525 



ARISTOLOCHIA. 



ARITHMETIC. 



628 



class of persons : if it means a form of government, whether the whole 

 community is included, or whether there is also a class of subjects or 

 slaves : if it means a class of persons, what is the principle which 

 makes them a political party, or on what ground they are jointly 

 opposed to other orders in the state. If attention is not paid to these 

 points, there is great danger, in political or historical discussions, of 

 confounding things essentially different, and of drawing parallels be- 

 tween governments, parties, and states of society, which resemble each 

 other only in being called by the same name. 



It has been proposed by Mr. Austin, in his work on ' The Province 

 of Jurisprudence," to use the term ariitocrafij as a general name for 

 governments in which the sovereignty belongs to several persons, that 

 is, to all governments which are not monarchies. There would, how- 

 ever, be much inconvenience in deviating so widely from the established 

 usage of words, as to make democracy a kind of aristocracy ; and it 

 appears that the word republic has properly the sense required, being 

 a general term including both aristocracy and democracy, and signifying 

 all governments which are not monarchies or despotisms. 



ARISTOLOCHIA, Medical mes of. The most valuable of the species 

 is the A. Serpentaria, which grows in North America, chiefly in Virginia, 

 and hence is called Virginian snake-root. Though the whole root is 

 used, the rootlets are more powerful than the solid root. These 

 consist of a large portion of woody fibre and gummy matter, which 

 have no virtues, along with some resin, bitter extractive, and a little 

 essential or volatile oil, on which principles its virtues depend. It 

 communicates its properties to water and to alcohol, which are em- 

 ployed as the means of extracting them, by forming an infusion or a 

 tincture. Decoction should never be employed, as the heat drives off 

 the volatile oil. 



Its odour and taste resemble valerian, angelica, and camphor. In its 

 action on the human system it most nearly approaches to camphor, 

 but its effects are more permanent. It chiefly influences the nervous 

 system, and seems to act most beneficially in those cases where 

 the capillaries, either from not receiving an adequate supply of blood, 

 or of nervous energy, are incapable of producing upon the blood 

 those changes which form secretions in the glands, the skin, and other 

 secreting surfaces, or which are essential for the maintenance of a 

 sufficient degree of vital action in every part of the body. . The 

 diseases or disordered states of the system in which it may be advan- 

 tageously employed can, therefore, be easily inferred. 



In protracted fevers, whether of a continued or intermittent kind, it 

 is often eminently serviceable. In those cases of continued fever, 

 which do not assume a very active character, but run on to a lengthened 

 period, commonly called low nervous fever, it is preferable to every other 

 agent, and may either be used alone, or in conjunction with cinchona 

 bark, or some of its preparations. Hence, under the title of Huxham's 

 tincture of bark, it is very much used : but a safer mode of adminis- 

 tration is that of an infusion of the serpentaria, to which sulphate of 

 quinine, and orange-peel, or other aromatic, may be added ; as recom- 

 mended under AGUE. 



In eruptive or exanthematous fevers, such as small-pox and measles, 

 when the eruption is imperfectly formed or threatens to recede, an 

 occurrence always betokening great danger, and indicating much 

 feebleness hi the powers of the system, serpentaria is an invaluable 

 agent. 



In the sore throat of scarlet fever, or in other affections of the throat, 

 where gangrene is to be apprehended, from the depression of the vital 

 powers, serpentaria, given internally, and used as a gargle, alone, or 

 with tincture of capsicum, is more likely to prevent so serious a termi- 

 nation than any other medicine. In none of these diseases should it 

 be exhibited tUl after the bowels have been thoroughly cleared out by 

 proper purgative medicines. But there are other diseases, not attended 

 with fever, in which serpentaria is extremely useful. In that form of 

 indigestion where no inflammatory state of the mucous membrane of 

 the stomach exists, and where the skin is harsh and dry, serpentaria 

 alone, or better with sulphate of quinine, is eminently serviceable. On 

 the same principle, in the state of torpor or exhaustion to which literary 

 persons are subject, from long-continued or intense mental exertion, 

 this combination is highly useful. ' 



In America, the infusion or tincture of serpentaria is sometimes 

 taken every morning in damp aguish situations, to prevent intermit- 

 teftts. It is likewise said to prove useful in the treatment of a kind of 

 pleurisy accompanied with great derangement of the biliary system, of 

 frequent occurrence in autumn, among persons exposed to the exhala- 

 tions of the marshes in America. 



This species, and several others, both in America and the East and 

 West Indies, are much employed as antidotes against the bite of 

 serpents; and hence the name snake-root. Dr. Hancock states, that 

 the quaco, used by the South Americans in such cases, belongs to 

 this tribe. 



ARI8TOLOCHIN. The name given to a non-azotised bitter prin- 

 ciple contained in snake-root, Arittolochia serpentaria. Its nature and 

 composition are unknown. 



ARITHMETIC, from the Greek itfiBiafrat^ (arlthmdlke), ' the art of 

 numbering,' should mean the science of numbers in general, including a 

 great part of what is commonly called aigebra. It is however usually 

 restricted to mean only the science of the expression of numbers by 

 *ymbols, and the application (not investigation) of all rules relating to 



them which are useful in the arts of life. Under this general head we 

 shall here confine ourselves to the elucidation, philosophical and histo- 

 rical, of the method of naming and representing numbers ; in doing 

 which we shall refer to such other articles as will, all together, furnish 

 the most complete view of the subject our work can afford. For the 

 method of applying principles in practice, see the names of the various 

 rules, ADDITION, SUBTRACTION, &c. For the account of what we must 

 call the psychology of arithmetic, see NUMBER ; and for the history of 

 this branch, see PYTHAGORAS, PLATO, THEON, EUCLID, DIOPHANTUS, 

 FERMAT, &c., in the BIOGRAPHICAL DIVISION. For that part of algebra 

 which particularly concerns pure arithmetic, see NUMBERS, THEORY OF. 

 For the arithmetic of concrete numbers, see WEIGHTS and MEASURES, 

 and such articles as YARD, POUND, &c. 



All the information possessed on the main points of arithmetical 

 history has been presented to the world in so complete a shape, that it 

 would be little better than affectation to make any more references 

 than one, in an article which has no pretensions to original research. 

 Of course we allude to Dr. Peacock's History of Arithmetic contained 

 in the ' Encyclopaedia Metropolitana', which is certainly the most com- 

 plete treatise yet written on any one point of mathematical history. 

 In using this work as our universal reference, we regret that our limits 

 will not allow us to make such a formal abstract of it, as would oblige 

 us to ask the permission of its owners before we published this number. 

 But as the treatise itself is of a length answering to more than 60 pages 

 of this Cyclopaedia, such an account of its contents would be impossible ; 

 and we therefore use it only as an authority for citations of fact, in 

 which we shall refer to the paging of the ' Encyclopaedia Metropolitana.' 

 We however feel bound to bear testimony to its correctness on all 

 points which our access to books has enabled us to investigate. 



We find ourselves in possession of a method of representing numbers 

 so simple and powerful, that the principle and practice of the most 

 complicated rules follow from it with ease. It is so well known that 

 we need not explain it ; but when we separate from the rest the part 

 which particularly distinguishes our Numeration from that of the ancient 

 Europeans, we shall find that our superiority consists in the adoption 

 of the following conventions : 



1. The value of a figure depends not only upon the simple number 

 for which it stands when alone, but upon the place in which it stands. 

 Thus, in 888, the three eights mean -eight, eight tens, and eight 

 hundreds. 



2. The place of a figure, considered as affecting its value, is deter- 

 mined by the column in which it stands, and in the absence of 

 succeeding figures to indicate the existence of other columns, their 

 place is supplied by ciphers, which of themselves are considered as 

 having no value. Thus the 8 in 800 is of the same value as that 

 in 863. 



To complete our particular system, on which however none of its 

 advantages depend, we must add that each figure is increased tenfold 

 for every place which it is removed to the left. In the first two con- 

 ventions consists what is called the ' local value ' of the figures ; in the 

 last is found the reason for the term ' decimal notation,' from the Latin 

 word decem, ten. 



There can be no doubt that the mere decimal notation, which has 

 been in use in almost every age and country, has arisen from the facility 

 which the ten fingers afford for making calculations. The names of 

 numbers have been almost universally formed distinct as far as ten, 

 after which compound names have been employed. The exceptions to 

 the rule are additional proofs of the generality of the principle ; they 

 are either deduced from five or from twenty, the number of fingers on 

 one hand, or the number of fingers and toes together. We call the 

 simple symbols of numbers digits, or fingers ; the Caribbees call the 

 number ten by a phrase which signifies ' all the children of the hand ' 

 (Peacock, 390) ; and in many languages the phrases for five, ten, and 

 twenty are connected, either by direct derivation or common ety- 

 mology, with those for the hand or fingers. In France the scale from 

 60 to 100 is strictly vicenary (by twenties), and in the Indian Archi- 

 pelago the ancient scales are vicenary. For more discussion on this 

 point we refer to NUMERALS. We shall here only quote two results of 

 observation, as laid down by Dr. Peacock (371), wliich appear to be 

 very well borne out. They are, that " the natural scales of numeration 

 alone have ever met with adoption," meaning, by natural scales, those 

 derived from the hands, or hands and feet ; and that " amongst all 

 nations, practical methods of numeration have preceded the formation 

 of numerical language." 



But this does not mean that every nation has gone high in the scale 

 of numbers. There are tribes which have never even risen to a quinary 

 scale (by fives), owing to their never wanting, and therefore never giving 

 names to, numbers as high as five. Aristotle (P. 391) mentions a 

 tribe of Thracians wliich never counted higher than four ; and the 

 Yancos on the Amazon have been stopped by the complexity of 

 their language. They count no higher than three, the name for 

 which in their language is (P. 390), according to La Condamine, 

 Poetturrarorincoaroac. 



One of the Abipoues, in describing a number of men greater than 

 ten, would mark out a space of ground sufficient to contain them. 

 This is, in its principle, the same resource as that to which the Greeks 

 were driven by their cumbrous notation, namely, tha substitution of 

 geometry for arithmetic. [SQUARE ; EUCLID, Bioa. Div.] 



