ARISUGAWA. a'rf-soo-gii'wfl. The name of a noble family in Japan whose members, besides showing marked ability, have been prominent in the rejuvenation of that ancient empire. The house was founded by the seventh son of the Mikado Go-Yozei, who reigned from 1587 to 1611 and died in lli.'iS. When in January. 1808, the duarchy of Jlikado and Shogun was abolished and the existing government of Japan established by the restoration of the Emperor Mutsuhito to undivided power, Arisugawa Taruiiito ( 1835- 80), uncle of the Mikado, born in Kioto, and carefully educated, was ajjpointed sujireme ad- ministrator and commander-in-chief of the army. Receiving the sword of justice and the brocade banner,he led the imperial troops against the reb- els, saved Veddo from destruction, and then di- rected the military operations in the north which brought the civil war to a happy conclusion. In 1809 he returned to the Kmperor the sword and banner in token of com{)lete pacification of the empire. In 1875 he was made President of the Senate, and in 1877 received supreme command of the forces, which. after seven months of fighting and the loss of 20,000 lives and $50,000,- 000, suppressed the Satsuma rebellion led by Saigo Takamori, for which Arisugawa was deco- rated with the Order of the Chrysanthemum and made field-marshal and junior prime minister, Arisugawa Takeiiito (1802-95), brother of the above, was adopted by the Emperor <when with- out an heir) in 1878. He traveled and studied in Europe, examining military systems, received the highest decorations, served for education as midshipman on H. B. M. ship Iron Duke, and aa captain in the Japanese navy in the war with China (1894-95), dying in service. The first memorial postage stamps ever issued in Japan showed his portrait. The allowance of the Arisugawa family out of the civil list is 30,000 yen.
ARITA, a-re'ta. A town of Japan situated
in the western part of Kiusliiu, about 58 miles
north of Nagasaki, with which it is connected
by rail. It is famous chiefly for its pottery
works, established at the end of the Sixteenth
Century. The porcelain of Arita used to be ex-
ported in large quantities to the Netherlands
and is very highly valued. Population, about
6000.
ARITH'METIC (Gk. ipiB/jj/TiK//. se. Hx^i,
arithnivtiki' trclnir. the art of reckoning, from
apiij/i(if, uritlnnoH, number). This primitive
mathematical science involves three phases:
the conception of number, the representation of
iiumbe^ by symbols, and the principles and
methods of computation. To these may be added
the rules of ordinary business, which have come
to be considered part of the elements of the sub-
ject.
The Conception of Number. Kant advanced the idea that the numberconoept is derived from sequence in time, and accordingly Sir William Hamilton speaks of "the science of pure time." In recent years the Kantian idea has led to a revival, in teaching arithmetic, of the older methods, based on the cultivation of a sense for rhythmic repetition, i.e., on counting — number being regarded as a product of reflection, of an activity of the mind. On the contrary, the Pestalozzian method, which was generally em- ployed until some years ago. followed the idea that perception alone forms the basis of all number work, and that the origin of the number- concept is to be sought not in time, but in space. This principle has often been over- worked. Some teachers have presented a variety of objects so systematically that the pupil learned to think of nine horse-s, nine feet, nine dollars, and was unable to think of the number nine without the aid of a group of ob- jects. The reaction against the Pestalozzian plan has led teachers to lay greater emphasis on phenomena taking place successively in time; thus, to distinguish nine from six, the pupil is made to hear the clock strike the hours. Representation of Number.s by Symbols. Aside from primitive number-pictures, such as the Egyptian hieroglyphics and the Babylonian cuneiform symbols, the ancients commonly u.sed the letters of their alphabets to represent num- bers — e.g., the a, f}, y, S, of the Greeks. Some- what more refined is the system of the Romans, who used only a limited set of letters, combin- ing these according to simple additive and sub- tractive principles. But even in the Roman notation no extended calculations were possible without the aid of some registering instrument; hence the early and extensive use of the abacus. (See Calculating Machines.) The notation in use at present, which consists in combining ten digits according to a simple position-system, originated with the Hindus, was transmitted to the Arabs, and came to the knowledge of Euro- peans chiefly through the labors of Leonardo of Pisa, about a.d. 1200. This powerful system freed arithmetic from the reign of the abacus. .^s to fractional numbers, the Ahmes papyrus, which is at least thirty-six centuries old, shows that the Egyptians had a knowledge of fractions at a very remote date. But while the concept and symbolism of the common fraction are thus very old, the decimal fraction, the decimal point, and other improvements in notation, are com- paratively recent, dating from the Sixteenth and Seventeenth centuries. Besides the decimal scale, fractions have also been written on various other scales, such as the binary (scale of two), ternary (scale of three), . . . duodenary (scale of twelve), and nota- bly the sexagesimal (scale of sixty) by the Egyptians and Babylonians. At present, the scale of ten is generally recognized as the most convenient. The scale of twelve, how- ever, has the advantage of producing simpler fractional forms. E.g., on the scale of ten the fractions %. %, Vg, are written, respectively, 333. ... 0.25. 0.125: on the scale of twelve they are written, 0.4, 0.3, 0.16. Arithmetic Computation. The methods of carrying out the basal operations of arithmetic have been considerably improved since the Fif- teenth Century. The old 'galley' method of di- vision was replaced by the 'Italian' method, the superiority of which may be seen from the fol- loAving examples: Oalleij. 975.35399 -^ 9876, carried for one figure only: jjJI 32.92^3.1416 Italian. 3.1416)32.9200(10.48 31416 150400 125664 247360
