80 A C C A C C question the motion became and continued uniform. If the motion is such that the velocity, thus measured, in creases or decreases by equal amounts in equal intervals of time, it is said to be uniformly accelerated or retarded. In that ease, if / denote the amount of increase or decrease of velocity corresponding to the unit of time, the whole of such increase or decrease in t units of time will evidently be ft, and therefore if u be the initial and v the final velocity for that interval, v = u ft, the upper sign apply ing to accelerated, the lower to retarded, motion. To find the distance or space, s, gone over in t units of time, let t be divided into n equal intervals. The velocities at the t 2 end of the successive intervals will be w / - , uf , n ?i 3t jf , &c. Let it now be supposed that diiring each of these small intervals the body has moved uniformly with its velocity at the end of the interval, then (since a body moving uniformly for x seconds with a velocity of y feet per second will move through xy feet) the spaces described in the successive intervals would be the product of the velocities given above by - , and the whole space in the time t would be the sum of these spaces; i.e., t t 2 = u -(1 + 1 ____ repeated n times) /- -^( ..... + n) It is evident, however, that as the increase or decrease of velocity takes place continuously, this sum will be too large; but the greater n is taken, or (which is the same thing) the smaller the intervals are during which the velocity is supposed to be uniform, the nearer will the result be to the truth. Hence making n as large as pos sible, or - as small as possible, t.e., = 0, we obtain as the n correct expression s = ut - ft 2 . In the case of motion from rest, u = 0, and the above formulae become v =ft, We have a familiar instance of uniformly accelerated and uniformly retarded motion in the case of bodies fall ing and rising vertically near the earth s surface, where, if the resistance of the air be neglected, the velocity of the body is increased or diminished, in consequence of the earth s attraction, by a uniform amount in each second of time. To this amount is given the name of the accelera tion of gravity (usually denoted by the letter a), the value of which, in our latitudes and at the surface of the sea, is very nearly 32J feet per second. Hence the space a body falls from rest in any number of seconds is readily found by multiplying 16 T ^- feet by the square of the number of seconds. For a fuller account of accelerating force, ex pressed in the notation of the Differential Calculus by 7 ^12 /= -7- or/= -=-- . the reader is referred to the article at at* DYNAMICS. ACCENT, in reading or speaking, is the stress or pressure of the voice upon a syllable of a word. The deriva tion of the term (Lat. accentus, quasi adcantus) clearly shows that it was employed by the classical grammarians to express the production of a musical effect. Its origin is therefore to be sought in the natural desire of man to gratify the ear by modulated sound, and probably no language exists in which it does not play a more or less important part. " Only a machine," says Professor Blackie (Place and Power of Accent in Language, in the Transac tions of the Royal Society of Edinburgh, 1871), "could produce a continuous series of sounds in undistinguished monotonous repetitions like the turn, turn, turn, of a drura; a rational being using words for a rational purpose to manifest his thoughts and feelings, necessarily accents both words and sentences in some way or other." That the accentuation of some languages is more distinct, various, and effective than that of others is beyond question, but there are none, so far as we know, in which its power is not felt. The statement sometimes made, that the French have no accent in their words, can only mean that their accent is less emphatic or less variously so than that of certain other nations. If it means more, it is not merely an error, but an absurdity. From this conception of the subject, it is obvious that accent must be funda mentally the same thing in all languages, and must aim more or less successfully at the same results, however diverse the rules by which it is governed. But there are, nevertheless, important differences between the conditions under which accent operated in the classical, and those in which it operates in modern tongues. It did not wholly determine the rhythm, nor in the least affect the metre of classical verse ; it did not fix the quantity or length of classical syllables. It was a musical element superadded to the measured structure of prose and verse. Passing over the consideration of the accentual system of the Hebrews with the single remark, that it exhibits, theugh with more elaborate and complicated expression, most of the characteristics both of Greek and English accent, we find that the Greeks employed three grammatical accents, viz., the acute accent ( ), which shows when the tone of the voice is to be raised ; the grave accent ( v ), when it is to be depressed ; and the circumflex accent ( A ), composed of both the acute and the grave, and pointing out a kind of undula tion of the voice. The Latins have made the same use as the Greeks of these three accents, and various modern nations, French, English, &c., have also adopted them. As to the Greek accents, now seen both in manuscripts and printed books, there has been great dispute about their antiquity and use. But the following things seem to be undoubtedly taught by the ancient grammarians and rhetoricians: (1.) That by accent (Trpoo-wSia, rovos) the Greeks understood the elevation or falling of the voice on a particular syllable of a word, either absolutely, or in relation to its position in a sentence, accompanied with an intension or remission of the vocal utterance on that syllable (e-TrtVao-is, aveo-is), occasioning a marked predominance of that syllable over the other syllables of the word. The predominance thus given, however, had no effect whatever on the quantity long or short of the accented syllable. The accented syllable in Greek as in English, might be long or it might be short ; elevation and emphasis of utterance being one thing, and prolongation of the vocal sound quite another thing, as any one acquainted with the first elements of music will at once perceive. The difficulty which many modern scholars have experienced in conceiving how a syllable could be accented and not lengthened, has arisen partly from a complete want of distinct ideas on the nature of the elements of which human speech is composed, and partly also from a vicious practice which has long pre vailed in the English schools, of reading Greek, not accord ing to the laws of its own accentuation, but according to the accent of Latin handed down to us through the Roman Catholic Church. For the rules of Latin accentuation are, as Quintilian and Cicero and the grammarians expressly mention, very different from the Greek; and the long syllable of a word has the accent in Latin in a hundred cases, where the musical habit of the Greek ear placed it upon the short. There is, besides, a vast number of words in Greek accented on the last syllable (like volunteer, ambuscade, in English),
of which not a single instance occurs in the Latin Ian-
