ing and delicacy of hue. On the other hand, chiaroscuro is totally wanting; so that, if we were to argue from the single case of Egyptian painting, as Mr. Gladstone has argued from the single case of Homeric poetry, we might arrive at the diametrically opposite conclusion, that early man possessed a developed colour-sense, but no perception of light and shade.

How then are we to explain the singular fact, which Mr. Gladstone undoubtedly succeeds in proving, that the Homeric ballads contain few actual colour-epithets ? In the following manner, it seems to me. Language is at any time an index of the needs of intercommunication, not of the abstract perceptions, of those who use it. Now, in nature, the bright-coloured objects are chiefly flowers, fruits, birds, butterflies, autumn leaves, and other organic products, of little practical importance to the Akhaian warrior. The objects which he needs to describe are earth, sky, clouds, sea, men, arms, cattle; all of them indefinitely coloured, and many of them liable to great changes in light and shade, or great variations between individuals. Hence the need for colour-terms does not practically arise. Again, the growth of colour-terminology seems to me to be greatly dependent upon the art of dyeing, and the consequent use of pigments for human decoration. In our own time, such colours as mauve, magenta, solferino, écru, &c., only come to have names as fashion introduces them into dress and the vocabulary of artists, house-painters, milliners, and drapers, is much richer in colour-terms than that of ordinary Europeans. So the two words which most express colour in the Homeric ballads are those which refer to the dye of the Tyrian murex and the so-called vermilion. Both of these were probably more or less reddish; and we know from modern experience that reds and purples are the colours which children and savages most admire. I have tried elsewhere to account for this preference: it is sufficient here to note that red seems everywhere the earliest colour used for decorative purposes. On the whole, I think we may conclude that while a loose chromatic sense is to be attached to two or three Homeric words, the majority of visual epithets occurring in the ballads are to be accepted as referring to light and shade alone; because the need for colourterms was not yet felt among a race of non-manufacturing warriors, and because the gleam of bronze, the light of day, the bright or lowering sky, the indefinite hues of man and horse and cattle, were far more relatively important than the pure tints of flowers and insects, or the almost unknown art-products of Egypt, Phoenicia, and Assyria. As for the range of Homeric colour-epithets, I think it sufficient to note that we ourselves talk of a red sky, red wine, red bricks, a red cow, red lips and red Indians; or of blue heavens, blue sea, blue eyes, blue frock-coats and blue slate.

It will be obvious that I have only given such principal headings as seem indispensable, and have been precluded from further illustration by want of space. But the three points I have tried to make out are briefly these; (1) That colour-perception is a common possession of men and animals; (2) That it is therefore, a fortiori, a

common possession of all normally-developed men; (3) That the want of colour-epithets in the Homeric poems is due to a defect of language rather than of perception, such as might naturally be expected from the circumstances of their authors. As to the existence and personality of a Homer, that is quite outside the present question.* GRANT ALLEN.

A short notice of the two tracts, by Dr. H. Magnus of Breslau, which called forth Mr. Gladstone's recent utterance on the subject, will be found below under the head of New Books. Prof. Robertson Smith, in a letter that appeared in Nature of Dec. 6th, gives brief expression to a view of the question essentially the same as Mr. Allen's (whose Note was independently written some weeks before), and cites a most interesting passage from Athenaeus, Deipnos. xiii., 81, which proves that the Greeks themselves were perfectly well aware of the looseness of their poetic vocabulary of colour.

EDITOR.

"Transposition of Traces of Experience."-To the process thus aptly designated Mr. Verdon devotes a short paragraph in his valuable article on 66 Forgetfulness" in the last number of MIND. In each instance of its occurrence, as there represented, we find involved two objects of memory,-(1) a pair of words, syllables, or sounds, and (2) their order in a sentence. The former of these, viewed independently, are supposed to be perfectly well remembered: failure of memory exhibits itself only in respect of the latter. The writer adds that "the whole family of Malapropisms is nurtured upon this peculiarity". Now this general statement may or may not be true in its fullest extent; but before we admit its truth, we must at any rate examine many other typical examples of transposition than those of the exact kind indicated by Mr. Verdon.

At the outset, Malapropism' may be referred to a more general 'Maladroitism,' which brings dumb actions within our purview. In fact, the transposition of these is often more striking, and sometimes more amusing, than that of words. Thus a man shall, like Will Honeycomb, be standing by a river-side with his watch in one hand and a pebble in the other: he shall "squirr away his watch" into the water, and shall (" with great sedateness") pocket the pebble. Here the two familiar actions transposed correspond to the two remembered words above referred to, and just as these may be accurately spoken, so may those be accurately performed. But here, and generally, the order of combination is totally new,-an arrangement proposed, and not formerly learnt. How far, then, and in what sense, is a perturbation of that order chargeable upon failure of memory? Shall we say that an order of procedure is directed by the mind and instantaneously forgotten? or is, perchance, the apparently perturbed order of procedure the one actually directed, while forgetfulness relates to the positions of the objects,-it being momentarily forgotten that the watch lies (say) in the right hand, and the pebble in the left? And

what, if those positions have not been accurately perceived? Can that be, strictly speaking, forgotten which has never really been apprehended?

In a certain sense, indeed, we may be said to forget everything but the object on which the mind is, at each successive instant, actually fixed; nevertheless mistakes that fall within the present moment (this being understood to correspond with a material rather than a mathematical point) are generally charged upon want of attention. It would seem sometimes, as if the mind, after directing the performance of two actions, instead of superintending the performance, leaves the limbs to act, so to say, automatically; and these excite that action first which, from a nerve-and-muscle point of view, is the more important, or to which the more energetic impulse has been given. Or, again, the operations of the mind being much more rapid than the movements of its material agents, these the limb, the tongue, the pen-necessarily lag behind, and are continually trying, as it were, to catch it up by leaping to that point in the line of thought to which the mind has preceded them; while the mind is as continually running back to bring them up abreast of itself. When these two movements occur simultaneously the result is some more or less grotesque transposition.

Hence, a general condition of complete interchange of two such actions, words, or what not, is that they fall pretty close together,close, i.e., in time. If hand or tongue lags behind by any long interval, the mind, in reverting to its agent, usually discovers, and if possible rectifies, the first mistake, or at any rate prevents the perpetration of the counterbalancing one. This is nearly always the case in the comparatively slow process of writing. In a rapid succession of actions, moreover, the attention may be forcibly recalled by the oddity or physical effects of the first mistake. Thus, a friend of mine, dressing in great haste, and intending to use his shaving-brush and tooth-brush in succession, dashed the former vigorously into his mouth. Need it be added that he did not apply the other to his chin?

But this uncompleted interchange must, in the case of words, be discriminated from a species of Malapropism in which no interchange is either intended or possible; as e.g., when Mrs. Malaprop herself talks of the burning lather running down Mount Vociferous. Here we step over our bounds into the region of what the Germans call Volksetymologie, and find ourselves among linguistic phenomena of the "sparrow-grass" type. A foreign or strange word (never correctly apprehended) is assimilated to a native or familiar one; and then some absurd reason is invented for the special application of the latter.

But purely phonetic interchanges may certainly be embraced under the general process. These, although curtly dismissed by Mr. Verdon, are perhaps more interesting and linguistically important than any others. The accidental slips (for example, with their h's), to which the best-educated people are liable, are indeed mere trifles, and are

explicable in the same way as the interchanges above referred to. But in other classes of society real or apparent varieties of such phonetic interchange, which I have elsewhere designated "Cross Compensation" (Grimm's Law, Trübner, 1876) have established themselves as dialectic characteristics. Thus the plant-seller that haunts our ways all the summer vociferates "Roots for your garding all agrowin and ablowin"; and the lavender girl that follows him sings "sweet-smellin lavingder," &c. This class of instances, therefore, offers for investigation not only an origin but a history.*

The object of this note, however, is not (as is obvious enough) to investigate these curious phenomena, so much as to suggest that they deserve investigation. If Mr. Verdon, or some other professed psychologist, would subject them to a thorough discussion, he would, besides amusing himself, instruct inquirers in other lines of study (language, for example) which, without being purely psychological, necessitate a frequent reference to psychological principles.

T. LE M. Douse.

Prof. Jevons's criticism of Boole's Logical System.-The appearance of a new edition of Prof. Jevons's Principles of Science shows that his partial adaptation of Boole's system has gained a wider circulation than its original, and renders not inopportune a few words on the two men.

So

In the preface to this second edition Prof. Jevons says: "As to my own views of Logic, they were originally moulded by a careful study of Boole's works, as fully stated in my first logical essay". it has seemed best to me to go back to this Pure Logic of 1864, and taking his first and last works together, to discuss carefully his criticisms of Boole. In both books one is struck by the fact that Prof. Jevons has never risen from the conception of the old Algebra of Number to the idea of Algebras in general. For him "all the wondrous branches of mathematical calculus" are merely developed Arithmetic (P. of S., p. 162). Yet he appreciates the importance of Descartes' mathematical discovery without noting that it was really making a new Algebra, the Algebra of Geometry, introducing the directed line, the variable, &c., and not being a mere outgrowth from the old Algebra of Number. He mentions also the new Algebra of Quaternions, which contains laws flatly contradicting those of number, yet he does not draw the obvious conclusion. Finally, though Boole's Algebra of Logic is founded on the condition 22 = x or x (1 − x) = 0, which is not true of numbers in general, Prof. Jevons persists in considering it "a numerical system ".

What would he say of Grassmann's system, of Mr. Spottiswoode's

Many examples may be collected by the student of English popular idioms. A collection from the German dialects has recently appeared in Herr J. F. Kräuter's treatise Die Lautverschiebung, pp. 60-62.

little paper on Recent Algebras, finally of the Linear Associative Algebras of Prof. Peirce? Are they all the same old original Algebra of Number? As Prof. Peirce says: "Qualitative relations can be considered by themselves without regard to quantity; the algebra of such inquiries may be called logical algebra, of which a fine example is given by Boole". Yes, in spite of Prof. Jevons's continued mistakes on this point, what Boole actually did was to create the first and greatest Algebra of Logic. And now we are able to rate at their proper worth all attempts to "divest his system of a mathematical dress".

From this foundation we are ready to take up in order the objections made by Prof. Jevons to his master's system, and I think we shall see that nearly all of them are mere corollaries of his First Objection, which itself is untenable. It has reference to the old question about the proper method of expressing alternatives. In popular usage, says Prof. Jevons (Pure Logic, p. 77), "the meanings of terms joined by 'and''or' vary from absolute identity up to absolute contrariety". But, as Mr. Venn says (MIND IV., p. 489)-"The really important thing is to improve upon popular vagueness, by keeping prominently before the mind the fact that there is this ambiguity. This is just one of the things that symbolic language can and should do, and Boole's expressions have the merit of great clearness and precision here. Sometimes what we mean is A or B or, it may be, both '; sometimes A or B but not both'. These are surely such distinctive meanings that it is a real blemish in common language to merge them together, for we certainly ought to know, in any given case, which of the two we have in mind. This Boole indicates by always using a(1 — b) + b(1 − a) for the exclusive sense, and a + b(1 - a) for the non-exclusive." I perfectly agree with Mr. Venn that Boole is here quite unassailable, yet Prof. Jevons's Second and Third Objections depend directly upon this First, and vanish into thin air with the hook on which they hung.

6

He words the Second Objection thus: "There are no such operations as addition and subtraction in pure logic," for which statement his proof is that in his Logic, which leaves the alternatives indefinite, one cannot safely subtract. This looks like an argument against himself, and is certainly no argument against Boole. Again, acknowledging that "subtraction is valid under the logical restriction that the several alternatives of a term shall be mutually exclusive or contrary," he tries still to uphold the point by saying that the result of the subtraction can be obtained by combination. What of that? In arithmetic the result of multiplication may be obtained by addition. Does that prove that there is no such operation as multiplication in arithmetic ?

The Third Objection hangs likewise on the untenable First. Boole found he could make a more perfect system by postulating that each two terms must be logically distinct, and so in his system there was no such thing as what Prof. Jevons has named the Law of Unity, (A + AA) Making what seems to me a puerile application of this law to a system which expressly excludes it, he says that xx