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in mind the true original significance of the terminations; and all words should, then, be considered to be strictly nouns, and to be adjectivally connected with one another, as the parts of compound words are always connected. The oversight of this necessary connection of two parts of compound words, the first as adjective to the second, has led to some common mistakes as to the real meaning of the compounds, and to the impression that the order of the component parts made no difference in the meaning. For example, it has been supposed that the meaning of the names Theodore and Dorothy were the same; Theodore would be God-gift, and Dorothy would be Gift-goddess. Spermophile, seed-loving, Anglophile, English-loving, Russophobe, Russian-fearing, are correctly used; but Phil-hellene means friendly Greek, and Philander, not man-loving, but a loving (or friendly) man. Philadelphi means friendly brothers, and Philadelphia means friendly brotherhood, not brotherly love. Philosophy would, accordingly, appear to be, not love of wisdom, but friendly wisdom, the occupation of the philosopher, or friendly wiseman, as contrasted with that of the mere sophist; and the modern word philology (perhaps meaning properly science of loving) should have been logology, or glossology. That universal acceptance and high authority are not a wholly unimpeachable guaranty against mistranslations is evident from flagrant errors that are to be seen outside the range of our present subject. For instance, a scholar profoundly versed in the Chinese language has given currency to the translation “Middle Kingdom” for the Chinese name of China proper; but the same expression is used in Japan for the Central Provinces, or Home Provinces (or our Middle States, which would be so written in Chinese), and that appears to be the true meaning. The Japanese (or Chinese) name for Corea, Chosen, has somehow come to be translated Land of the Morning Calm; but its real meaning is Morning Earliness, sen meaning fresh, or new, as recently caught fish is fresh. While Japan means Sun-rising, the country next westward is appropriately called Morning-early. Evidently, we cannot put implicit faith in what has come from high sources and has been widely accepted.

In Chinese, totally without welded terminations, words are plainly connected only in the adjectival way, and as, in the writing, there

are no punctuation-marks, the meaning is not always clear to a beginner. We have the same source of obscurity in English, especially in shop-signs and brief inscriptions. A Chinaman might, for example, find it difficult to know the precisely correct meaning of an inscription on a certain wagon in Philadelphia: “The largest old book store in the city"; or of the signs: “Circular Saw Mills ”; "Fine Fur Felt Hats”; “North Broad Street Farmers' Market”; or the advertisement-heading: “Excelsior Straightway Back Pressure Valve”; or: “The Vare School Garden Base Ball Team.” In the spoken language, the pauses and intonations indicate the grouping of the words and the consequent meaning. The grouping might well be shown in printing with the hyphen; but that would be irksome in manuscript writing, unless the hyphen should conventionally be written with a little quirk, too small to be taken for the letter e, and without lifting the pen: “Old-book store."

It is clear, then, that the so-called Japanese verb is in reality merely a verbal noun, and that much is to be gained by calling it by its right name, and bearing its true character in mind, and remembering that its connection with other words is precisely adjectival, either as an adjective itself, or as the substantive to an adjective. It is plain, too, that in European languages the terminations that give to words the distinctive meaning of different parts of speech were originally separate words connected in the same adjectival manner to the present roots, and that the original significance of those separate words before being welded into mere terminations was, in the case of the Latin and English genitive and plural terminations in s and the Latin infinitive termination in se (now re), simply thing; which, also, is the original meaning of the German possessive, plural and infinitive terminations in en, and of the antiquated English plural termination in en; and of the termination ing of English verbal nouns. The resemblance between the two western terminations in s and en and the Japanese particles tsu and no of like meaning, though not at all essential in identifying the character of the terminations, is interesting, whether regarded as merely a coincidence in languages grammatically far apart, or as possible relics, together with many others equally remarkable, from some

PROC. AMER. PHIL. SOC., LI. 204 D, PRINTED MAY 23, 1912.

extremely ancient common language, leading back towards the original human language and even towards the utterances of brute animals. Evidently, the earliest languages must have had their words connected purely as adjectives and substantives, as is still common in English, and is universally the case with the parts of compounds. The English language shows that the grammar of a language may within a few hundred years become radically changed; and, in spite of historical and geographical remoteness, has acquired grammatical resemblance to Chinese.

THE VALIDITY OF THE LAW OF RATIONAL INDICES, AND THE ANALOGY BETWEEN THE FUNDAMENTAL LAWS OF CHEMISTRY AND

CRYSTALLOGRAPHY.

BY AUSTIN F. ROGERS.

(Read March 1, 1912.)

Some fundamental law of nature governs the position of the faces of a crystal and limits in number the faces which occur on the crystals of any one substance. Crystal faces are designated by intercepts on coördinate axes, which are chosen so as to yield simple relations. Now it is found that the intercepts of the various crystal faces of a given substance, on each coördinate axis taken separately,

Fig. 1. The coördinate axes of a crystal.

usually bear a simple ratio to each other such as 1:0, 1:2, 1:3, 2:3, 3:1, etc. A selected face chosen because of its prominence is taken as a standard and the other faces are expressed in terms of it. The selected face is called the unit face, as its intercepts on the three axes establish a unit which, in general, is different for each axis, as represented in Fig. 1. The intercepts of the unit face which are, in

general, irrational constitute the axial ratios which are constants for each crystallized substance. For convenience in calculation the reciprocal ratios of the intercepts are used. These reciprocals are called indices or Miller indices, as Miller, an English crystallographer, was the first to make extensive use of this method. The indices are usually simple numbers such as (110), (210), (130), (211), (321), (441), etc., the unit face being (111).

If we examine the statements concerning the rationality of the indices of crystal faces in text-books and treatises we find a difference of opinion as to the exact definition of the law. Some authors insist that the indices are small whole numbers, while others simply state the fact that the indices are whole numbers, usually, but not necessarily small. One crystallographer, Viola, goes so far as to doubt the validity of the law of rational indices. Another investigator, G. H. F. Smith, believes that the law of simple rational indices is valid except in one particular instance, that of calaverite from Cripple Creek, Colorado. But, as he shows, by assuming several interpenetrant space-lattices it may be valid even in this case.

Thus there are three possibilities to consider: (1) The indices are always small rational numbers. (2) The indices are rational numbers, but not necessarily small. (3) The indices are not always rational and the law has no meaning. This subject is such a fundamental one in both theoretical and practical crystallography that it seems advisable to enquire into the history and status of the law. Such is the object of this paper.

The credit of the discovery of the rationality of the indices is due to Haüy, professor of the humanities in the University of Paris, who developed it from his theory of crystal structure based upon cleavage observations. Haüy believed that crystals are composed of minute cleavage fragments which he called molécules intégrantes. Primary faces, according to his view, are due to the association of the molécules in parallel position, while secondary faces are due to the omission of molécules on the exterior of the crystal in step-like

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* Zeitschrift für Krystallographie und Mineralogie, Vol. 34, pp. 353-388 (1901).

Mineralogical Magazine, Vol. 13, p. 122 (1902).

Essai d'une Theorie sur la Structure des Crystaux." Paris, 1784.

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