I have given the name of Radiant Spectrum to a phenomenon which I discovered in 1814, and which I described to this Society in the early part of that year.

It will be understood from fig. 1, which represents the brilliant radiation which surrounds a very small image of the sun, when it is formed either by reflection or refraction, or otherwise.

In this paper the solution of the well-known and hitherto refractory problem, “to investigate the law of motion of a uniform elastic plate,” is presented as an example of the application of the theory of primaries to physical research. This problem, on account of its importance in the theory of acoustics, has attracted the attention of the most celebrated mathematicians.

If we suppose a physical elastic line, flexible only in one plane, to have a number of masses fixed at intervals along it—if we investigate the law of the motions of these masses—and if, thereafter, we imagine the masses to be indefinitely subdivided and their parts distributed along the intervals, we shall arrive at the law of vibration of an elastic plate.

In an excellent little work recently published on elementary physiology, its author, when treating of the blood and its coagulation, remarks that a low temperature retards its coagulation; and that “blood kept at the freezing-point of water will not coagulate at all.” He adds: “Blood thus kept fluid will, however, coagulate when its temperature is raised; and blood has been thus cooled and warmed till near coagulation for three successive times without losing its coagulability.”

That the lowering the temperature of the blood retards its coagulation is now unquestionable; but the statement that it does not coagulate at all at the freezing-point of water, is new to me.

This ordeal poison is referred to in the works of Du Chaillu and Winwood Reade; and several of its toxic properties have been described by MM. Pecholier et Saintpierre. A few specimens were sent to this country in 1864 by the Rev. A. Bushnell of Baraka, and these were very kindly given to the author by Mr Thomson of Glasgow; and a further supply came from the same quarter in 1865. These gentlemen, and Dr Nassau of Bonita, supplied valuable and interesting information regarding its employment.

The poison is known in Africa as Akazga, Boundou (or M'Boundou), Ikaja, and Quai; Akazga being probably derived from nkazga, which signifies pain or hurt. It is used as an ordeal for the detection of real and superstitious crimes on the West Coast of Africa, in a large district which extends north and south of the equator, and many miles inland, and also in the adjacent island of Corisco.

In this paper the author's object was to show what propelling power was required and produced to push the fœtus through the passages into the world in the easiest deliveries. The fact chiefly founded on, as affording a basis for the necessary calculations, was the occasional birth of the ovum entire, that is, the membranes containing the fœtus and liquor amnii being entire after passing through the maternal passages. In such cases the strength of the amniotic membrane was greater than that of the parturient or expulsive power. The expulsive power was in them never so strong as to break the bag of membranes; and the tensile strength of the membrane being ascertained by experiment, the propelling power could be calculated from it.

The following problem, originally proposed by Fermat to Torricelli, To find the point the sum of whose distances from three given points is the least possible, seems to have given considerable trouble to the older mathematicians, and even in modern times (see Gregory's Examples, p. 126) to have been solved in a very tedious manner. Simpler solutions have since been given (e.g., Cambridge and Dublin Mathematical Journal, viii. p. 92), but none, to my knowledge, so direct as that indicated by Quaternions. The object of this note is to show the simplicity of the quaternion method.

This was a preliminary notice of a set of experiments, then in progress under very unfavourable circumstances, on the rare occasions when a ray of sunlight was procurable. The production of the phenomenon was traced to the peculiar texture of the membrane covering the cornea. The dependence of the whole on parallax was confirmed by the appearance of the radiant spectrum in precisely the same position with reference to the bright spectrum, when it was produced artificially by interposing a plate of slightly ground glass in the course of the light, so long as this plate was sufficiently near the eye to produce the phenomenon at all. A farther confirmation was given by the fact that, if the eye be near the prism, the appearance is the same on whichever side of the prism the ground glass be placed. The effects of achromatic prisms, of absorption by coloured glasses, and of the use of various kinds of homogeneous light taken from a pure spectrum, were also described.

A notice of a Gravimeter, proposed by me, appeared in the Proceedings of the Royal Society of Edinburgh early in 1861. The instrument, with various modifications, was forwarded to me in India about three years thereafter, and was found to have several imperfections which could have been corrected only by my own supervision of the work as it proceeded. His Highness the Rajah of Travancore has been good enough to sanction a sum of money for the construction of a second instrument, with all the precautions experience has suggested.

If U, V, &c., are rational and integral functions (*) (x, y, z)r, all of the same degree r, in regard to the co-ordinates (x, y, z), then is a polyzome, and the curve = 0 a polyzomal curve. Each of the curves (or say the curves U = 0, V = 0, &c.), is on account of its relation of circumscription to the curve , considered as a girdle thereto (ζωμα), and we have thence the term “zome” and the derived expressions “polyzome,” “zomal,” &c. If the number of the zomes , then we have a v-zome, and corresponding thereto a v-zomal curve; the curves U = 0, V = 0, &c., are the zomal curves or zomals thereof. Then cases v = 1, v = 2, are not, for their own sake, worthy of consideration; it is in general assumed that v is = 3 at least.

The object of the present Note is to show, by a few examples (of which, however, the last is the only one of any real importance), how easily the geometrical ideas supplied by Hamilton's beautiful invention of the Hodograph enable us to dispense with analytical processes in the establishment of some of the fundamental propositions connected with the motion of a single particle, besides many others which are merely curious; and also how they help us to understand the full bearing of some of the analytical methods. Some of the simplest of such geometrical investigations are given in “Tait and Steele's Dynamics of a Particle,” and will not be reproduced here; though a few of the results will be assumed,—as, for instance, that when the acceleration is directed to a fixed point, and varies inversely as the square of the distance from it, the hodograph is a circle, and the path a conic section, of which the point is a focus.