved.

‘Dead’ matter has two forms of inertia—that of rest (mass), and that of motion (momentum) —and it seems to me that living matter possesses a property, not hitherto recognised as such, which might be called functional inertia, or metabolic inertia of protoplasm whether animal or vegetable. It is owing to the inertia of matter at rest that the heavy gate, swung even on almost frictionless hinges, cannot be instantaneously set in motion; and when it has been set swinging, it is owing to its inertia of motion (momentum) that it continues to swing for some time after we have ceased to push it. By functional inertia of protoplasm I mean the power or property of protoplasm to remain in the metabolic status quo ante; if resting—anabolising—to remain doing so, even after the reception of a stimulus tending to bring about the opposite metabolic state, this might be called anabolic inertia; if active—katabolising—to remain so even after the reception of a stimulus tending to induce anabolism, or after the cessation of the stimulus that elicited the activity—katabolic inertia or functional momentum. Functional inertia is the power or property which bioplasm has of maintaining its functional status quo for a longer or shorter time according to the function considered; it is that power of continuing to exhibit the particular phenomena it has been exhibiting even after the death of the organism of which it is a constituent.