There are two main distinct methods of attacking the problem of the retaining wall. The first in chronological order is due to Coulomb, and is variously named, perhaps most commonly as the method of the Wedge of Least Eesistance. Briefly characterised, it might be said to depend upon the mathematical artifice of finding the resultant force due to the mutual action of the earth mass, and the wall a maximum, the earth being supposed to yield incipiently under the action of its weight, and in opposition to friction and the reaction in question, along an inclined plane determined so as to fulfil that imposed condition. Coulomb's method has been developed by various writers, and may be regarded as complete.

The opinion of the most profound workers in the so-called “germ diseases” is, that these diseases are really due to the pathological effects of chemical substances (ptomaïnes) elaborated and secreted by certain micro-organisms. That is, a given contagious disease is rather the result of one or more compounds formed by the life-history of a micro-organism, than the mere presence of that micro-organism itself. By looking at certain cases in the above light, we can well understand why persons suffering with cholera die so rapidly. The alkaloid or ptomaïne (discovered by Pouchet in 1885) which the Comma bacillus secretes or forms is rapidly absorbed into the blood, long before the bacillus itself is capable of being absorbed by the mucous membrane of the intestine, and then into the blood. It is a well-known fact that most micro-organisms multiply with great rapidity in the media in which they live, and if particular organisms can be destroyed, the harmful effects of the products produced by their life-histories will not increase, and the disease will soon be at an end.

In the course of some remarks on the design proposed for the Forth Bridge, the author of this paper had enunciated the remarkable theorem, that any symmetric structure built on a rectangular base, and depending on linear resistance alone, is necessarily unstable. The proof of it, given in the eleventh volume of the Transactions of the Royal Scottish Society of Arts, is derived from considerations affecting the special case; but this theorem is only one of an extensive class, and therefore the subject of instability among linear structures in general is here taken up.

In the case of regular or semi-regular arrangements, having the corners of an upper supported from the corners of an under polygon, it is shown that when the figures are of odd numbers the structures are stable, while those with even numbers are unstable ; unless indeed the polygons be placed conformably, in which case the stability extends to both classes.

In a paper communicated to this Society last Session I described some preliminary experiments on this subject, which led to the approximate empirical formula connecting current-strength and time

Many of the victims of the dynamite explosion, a year or two ago, in the London Underground Railway, are said to have lost the drum of one ear only, that nearest to the source. This seems to point to a projectile, not an undulatory, motion of the air and of the gases produced by the explosion. So long, in fact, as the disturbance travels faster than sound, it must necessarily be of this character, and would be capable of producing such effects.

Another curious fact apparently connected with the above is the (considerable) finite diameter of a flash of forked lightning. Such a flash is always photographed as a line of finite breadth, even when the focal length is short and the focal adjustment perfect. This cannot be ascribed to irradiation. The air seems, in fact, to be driven outwards from the track of the discharge with such speed as to render the immediately surrounding air instantaneously self-luminous by compression.

This problem, for the case of uniform temperature, was first, I believe, proposed by Tait in the following highly interesting question, set in the Ferguson Scholarship Examination (Glasgow, October 2, 1885):— “Assuming Boyle's Law for all pressures, form the equation for the equilibrium-density at any distance from the centre of a spherical attracting mass, placed in an infinite space filled originally with air; Find the special integral which depends on a power of the distance from the centre of the sphere alone.”

In the many theories that have been advanced to explain the comparative constancy of solar radiation in long past ages as evidenced by geological history, it has been generally assumed that the temperature of the sun has not varied much, and to account for its not falling in temperature a number of theories have been advanced, all suggesting different sources from which it may have received the energy which it radiates as heat. Since the chemical theory was shown to be insufficient to account for the vast amount of heat radiated, other theories, such as the meteoric theory and the conservation of energy theory, have been advanced.