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.