TAtLES OF MONEY, ETC. ] 



MATHEMATICS. ARITHMETIC. 



439 



7) 38214 

 9) 6459... 1 



606...36rem. 



.5 



r.'.Y..41rem. 



III. When the Diriinr i$ composed of Factors, none 

 of which exceeds 12. 



The operation just explained is called long division, to 

 distinguish it from the shorter process of the preceding 

 case, where the divissr is not greater than 12. If any 

 divisor be found to be the product of factors, each of 

 which does not exceed this limit, the division may be 

 performed by successive applications of the shorter rule : 

 for we may divide first by one factor, then the quotient 

 by another factor, the new quotient by a third factor; 

 and so on, till all the factors have been used. 



It is possible that the division by the first factor may 

 leave a remainder ; if so, it must, of course, be preserved : 

 the division by the second factor may also leave a remain- 

 der; if so, multiply it by ti>e first divisor, and add in the 

 former remainder; the result will be the complete re- 

 mainder as far as the operation has been carried : if there 

 be a third division, and a third remainder, we must 

 multiply it by both the first and second divisors, adding 

 in the former complete remainder : and so on, till all 

 the divisions are completed. For example, suppose we 

 have to divide 38214 by 63 : then 

 since 63 = 7x9, we may operate 

 a* in the margin : the final quotient 

 being 606J J. In like manner, if 

 ire have to divide 24611 by 126 ; 

 then, since 126=3x6x7, the 

 operation by short division, is 

 that here annexed : the remainder 

 from the first division is 2; that 

 from the second is 1 ; and this 1, 

 multiplied by the first divisor 3, 

 and the former remainder being 

 taken in, gives 5 for the complete 

 second remainder: the remainder 

 from the third division is 2, which 



multiplied by 3, and by 6, both the former divisors, that 

 is by 18, gives 36 ; which, with the preceding remainder 

 5, makes 41 ; the final complete remainder : hence the 

 complete quotient is 195 Jj^. 



The method here described of obtaining the final 

 remainder, and thence completing the final quotient, 

 cannot be clearly explained till some knowledge of frac- 

 tion* be acquired : parts of a whole, as one-half, one- 

 third, two-fifths, <tc. , and which are denoted by \, }, J, 

 &c. , are called fractions : when you are a little acquainted 

 with the management of these, the reason of the fore- 

 going directions will be plainly seen. 



Upon the principles now delivered depend all the 

 operations of arithmetic. In what has preceded, they 

 have been applied only to what are called abstract num- 

 bers, without any reference to particular objects or 

 articles. It remains to show the application of the same 

 principles to concrete quantities ; that is, to real com- 

 modities, or things as to money, weights, measures, 

 &c. And, in order to this, a few Tables connected with 

 these matters must first be given. 



We may urge on the student the necessity of learning 

 the whole of these tables by heart. He will find such to 

 afford him great assistance; and it will prevent the 

 necessity of frequent reference to them. ED. 



TABLES OF MOXEY, TIME, WEIGHTS, AND 

 MEASURES. 



I. MOITBT. 



Gold Coins. 

 Name. Value. WcigTit troy. 



i. d. dwt. gr. 



Sovereign (one pound) . 20 . 5 



Half-sovereign . . 10 . 2 



meat ... 21 . 6 9 



Half-guinea . . . 10 6 . 2 16 



The mark <t<ct. ftandi for pmnywrij/hti. and fr. for fraini: let the 

 Ubie of Trojr Wright. The reader can ncarcely re-quire to be informed 

 that atanda for pnundi, i. for Mhillinai, and A. lor pmct. 



t The coin guinea haa been long abnliitheri, but the name ia otill retained 

 for 21. The name pound U given to 20., becauae the quantity of ailrer 

 in thia turn originally weighed a pound troy. 



Name. 



Crown . . 



Half-crown . 



Shilling 



Sixpence 



Fourpenny-piece 



Threepenny-piece 



4 farthings make 

 12 pence 

 20 

 24 

 30 

 36 

 40 

 48 

 50 

 60 

 70 

 72 



Silver Coin}. 

 Value. 

 . d. 

 5 

 2 6 

 12 

 6 

 4 

 3 



Pence Talik. 



Weight troy, 

 dwt. gr. 

 18 4^- 

 tjfr 



1 



1 



nft 



80 pence make 



84 



90 



96 

 100 

 108 

 110 

 120 

 130 

 132 

 140 

 144 



6 



7 

 7 

 8 

 8 

 9 

 9 

 10 



10 10 



11 



11 8 



12 



A farthing that is, one-fourth of a penny is repre- 

 sented thus, \d. ; a halfpenny, thus, ^d. ; and three 

 farthings, thus, ^d. To express a fraction of a farthing, 

 the letter/ is put against the fraction: thus, ^/. means 

 half a farthing ; J/, three-fifths of a farthing, &c. 



II. TIME. 



60 seconds . . . make 1 minute. 



60 minutes ... ,, 1 hour. 



24 hours .... 1 day. 



7 days .... 1 week. 



52 weeks 1 day, or 365 days ., 1 year. 



366 days .... ,,1 leap year. 



III. AVOIRDUPOIS WEIGHT. 



16 drams (dr.) 

 16 ounces (oz.) . . 

 28 pounds (K>.) 

 4 quarters (qr.), or 112 Ib. 

 20 hundredweight (cwt.) 



make 1 ounce. 

 1 pound. 

 1 quarter. 

 ,, 1 hundred wt. 

 Iton. 



IV. TKOY WEIGHT. 



24 grains (gr.) . . . make 1 pennywt. 

 20 pennyweights (dwt.) . . 1 ounce. 



12 ounces (oz.) . . . ,, 1 pound. 



V. APOTHECARIES' WEIGHT. 

 20 grains (gr.) . . . . make 1 scruple. 



3 scruples (3) ....,, 1 dram. 



8 drams ( 3 ) > . ,, 1 ounce. 

 12 ounces (oz., or J ) . . . ,,1 pound. 



VI. MEASURES OF LENGTH, OR LONO MEASURE. 

 12 inches . . make 1 foot. 



3 feet . ,, 1 yard. 



6 feet . . ,, 1 fathom. 



5| yards . . ,,1 rod, pole, or perch. 



4 perches, or 100 links ,, 1 chain (22 yards). 

 40 poles . . 11 1 furlong. 



8 furlongs . . 1 mile. 



3 miles . . ,, 1 league. 



Cloth. 



2 ! inches . . . make 1 nail. 



4 nails . . ,, 1 qr. of a yard. 



5 quarters ... ,, 1 English ell. 

 3 quarters ... 1 Flemish ell. 



VII. MEASURES OF SURFACE, OR SQUARE MEASURE. 

 144 square inches . . make 1 square foot. 

 9 square feet . . ,,1 square yard. 

 30; square yards . . ,, 1 sq. rod, pole, or perch. 

 40 square perches . ,, 1 rood. 

 4 roods, or 160 sq. perches ,, 1 acre. 

 10 sq. chains, or 100,000 1 , 



sq. links .... / 

 640 acres . . . 1 square mile. 

 100 square feet . . 1 square of flooring. 

 272J square feet . . 1 sq. rod of brick-work. 



