

1 >K<' I.M A L SVSTKM 



I)K< K 



7.M 



.U where the denominator divides 10, or 

 loO, \'c , without remainder. Thus, of the above 

 denominators, - is contained in 10, 5 times ; 4 in 

 100, 25 times ; and 25 in 100, 4 times ; there- 



1 _ 1 x 5 5 1 _ 1 x 25 _ 25 



>Te ' 2 ~2x5~10~' ; 4~ 41T25 " Km 



25; o = 







IB 86x4 



100 



But neither 3 nor 



7 will divide 10 or any power of 10; and then-fine 

 tin-si- numbers cannot produce powers of 10 liy 

 multiplication. In such cases, therefore, and in 

 fact in the cose of any vulgar fraction (in its loue-t 

 terms ) whose denominator contains any other prime 

 i.t'-i'ir tli.-in '_' or .*>, an equivalent decimal cannot be 

 found. If we try to find it, the result is an infinite 

 series, which is called a repeating, recurring, or 

 circulating decimal. Thus if 'OWJO, &c., where 

 the 6 repeats for ever i.e. J cannot be expressed as 

 a decimal. The non-terminating result, '6<jC, &c., 

 is written '&. 



Decimal System* This name is applied to 

 any system of weights, measures, money, &c., in 

 which the standard unit is divided into tenths, 

 hundredth*, \-e., for the denominations below it, 

 and multiplied by 10, 100, &c., for those above it. 

 The nature of this method of division will be best 

 explained by an example from the French system, 

 where it has been most rigidly carried out. The 

 mitre ( = 39'37 English inches nearly) is the unit of 

 length, and the foundation of the whole system. 

 For the higher denominations of length, the Greek 

 words if tea, hecto, kilo, and myrla, are prefixed to 

 signify multiplying by 10, 100, 1000, 10,000; so 

 l\\&ldJcaiiietre = 10 metres, kilometre = 1000 metres, 

 \'c. The Latin words deci, centi, milli, on the other 

 hand, are used to express division by 10, 100, &c., 

 and thus furnish names for the lower denomina- 

 tions ; tUdmitre = -iV f a metre, centimetre = y^ 

 of a metre, &c. Similarly with money ; the franc 

 being the unit, n. decline is the tenth part of a franc ; 

 and a centime, the hundredth part. 



In 186. 1 ) Belgium and Switzerland adopted the 

 French decimal system of money, weights, and 

 measures. Afterwards the Italian lira, the Greek 

 drachme, the Spanish peseta, and more recently the 

 Roumanian lei, and the Servian dinar, were assimi- 

 lated to the/raHC. Other countries, though retain- 

 ing each its own special unit coin, divide it into 100 

 parts viz. Germany, Austria, Russia, and the 

 United States of America. The following have 

 adopted the metrical system of weights and 

 measures, though rejecting the franc: Germany, 

 the Netherlands, Spain, Portugal, Norway, and 

 Sweden. Engineers, too, have their own decimal 

 systems of measurement. 



The method of decimal gradation in weights and 

 measures naturally suggest* itself to the arith- 

 metician, on account of the language of numl>ers, 

 and the Arabic notation. Practical legislators, 

 however, have pronounced the number ten to be 

 most unsuitable as a basis, especially for the pur- 

 poses of 'retail trade.' In France the prices 1*25, 

 4 '25, 6'75, &c. are extremely common ; yet if half a 

 yard of cloth, for example, is Inrnght at 1 "25 the 

 yard, the exact price cannot be paid, and the buyer 

 therefore suffers. He is compelled to pay more than 

 the proper value by reason of the limitations in- 

 separable from the decimal system. The analogous 

 price in English money is Is. 3d., which allows not 

 only half a yard to be sold at the exact price, but 

 even a quarter of a yard. To estimate the loss 

 undergone by the poorer classes in France on 

 account of the imperfections inherent" to their 

 monetary system, the most ordinary case^ will 

 Bufh'ce e.g. if sugar is sold at 25 centimes a pound, 

 then any one who buys half a pound must pay 



exactly 4 per cent, more than the proper price. 



The same scriuus dra \\liiu-k i- in-|iai;il>l- from tin- 

 monetary system of the United State*, a com 

 pared with that of Great Britain. In Huch a cane 

 as that just <|iioted, the poor buyer in New York \ 

 defrauded still more than in Paris ; \\ln-M-a-, in 

 Edinburgh, London, or Dublin, the buyer will not 

 only lose nothing by such a transaction, but can buy 

 even a quarter of a pound at the proper price. 



In 18*21, after an able report drawn up by John 

 IJuincy Adams, the United States government 

 rejected the metrical system as unsnited to practical 

 life. The question of adopting the rYcndi -cheme 

 has also been repeatedly discussed in the House of 

 Commons, but though many, in the interest* of 

 certain scientific pursuits ami international transac- 

 tions, advocated a change, there seems little prob- 

 ability of uprooting our existing method, with iu 

 excellent supply of binary factors, and the much 

 greater ease with which it lends itself to mental 

 arithmetic. Although proposed in 1795, the decimal 

 system in France required repeated legislation 

 1 " -tore it could gain footing, and though it was made 

 obligatory from January 1, 1840, the people still 

 retain traces of the older and less arbitrary mode of 

 computation, just as the shilling and sixpence still 

 exist in the United States as terms of reference. 

 The centesimal division of the rig^ht angle was also 

 proposed at the French Revolution, but has long 

 been abandoned, even in France. It was also used 

 as a basis in dividing the thermometric scale ( mis- 

 named centigrade for heclogrnde ), but Fahrenheit's 

 is often preferred because there are more sub- 

 d i visions, and because it avoids the use of negative 

 numbers. The application of the system to the 

 division of time was so unworkable as scarcely to 

 to'erate even a trial. There, as elsewhere, the 

 duodecimal mode, as compared with the decimal, 

 is vastly and incontestaoly superior. For the 

 decimal system in numerical notation, see NOTA- 

 TION, NUMERALS; and for the system of measure- 

 ments based on the metre, see M KTRK. 



Decimation, a Roman military punishment, 

 whereby when a considerable Ixnly of troops com- 

 mitted some grave military offence, which would 

 be punished with death in an individual, the 

 punishment was awarded to one-tenth of them by 

 lot, instead of to the whole number, that so the 

 army might not be too much weakened. The 

 practice was borrowed from the Romans by Essex 

 at Dublin (1599), by the Austrians at Leip/ig 

 (1642), and by the French at Treves (1675); but 

 Blacker tried vainly to employ it against the 

 mutinous Saxon battalions at Liege ( 1815). 



Decius, a Roman emperor, whose name in full 

 was C. MESSIUS QUINTUS TRAJAN rs DK n s. He 

 was born at Budalia, in Lower Pannonia, towards 

 the close of the 2d century, and was sent in 249 by 

 the Emperor Philippus to reduce to subordination 

 the rebellious army of Ma-sia. The soldiers pro- 

 claimed him emperor against his will, and forced 

 him to march UJKHI Italy. Philippus encountered 

 the forces of Decius near Verona, but was defeated 

 and slain. Decius assumed the government of the 

 empire in the end of the year 249, but his brief 

 reign was one of restless warring with the iioths, 

 lighting against whom he was killed near Abricitim 

 in the close of the year 251. In his reign the 

 Christians were persecuted with great severity. 

 At Rome. Antioch, and Jerusalem ihe bishops were 

 ma--acred. the great Origen was cruelly tortured, 

 and dreadful cruelties were perpetrated at Alex- 

 andria. 



Deck, in ship structure, is a horizontal platform 

 extending from one side of a vessel to the other, 

 thereby connecting them together, ami forming in 

 addition a flooring to the persons above it, and a 



