ARITHMETIC. 



259 



mode of writing, or in the order from right to left. 

 In imitation of the Greeks also, the a which occupied 

 the blanks in the sexagesimal system, is there sup- 

 plied by a corresponding letter. Yet the Arabians, 

 as well as the Persians, in copying the numeral 

 characters, inverted their usual order of writing, and 

 proceeded from left to right, as it is universally prac- 

 tised wherever such a notation has prevailed. These 

 circumstances, taken into combination, sufficiently 

 prove that the decimal arrangement had been invent- 

 ed by a very different people. Our modern system 

 of arithmetic has thus its origin distinctly referred to 

 the genial climes of the East, where the human 

 species was early ripened into some degree of refine- 

 ~ment. Yet it does not thence follow, that the dis- 

 covery was completed at a period of very remote 

 antiquity. The ancient Egyptians, who, perhaps 

 from their early communication with the people of 

 Hindostan, entertained the same veneration for cer- 

 tain mystical properties of numbers, were yet 

 unacquainted with the use of the numeral characters. 

 If such an improvement in arithmetic had actually 

 taken place when Pythagoras visited India, we can 

 hardly suppose that the philosopher would have 

 neglected to transport it into Greece, or imagine that 

 an art so very simple could ever afterwards be entirely 

 forgotten. The Brahmins themselves were not 

 aware of the principle which they had struck out. 

 They stopped short in their progress, and did not, 

 like the Greeks, attempt the descending scale of 

 numeration. The use of decimal fractions, we are 

 assured, is even at present unknown to the natives of 

 India; and accordingly, wherever fractional parts 

 are concerned, they perform their operations with far 

 less expedition than the Europeans. The people of 

 Upper Asia have reached the precise stage of numer- 

 ation which the Romans had attained. The Chinese 

 employ two kinds of numerals; the one very com- 

 plex, and formed by uniting their hieroglyphical 

 characters ; the other simpler, and, allowing for 

 their mode of writing from top to bottom, very nearly 

 resembling the Roman, both in shape and composi- 

 tion. They express one, by a slender horizontal line, 

 which was repeated downwards, and variously con- 

 tracted, to signify the other digits ; ten, they denote 

 by a thick vertical stroke, crossed by a horizontal 

 line ; twenty, thirty, &c. are marked by repeating and 

 condensing these strokes, always crossed by a slender 

 line ; a hundred is represented by two vertical 

 strokes, with the addition of a third oblique one, and 

 connected by three horizontal lines. To signify a 

 thousand, the symbol for ten is used, with the addition 

 of a broad oblique stroke ; and to represent 2000, 

 3000, &c. the same compound character is employed ; 

 only the marks for two, three, &c. are annexed. Such 

 involved symbols are evidently altogether unfit for 

 aiding the purposes of calculation. The Chinese 

 have, therefore, recourse to palpable arithmetic ; and 

 their swan-pan is almost exactly the same as the 

 Roman abacus. That instrument, universally used 

 by all ranks throughout China, consists of a frame of 

 wood, divided by a perpendicular bar into two com- 

 partments, which are intersected by a series of 

 parallel wires having small balls strung on them, five 

 h;il Is being allotted on the left hand to each wire of 

 the larger, and two, equal i power to ten, on the 

 right and in the smaller compartment. The swan-pan 

 is rather more extensive than the abacus, being com- 

 posed generally of more than nine wires, and which 

 mark so many places in the decimal system of ar- 

 rangement. The Chinese appear also to have 

 advanced a step beyond the Romans ; for, commenc- 

 ing the units from any intermediate wire, they 

 proceeded either by the ascending or descending 

 scale of numeration. Following the same principle. 



the subdivisions of weights and measures used in 

 China are almost entirely decimal ; a circumstance 

 which greatly facilitates their ordinary computations . 

 The following cut represents a Chinese swan-pan. 



Among the many machines that have been invented 

 for calculating numbers, none equal the one designed 

 by Mr Babbage. That engine not only performs the 

 operations of common arithmetic, but am also extract 

 the roots of numbers, and approximate to the roots 

 of equations, and even to their impossible roots. Its 

 function, in contradistinction to that of all other con- 

 trivances for calculating, is to embody in machinery 

 the method of differences, which has never before 

 been done ; and the effects which it is capable of pro- 

 ducing, place it among the most astonishing efforts of 

 mechanical genius. Great as the power of mechanism 

 is known to be, many will scarcely admit it to be 

 possible, that astronomical and navigation tables can 

 be accurately computed by machinery ; that the ma- 

 chine can itself correct the errors which it may com- 

 mit ; and that the results, when absolutely free from 

 error, can be printed off without the aid of human 

 hands, or the operation of human intelligence. " All 

 this, however," says Sir David Brewster, in his enter- 

 taining Letters on Natural Magic, " Mr Babbage's 

 machine can do ; and, as 1 have had the advantage of 

 seeing it actually calculate, and of studying its con- 

 struction with Mr Babbage himself, J am able to 

 make this statement on personal observation/' It 

 consists essentially of two parts, a calculating, and a 

 printing part, both of which are necessary to the fulfil- 

 ment of' the inventor's views, for the whole advantage 

 would be lost if the computations made by the ma- 

 chine were copied by human hands and transferred to 

 types by the common process. The greater part ol 

 the calculating machinery, of which the drawings 

 alone cover upwards of 400 square feet of surface, is 

 already constructed, and exhibits workmanship of 

 such extraordinary skill and beauty, that nothing ap- 

 proaching to it has hitherto been witnessed. In the 

 printing part, less progress lias been made in the 

 actual execution, in consequence of the difficulty of 

 its contrivance, not for transferring the computations 

 from the calculating part to the copper, or other plate 

 destined to receive them, but for giving to the plate 

 itself that number and variety of movements which 

 the forms adopted in printed tables may call for in 

 pmctice. The practical object of the calculating 

 engine is to compute and print a great variety and 

 extent of astronomical and navigation tables, which 

 could not otherwise be done without enormous intel- 

 lectual and manual labour, and which, even if exe- 

 cuted by such labour, could not be calculated with 

 Lhe requisite accuracy. On the means of accomplish- 

 ing this, Mr Babbage says, " As the possibility of per- 

 forming arithmetical calculations by machinery may 

 appear to non-mathematical readers too large a pos- 

 tulate, and as it is connected with the subject of the 

 division of labour, I shall here endeavour, in a few 

 lines, to give some slight perception of the manner 

 in which this can be done ; nnd thus to remove a 

 small portion of the veil which covers that apparent 

 mystery. That nearly all tables of numbers which 

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