NUMERATION. 678 NUMISMATIC SOCIETY. millions, billions, trillions, etc. Each group of integers includes three orders, viz. : ( I ) the order of the group itself; (2) the tens of that order; and (3) the hundreds of that order. Siiiiiliirly, in each group of decimals the three orders are: (1) the order of the group it.self; (2) the hun- dredths of the order of the preceding group; and (:j) the tenths of the order of the preceding group. Tlius, for example, the number 9,;i21.;i4oU7 is expressed: Thousands Units ThouMandtha Milllonths 9 O .a X .=
- f 3 =
111 9 32134 5 670 Usage has not fully determined the names to be employed beyond hundred millions. The French and Americans call 1000 millions a bil- lion; the Knglish and Germans use the word billion to designate a million million, and so on in groups of six figures. NUMERICAL NOTATION. In modem music, a syslcm used in t lic<iretical works on nuisic, of indicating single tones or entire chords by means of numerals. Kvcry tone of a musical instrument can be denoted l)y a numerical sign indicating accurately its pitcli. Middle (' (the first note of the treble-clef rwiuiring a leger-line beloiv, or the first note of the bass-clef requir- ing a legerline above) is denoted by the small letter c with the number 1 placed on the right side above, c". The tones of the octave below this middle C are indicated by the small letters of the alphabet uilhout any numbers, c, d. e, f. g, a, b; the next lower octave by the capital let- ters, C, P. E. F, t;. A, H: the "octave below this by capitals with the numlM-r 1 (either on the right side above, or. better. <m the left side l)elow), ,C. ,D. ,E. or (", B', E", etc. The octave begiiming with nii<ldle C adds the num- ber 1 to the small letters^ c', d', e'. etc.; the next octave adds 2, c', d", e', etc. ; the next 3, c", d', e', etc. This system of notation is espe- cially used in indicating the range of various instruments. The range, therefore, of the piano can briefly be indicated as from ,A — c The pitch of the dilVerciit strings of the violin is accuratelv indicated bv g. d", a', e-; of the cello by C, a,' (I a. Arabic figures are also used to indicate the fingering in compositions. For finger-marking on the violin only four numbers are useil, as the thumb is not used in playing that instrument. 1 refers to the index. 2 to the middle finger, etc. In marking the fingering of piano compositions the thumb is indicated by 1, the index by 2. middle finger by 3, etc. The older system of marking the thumb by x. and the othiT lingers as in violin-nnisic, has fallen into complete dis- use. For use of figures in figured bass notation, see Ftr.rREn B,.ss. In violin music the Roman numerals I, II, III, IV represent the strings e. a. d, g, respec- lively, but ordinarily Riinian figures are employed to indicate chords. A large figure indicates a major, a small a minor, triad. The name of the key is placed before the figure, a capital letter to denote a major, a small letter to denote a minor key. Thus A 1' means the sub- dominant of A major (a major chord on the fourth degree of A) ; t' iii, the minor triad on the third degree of t' major: a ', the dominant of A minor (a major triad on the fifth de- gree). A diminished triad is marked by a small figure with a on the upper right side; an augmented triad, by a jnime ('). Thus Dvii" means the diminished triad on the seventli degree of 1) major (c;, e, g) ; fill', the augmented triad on the third degree of F minor (ab, c, e). Chords of the seventh are indicated as the triads with an Arabic 7 on the lower right side; GV, means the chord of the dominant seventh in G (d, fjt, a, c) ; bvii^.the chord of the diminished seventh in H minor (alt, cJJ, e, g). This system was introduced by the eminent theori>t (i. Weber. NUMIiyiA ( Lat., from Xumida, Mumidian, nomad, from Gk. vo^ds, itttnias, nomad, from vdficiv, nrmcin, to pasture, to distribute). Urig- inally the Roman name for that part of Xorthern Africa lying between the provinces of Africa Pro- pria and JIauretania, corresponding very nearly to the modern Algeria. It was bounded on the west by the river Jlulucha (now Jluluya), which separated it from Mauretania, and on the east by the river Tnsca (now Wadi-el-Berber). On the south it reai'hed to the chains of Mount Atlas and the T.acus Tritonis. which separated it from the land of the Ga'tulians and Libya. The inhabitants of Numidia, as of ilauretania, belonged to the race from which the modern Berbers are desccndcil. They were a warlike race and excelled as horsemen, but were faithless and unscrupulous. Of their tribes, the Massyli in the east and the Masudsi/li in the west were the most powerful. In the gri'at struggle be- tween the Carthaginians and the Romans they at first fought on the side of the former, but sul)se(|iicntly the King of the eastern Xumidians, Masinissa (q.v. ). joined the Romans, and ren- dered them etfective service in the war with llaniiibal. Favored by the conquerors, he united all Numidia under his sway. Of his successors in this kingdom, .lugurtha and .luba I. are the most famous. After the victory of CiPsar over .luba in the African war, Numidia became a Ixonian province (B.C. 4(i) under the name of Africa Nova, but Augustus afterwards gave the western part — from the river Am])saga, now Wadi-el-Kebir — with Mauretania to .Tuba II., and the eastern part was united with Africa Vctus to form the new Province of Africa. The Emperor Septimius Scvcrus erected Numidia once more into a (irovince. It was conquered suc- cessively by the Vandals, the Byzantines, and the Arabs. B<'fore tiie invasion of the Vandals, Numidia was a stronghold of .frican Chris- tianity, and the jealousy between the Numidian bishops and the clergy of Carthage was one of the causes that brought about the Donatist Schism. See Donatists. NUMIDIAN CRANE. See Cham;. NUMISMATIC AND ARCH.a:OLOGICAL SOCIETY, TuK .XMFUticAN-. .
association or-
- aiiizid in IS.'iS and ineorporate<l in bSli.'). Its
objects are the collection of coins and medals, the investigation of matters connected therewith, and tiie spreading of the science of numis- matology. The society has a membership of three hundred, and its headquarters are in New ™ i
