MOLECULAR MECHANICS.
Among the theories proposed to explain the constitution of material substance, and to account for the facts relative to it disclosed by modern science, one developed in a recent work with the above title, by Rev. Joseph Bayma, of Stonyhurst, is specially worthy of notice for its ingenuity and the field which it opens to the mathematician. Whether it be true or not, it is at any rate such that its truth can be tested; and though this may be somewhat difficult, on account of the complexity of the necessary formulas and calculations, still the difficulty can probably be overcome in course of time, should the undertaking seem promising enough.
It is briefly as follows. Matter is not continuous, even in very small parts of its volume, but is composed of a definite number of ultimate elements, each of which occupies a mere point, and may be considered simply as a centre of force. This force is actually exerted by each of them following the law of gravitation as to its change of intensity with the distance; but is attractive for some elements and repulsive for others, which is obviously necessary to preserve equilibrium. These elements are arranged in regularly formed groups, in which the balance of the attractive and repulsive forces is such that each group, as well as the whole mass, is preserved from collapse or indefinite expansion; these are what are known chemically as molecules; and in the simple substances they probably have the shape of one of the five regular polyhedrons.
The simplest possible construction of a molecule would be one of the polyhedrons, with an element at each vertex, and one at the centre, whose action must be of an opposite character to that of those at the vertices; for these last must all exert the same kind of action, attractive or repulsive, for any kind of equilibrium to be maintained, and the centre must act in the opposite direction to prevent collapse or expansion of the mass. Furthermore, the absolute attractive power, or that which the molecule would have if all collected at one point, must exceed the repulsive, slightly at any rate, since the force exerted at distances compared with which its dimensions are insignificant is known to have this former character.
This system admits of two varieties, according as the centre is attractive or repulsive. In either case, for the maintenance of equilibrium the force of the centre must always be less than half that of the vertices combined, as the author shows, (giving the values for each polyhedron;) and it would seem that the first supposition would therefore be untenable, since the attractive force in each molecule, as just stated, necessarily exceeds the repulsive. Equilibrium certainly cannot be maintained in this case; but this will not involve the permanent collapse of the molecule, but merely a continual vibration of its elements back and forward through the centre.
The second hypothesis, on the other hand, requires either a centre so weak as to produce very little repulsion outside of the molecule, or else a continual tendency to expand under a central power too great for equilibrium. Both will tend to bring the molecular envelopes near to each other, and produce adhesion or mixing among them; also, it may perhaps be added, that the envelopes themselves will, on account of the mutual attraction of their elements, be unstable.
Of these two constructions, then, the first would seem most probable; but both are open to objection on account of there being no internal resistance in the individual molecules to a change of diameter proportional to a change produced by external action in that of a mass of them; and if such a change should take place, the mass would be in just the same statical conditions as before, only differing in the relative dimensions of its parts, and the resistance to pressure which is exhibited more or less by all matter would not be accounted for. But it does not seem quite certain that pressure or traction of the mass would operate upon the separate molecules in the same sense.
We are not, however, restricted to such a simple structure; for there may be several envelopes instead of only one, and of these some may be attractive and others repulsive; the centre also may be repulsive. There would have to be an absolute predominance of attractivity, of course, as in the previous more simple supposition. It seems probable that in this supposition the envelopes would be all tetrahedric, or that either the cube and octahedron, or the other two, which are similarly counterparts of each other, would alternate. Many of these forms are examined mathematically by the author, as to their internal action.
The exact discussion of their external action, however, would be exceedingly intricate, and would not be worth undertaking without a more definite idea than we yet have of the actual shapes presented by the molecules of the various known substances. The forms of crystallization may throw some light upon this, and they seem to indicate, as the author acknowledges, that the elements are not always grouped in regular polyhedrons; if they are not, they must have unequal powers, and this may be sometimes the case. But irregular crystalline forms are not impossible, or even improbable, with regular molecules. He also suggests and applies a method for obtaining the forms of the simple chemical substances by considering what combinations with others each polyhedron is capable of, and comparing these results with the actual combinations into which these various substances are known to enter, and deduces the shapes, with some plausibility, of the molecules of oxygen, nitrogen, carbon, hydrogen, phosphorus, chlorine, sulphur, arsenic, and iodine. Whether we shall ever be able to obtain more positive proof of these interesting conclusions remains to be seen; but if any molecules have really the number of envelopes that would be indicated by their chemical equivalents, the perfect determination of their exact mechanical conditions of combination, and even of their separate construction, will probably, as F. Bayma remarks, be a problem always above the power of the human mind. If mathematicians are at all inclined to plume themselves on having unravelled the complications of the solar system, they can find sufficient matter for humiliation in not being able to understand the status of a material particle less than the hundred millionth of an inch in diameter; for to this extent subdivision has actually been carried.
One of the most remarkable points in this theory is that part of it which relates to the ethereal medium which seems to pervade all space, if the undulatory theory of light is true, as is now perhaps universally believed. Instead of assuming it to be extremely rare, as is usually done without hesitation, the author regards it as excessively dense; "immensely denser than atmospheric air," to use his own words. Of course this seems absurd at first sight, as such a medium apparently would exert an immense resistance to the movements of the heavenly bodies, and in fact to all movements on their surfaces or elsewhere. This would certainly be the case if it were similar to ordinary matter; and to avoid this difficulty, it is assumed to be entirely attractive. The reason for supposing a great density for this substance is its immense elasticity and power of transmitting vibrations; which seems incompatible with great distances between its particles, unless these particles are extremely energetic in their action, which comes to the same thing; and this argument has considerable force.
But it does not seem evident that an attractive medium would not also interfere with the passage of bodies through it, though not in the same way as a repulsive one; and the oscillation through its centre necessary for its preservation complicates the theory somewhat. Also, any marked accumulation of a powerfully acting medium round the various celestial bodies would cause, if varied in any way by their changes of relative position, perturbations in their movements. The very fact, however, that its own action was so energetic might make the disturbance in its arrangement produced by other masses small, especially if it penetrates those masses, as is probably generally maintained. The subject is, of course, one of great difficulty, and objections readily suggest themselves to any hypothesis regarding it; still, it would appear that on some accounts it might be better, instead of assuming the medium to be wholly or predominantly attractive or repulsive, to suppose it to have the two forces equally balanced in its constitution; and if it be, like other matter, grouped in molecules, the balance would naturally exist in each molecule, making it inert at any but very small distances, and exerting at these very small distances a force the character of which would vary according to the direction.
We have said that the discussion of the exterior action of the molecules—that is, of their action on each other, or on exterior points in general—would be exceedingly complicated. The only way in which it seems practicable is that in which the mutual actions of the planets have been investigated, namely, a development of the force in the form of a series; but this cannot be done advantageously unless the distances between the molecules are considerably greater than the molecular diameters. If, however, we make the development of the ratio of the attraction (or repulsion) exerted by the vertices of a regular polyhedron in the direction of its centre, to what it would exert if concentrated at that centre, in a series of the powers of the ratio of the molecular radius to the distance of the point acted on from the centre, it will be found that the coefficients of the first and second powers vanish in all cases; and that in all, except that of the tetrahedron, those of all the odd powers also disappear, as well as that of the fourth in the dodecahedron and icosahedron. If, then, the absolute attractive or repulsive power of any envelope is very nearly compensated by that of an opposite character prevailing in the rest of the molecule, (as seems probable,) the whole series can be reduced, at any distance which is very great compared with the molecular diameter, to two terms—one a constant with a very small value, and the other containing the third, fourth, or sixth power of the small quantity which the ratio of the diameter to the distance has now become. This should have a negative multiplier, in order that the force should become zero; and this it will have for a considerable distance around the vertices of all the polyhedrons, the negative value always covering as much as two fifths of the spherical surface about the centre of the molecule, and compensating even in this case for its less extent by a greater intensity, as the mean of this coefficient over the whole surface is always exactly zero. Within this distance of no action, for some space about the centre of the prevailing polyhedric face, attraction would prevail till the higher powers became sensible, and even (as it would seem) quite up to the centre in the case of a single envelope, the repulsive action of which, when combined with the slight force of the centre, would apparently be limited to quasi-ellipsoidal spaces extending out from each vertex, and having a longer axis equal to this outer distance of no action. But this limitation of the repulsive action will be still greater if the excess of the absolute attractive power in the molecule is more considerable, as long as the distribution of the force in the different envelopes remains unaltered; and though the molecules can approach within tolerably short distances of each other in certain directions, this is not objectionable, since such an approach may even be required for chemical union and cohesion. Introsusception would hardly be probable, unless they were very different in size. The compound molecule once formed, whether its components were of the same or of different substance, might exercise a repulsive force at a considerable distance in all or nearly all directions; nevertheless, it might still admit of further increase or of disruption by an agitation among the molecules, due to heat, light, or electricity. Of course, even on this theory, for the maintenance of physical equilibrium the mean distance of the molecules would have to be considerably less than that of no action, in order that a repulsion should be produced to balance the attraction of those beyond this distance. Still, if the excess of attractive force in each molecule, and consequently the size of each, be made small enough, their dimensions may still be small compared even with this mean distance; so that in no case, except that of chemical union, would it be necessary to take account of the higher powers. Any motion communicated from one molecule to another would then probably be by means of an actual relative movement of the centres of gravity, instead of by internal vibrations.
It may be worth noticing that a regular polyhedron—the elements of which exert a force not varying at all with the distance, and in which the absolute energy of the centre is precisely equal to that of the vertices combined—gives a resulting force following the law of gravitation, at any distance compared with which its own dimensions can be neglected; and within this distance the force will change its sign under the same conditions of direction as specified in the previous case. But, as the intensity of this force will change with the size of the molecule, it does not appear that a system of this kind would be admissible, since, besides the periodical change due to its own internal vibration, it would probably be changed in size, or even in shape, which would be worse, by compression or expansion of the mass; which would be the more likely, as the molecules could approach much nearer than in the former supposition. The law followed by gravitation also seems to be almost or quite necessary for forces radiating from a point.
The author's theory seems, on the whole, extremely plausible. That each element of matter exerts a force following the law of gravitation, is almost demonstrable à priori; that the elements are mere points, will also generally be admitted; that some of the actions should be repulsive, is obviously necessary; that each molecule is composed of a definite number of atoms, is suggested by chemical laws; and the polyhedric forms seem certainly the most reasonable, though crystalline forms would indicate that others may be occasionally found. The possibility of the construction of irregular molecules out of elements of unequal powers seems, by the way, to be worth examining.
Further developments of the theory may have recently been made; of course, the author does not claim in this work to have laid down more than its first principles. At present, it seems, to say the least, to furnish the best basis for the mathematical investigation of the internal constitution of matter that has been suggested, and such investigations would be almost certain to lead to valuable results, whether confirmatory or otherwise.
THE HOLY-WEEK OF 1869 IN HAVANA.
PALM-SUNDAY. THE TENEBRÆ. MAUNDY-THURSDAY.
So much had been told me of the antiquated observances of the Holy-Week in Havana, of the religious processions presenting to us of the nineteenth century an image of the naïf faith of the middle ages, of the rare spectacle of a whole city in mourning for the death of the Saviour, that even had my duty not called me to the church, my curiosity would have carried me thither. As it was, I resolved this Lent that, although I resided at an inconvenient distance from town, and ladies who have no carriage of their own find it sometimes unpleasant to go on foot in a country where walking is unfashionable, and considered even unfeminine, yet I would disregard disagreeables of every kind, and attend all the impressive ceremonies of this great week in the cathedral.