ment. On the one hand, Müller, who had had a great influence in guiding public opinion in this region, stoutly asserted that out of the three primal elements, as from a root, no further growth of what we called human language, for reasonable social purposes, could take place; while, on the other hand, Wedgwood-who in this whole matter had, in his opinion, received scant recognition from the scholars of his own country-as stoutly maintained that from these three elements, as their natural root, the whole organism of the beautiful growth of language, stem, leaf, and fruit, could be satisfactorily explained. After carefully studying the arguments of the learned Oxford Professor, he was of opinion that Wedgwood was in the main right. To this conclusion he came from a course of independent investigation some years ago, and when, curiously enough, he had only used Wedgwood's dictionary for occasional consultation, without having read and pondered the discourse prefixed to the last edition of that work. The grounds of his opposition to Müller were stated to be simply these:-While in perfect agreement with him that roots significant of ideas are the ultimate facts in the analysis of languages as we now have them, and believing also that such conceptional roots are the natural and necessary expression of reason in a reasoning animal, and explicable only on the supposition of an indwelling plastic reason in man, I am at the same time unable to see why this plastic reason in the formative process of language-making should not have used the materials so amply supplied by the interjectional and mimetic elements of the simplest germs of speech. The interjectional element, I call the principle of significant vocal response; and the onomatopoetic principle, I call the mimetic, dramatic, or pictorial element in language; and I am prepared to show that, even under the many defacements and obliterations which spoken words, like old sixpences or waveworn pebbles, suffer from the tear and wear of time, they yet show in hundreds of cases on their face the manifest superscription of their mimetic origin. For we must take note, first, that not only pigs and cuckoos, cats, curs, and crows, but all nature, is full of sounds, and that there is no absolute silence anywhere but in death; and, further, that not only an immense variety of sounds can be approximately expressed by imitation in articulated vocal breath, but that by an easy transference the impressions of the other senses can be analogically expressed in the flexible material of significant

sound. It is also not only an easy but a natural and necessary process of the human mind in the formation of general concepts to use the material presented by mere sensuous impressions; and thus, while we expressly deny the perverse doctrine of the sensationists that mind can be explained from sense, or the imperial unity of thought be generated from a multiplicity of external impressions, we can see no difficulty in deriving such general concepts as character and type, for instance, from the roots xapáσow and TÚTTW, which originally were mere mimetic reproductions of an external sound, as in our word scratch. Language, therefore, was formed by the gradual extension of words originally expressing sensations and feelings to intellectual purposes; and there is nothing ignoble in this, for the mind uses the materials supplied by sense just as the architect uses the stones dug by the quarryman or the lime carried by the hodman. Neither can one at all see the logical justice of Max-Müller when he exposes the historical falsehood of some of Wedgwood's onomatopoetic etymologies; for the erroneous application of a principle does not in the least imply that the principle itself is erroneous; and, besides, the oldest roots to which certain very recent forms of Romanesque words may be traced back in Sanscrit can be shown in not a few cases to have been the product of that very mimetic process which Müller so persistently ignores. But while Müller seems actuated by some strange prejudice in his stout determination to make no use of the onomatopoetic element so thickly strewn in language, Professor Whitney has introduced no little confusion into this matter by talking of language as an institution, and reviving the doctrine of the old Greek Sophists, that language is ére, not pure. Every simile limps; but if we must have similes, it is far nearer the truth to talk of language as a growth and a living organism than to call it an institution. In some sense language is certainly a growth; in no sense is it an institution. Institutions like the Sabbath, for instance, are then creatures of positive law; but language is a direct efflux of plastic reason, and no more an institution than the song of the nightingale or a sonata of Beethoven. As to the connection between Darwinism and the origin of language, while the Darwinian philologers, with Schleicher at their head, will no doubt find a special delight in tracing the splendid roll of a Platonic period from the grumph of

the primeval pig, and the mew of the pre-Adamitie kitten, those who with me look on Darwinism as a mere pleasant conceit of men besotted in the one-sided study of physical science, can, so far as philological conclusions are concerned, leave the conceit to shift for itself, being firmly convinced that whenever reason does show itself whether on the original appearance of man or at some after-stage of his development, it appears as a force altogether different from, and in some of its functions, as Professor Ferrier wisely maintained, essentially contradictory of, and antagonistic to, every kind and degree of mere sensation; and in this character brings forth language as the natural manifestation and organised body of itself.

Monday, 7th February 1876.

SIR WILLIAM THOMSON, President, in the Chair. The following Communications were read:

1. Note on Certain Formulæ in the Calculus of Operations. By Professor Stokes, Hon. F.R.S.E. (In a letter to Professor Tait.)

*

66 'January 14th, 1876. "Formulæ like those you sent me are readily suggested by supposing the function operated on to be of the form Axa, or say, for shortness, xa, with the understanding that no transformations are to be made which are not equally valid for ΣAxa.

and

Thus

( d x d )"xa = a2(a− 1)2 . . . (a− n+1)2x2-^

dx dx

The direct transformation may readily be effected by noticing,

in the first instance, that any two operations of the form

into which m and n enter symmetrically.

Replacing the operations in the left hand member of the first formula by convertible operations, which will be separated by points, we find

2. A Further Contribution to the Placentation of the Cetacea

(Monodon Monoceros). By Professor Turner.

In the year 1871, I read before this Society a memoir on the Gravid Uterus of Orca gladiator, in which I discussed the placentation of the Cetacea. This memoir was published in the Transactions for that year. On the present occasion I purpose describing the placenta in a Cetacean genus in which it has not hitherto been examined.

In the month of December 1875 I received, through the intermediation of my friend Mr C. W. Peach, from Mr John Maclauchlan, the chief Librarian and Curator to the Free Library, Dundee, a cask containing the gravid uterus of a Narwhal (Monodon Monoceros), which had been procured by the captain of the Dundee whaling steamer "Erik." The uterus had been preserved in strong brine, and was in good condition for anatomical examination.

The uterus was two-horned, and contained a foetus 5 feet 5 inches long in the left cornu. The gravid horn measured 7 feet 4 inches along its great curvature; the non-gravid, 4 feet. The girth of the gravid horn, at its thickest part, was 4 feet 4 inches. The length of the corpus uteri was 1 foot; that of the vagina, 1 foot 8 inches. The os was occluded by an extremely viscid mucus.

The uterine cornua were opened into by a longitudinal incision along the greater curvatures. The uterine wall was comparatively thin, and the chorion was closely adherent to its mucous lining. By an incision through the chorion, along the greater curvature of the gravid horn, the sac of the amnion was opened into and the foetus exposed. The foetus lay with its back in relation to the greater curvature of the cornu, its belly to the lesser curvature, its head close to the corpus uteri; whilst its caudal end was directed to the narrow end of the horn, but did not reach to within two feet of the Fallopian tube. The tail was curved forwards under the hinder part of the ventral surface of the foetus. The pectoral flipper was directed backwards parallel to the long axis of the body. The umbilical cord was 3 feet long, spirally twisted, and bifurcating where it reached the sac of the allantois. The amnion formed an immense bag, which reached to 5 inches from the free end of the gravid horn of the chorion, but it did not extend into that part of