ĕ, ū and ŭ, ō and ŏ. These were:

(1) The doubling of the vowel when long, as in modern Dutch; thus, vootum = votum; aara = āra. This method was persistently used by the poet Attius^[1].

(2) By the use of a species of accent (apex) over the long vowel. This became quite general in the Augustan Age.

(3) The length of the vowel ī was denoted sometimes by making it longer than the other letters and sometimes by writing it ei; thus, DICO, PVEREI.

The Roman numerals V, X, L, C, D, M originated in various ways^[2].

V represented originally the open palm with the thumb extended, just as our 0 (zero) is thought to represent a closed hand.

X perhaps = , an old form of θ;; according to others, it is merely two V's placed together.

L = = or χ, a Greek letter which the Romans did not need in their alphabet and hence used only as a numeral.

C = , another form of θ, and confounded with C as though standing for centum.

M = φ, becoming first CI and then M, as though standing for mille, D is one half of this figure, or I^[3].

[1]. Quintilian, I. 7, 14. When i is doubled it always denotes the consonantal i (j); e.g. maiior.

[2]. Cf. Ball's History of Mathematics, pp. 119, 120.

[3]. See, on the whole subject, Taylor, The Alphabet (London, 1883); Kirchhoff, Geschichte des Griechischen Alphabets (4th ed, Gütersloh, 1887); Berger, Histoire de L'Écriture dans l'Antiquité; (Paris, 1891); Cantor, Vorlesungen über die Geschichte der Mathematik (Leipzig, 1880); Martin, Les Signes Numéraux et l'Arithmétique chez les Peuples de L'Antiquité; (Rome, 1864); and Friedlein, Die Zahlzeichen (Erlangen, 1869).

IV.

SOUNDS OF THE LETTERS.

1. A: ā had the sound of a in English "far"; ă had the sound of a in English "trespass."

There is no disagreement of opinion regarding the proper pronunciation of Latin a. All the modern languages derived from the Latin practically agree in the sounds which they give to this character. Furthermore, its pronunciation is described for us by Terentianus Maurus (p. 328 in the edition by Keil); by Marius Victorinus (p. 32 in the edition of the same editor); and also by Martianus Capella (III. 261).

[NOTE.—It must be remembered in the pronunciation of the Latin vowels that the short vowel does not differ in quality from the corresponding long one, but only in quantity, i.e. it occupied less time in pronouncing. This is an important distinction between Latin and English.]

2. B: had in general the sound of English b; but before s or t, the sound of p.

(a) The ordinary sound of Latin b is described for us by Martianus Capella (III. 261); and by Marius Victorinus (p. 32 Keil).

(b) That it was sounded like p when it stood before s we know because very often in inscriptions it is so written, e.g. pleps for plebs; Araps for Arabs; urps for urbs. In certain verbs this usage has modified the common orthography, e.g. scripsi for scribsi from scribo; and opseguor for obsequor. And so before t, as we learn both by the spelling of certain words (optulit, scriptum); and from the statement of Quintilian (I. 7. 7): "When I pronounce the word obtinuit, our rule of writing requires that the second letter should be b: but the ear catches the sound of p."

3. C: always had the sound of English k.

The facts upon which this statement is founded are as follows:

(a) The pronunciation of this letter is so described for us by Martianus Capella (III. 261) as to prove it a hard palatal.

(b) C took the place of an original k in the early alphabet as previously stated; and in succeeding ages at times c reappears in inscriptions indifferently before the various vowels. Thus we have the form Caelius alternating with Kaelius, Cerus with Kerus, and decembres with dekembres,—showing that c and k were identical in sound. Quintilian (I. 7. 10) says: "As regards k, I think it should not be used in any words...This remark I have not failed to make, for the reason that there are some who think k necessary when a follows; though there is the letter C, which has the same power before all vowels."

(c) In the Greek transliteration of Latin names, Latin c is always represented by k; and in Latin transliteration of Greek names, k is always represented by Latin c. And we know that Greek k was never assibilated before any vowel. Suidas calls the C on the Roman senators' shoes, "the Roman kappa."

(d) Words taken into Gothic and Old High German from the Latin at an early period invariably represent Latin c by k; thus, Latin carcer gives the Gothic karkara and the German Kerker; Latin Caesar gives the German Kaiser; Latin lucerna gives the Gothic lukarn; the Latin cellarium gives the German Keller; the Latin cerasus gives the German Kirsche. Also in late Hebrew, Latin c is regularly represented in transliteration by the hard consonant kôph.

[Advocates of the English system claim that Latin c had the sound of s before e or i because every modern language derived from the Latin has in some way modified c when thus used. It is true that modern languages have so modified it; but, as already noted, the modern languages are the children not of the classical Latin spoken in the days of Cicero, but of the provincial Latin spoken five or six centuries later. There is no doubt that at this late period, Latin c had become modified before e or i so as to be equivalent to s or z. Latin words received into German at this time represent c before e or i by z. But had this modification been a part of the usage of the classical language, it would have been noticed by the grammarians, who discuss each letter with great minuteness. Now no grammarian ever mentions more than one sound for Latin c. Again, if Latin c had ever had the sound of s, surely some of the Greeks, ignorant of Latin and spelling by ear, would at