Soc.), regards the property as occasioned by internal vibrations within the molecule conditioned by a symmetrical double tautomerism, light of one wave-length being absorbed by one form, and emitted with a different wave-length by the other.
It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density.
Owen for that division of ungulate mammals in which the toe corresponding to the middle (third) digit of the human hand and foot is symmetrical in itself, and larger than those on either side (when such are present).
In the tapirs and many extinct forms the fifth toe also remains on the fore-limb, but its presence does not interfere with the symmetrical arrangement of the remainder of the foot on each side of the median line of the third or middle digit.
The partition method of treating symmetrical algebra is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies.