CHAMBERS'S INFORMATION FOR THE PEOPLE. 





THE ARITHMETIC OF COMPOUND QUANTITIES. 

 TABLES OF WEIGHTS AND MEASURES. 

 LENGTH. 



Inch = -h of a foot. 



Foot = | of a yard. 



Yard = unit. 



Pole =5} yards. 



Furlong . . . = 220 yards. 

 Mile = 1760 yards. 



Square inch. = -,\ f of a square foot. 

 Square foot = { of a square yard. 

 Square yard = unit. 

 Square pole. = 30^ square yards. 



Rood = 1210 square yards. 



Acre at 4840 square yards. 



VOLUME. 



Cubic inch = T^U of a cubic foot. 



Cubic foot =^ of a cubic yard. 



Cubic yard = unit. 



CAPACITY (LIQUID MEASURE). 



Gill = J of a pint 



Pint = i of a quart. 



8uart = J of a gallon, 

 allon .. 



= unit. 



CAPACITY (DRY MEASURE). 



Gallon = unit 



Peck =2 gallons. 



Bushel =8 gallons. 



Quarter =64 gallons. 



TROY WEIGHT. 



Grain = ^ of a pennyweight 



(dwt.). 

 Pennyweight.. = ^ of an ounce (oz). 



Ounce = -i>j of a pound (lb.). 



Pound = unit. 



APOTHECARIES' WEIGHT.* 

 Grain .. = A of a scruple. 

 Scruple = J of a dram. 

 Dram.. = j of an ounce. 

 Ounce. = t*j of a pound. 

 Pound. = unit. 



AVOIRDUPOIS WEIGHT. 



Dram = -ft of an ounce. 



Ounce = ^ of a pound (lb.). 



Pound = unit. 



Stone = 14 pounds. 



Quarter = 28 pounds. 



Hundredweight = 112 pounds. 



Ton =20 hundredweights (cwt). 



i Pound avoirdupois = 7000 grains Troy 



TIME. 



Second = ^n of a minute. 



Minute = &, of an hour. 



Hour = ^j of a day. 



Day = unit. 



Year = 365 J days. 



Farthing 

 Penny . . 

 Shilling 

 Florin . . 

 Pound. . 



MONEY. 



. = J of a penny (d.). 

 . = fj of a shilling. 



. = Jx of a pound. 

 . = unit. 



When a quantity is made up of several other 

 quantities expressed with reference to different 

 units, it is said to be compound. Thus, ^5, 143. 

 iofd., 7 tons 12 cwt. 3 qrs. 15 Ibs., are compound 

 quantities. Now, it will at once appear that the 

 ' law of diminution,' which simplifies so much all 

 questions relating exclusively to whole or decimal 

 numbers, cannot be applied to numbers represent- 

 ing compound quantities, and referred to different 

 units, for we see, from the above tables, that the 

 divisions of the units which serve to measure 

 quantity in this country are not in accordance 

 with the decimal system. The inconvenience 

 thus arising is so great that nearly all the nations 

 of Europe, except Britain, have discarded their 

 old subdivisions, and adopted the decimal division. 



Reduction. 



If a quantity is expressed with reference to any 

 unit which measures it, it is easy to express it 

 with reference to any other unit. For 

 example, let it be required to express 

 .5, 145. lofd. as farthings. Here 

 we begin by changing the pounds 

 into shillings, and this we do by 

 multiplying by 20 ; as there are 20 

 shillings in the pound, this gives 100, 

 and the 14 shillings we had to begin 

 with gives 1 14 shillings in all. These 

 are now changed into pence by mul- 

 tiplying by 12 ; this gives, after add- 

 ing in the 10 .pence we had to begin with, 1378. 



* In the new British Pharmacopoeia, medicines are now dis- 

 pensed by avoirdupois weight. 

 602 



5 

 20 



114 

 12 



1378 



4 

 5515 



12)44214 



These pence are now changed into farthings by 

 multiplying by 4 ; and this gives, after adding the 

 farthings we had to begin with, 5515 the number 

 required. 



Again, let it be required to 4)17686 

 change 17686 farthings into 

 pounds ; we begin by first chang- 

 ing the farthings into pence, and 

 this we do by dividing by 4, as it 

 takes 4 of them to make a penny. 

 We then change the pence into 

 shillings by dividing by 12, and the shillings into 

 pounds by dividing by 20. 



Addition and Subtraction of Compound Quantities. 



Let it be required, for example, to add the sums 

 of money here given in the margin. 

 We begin by first adding the far- 

 things, and we find their sum to be 

 9 that is, 2 pence and i farthing. 

 We write the farthing under the far- 

 things, and take the 2 pence, and 

 add it along with the pence ; this 

 we find will make 41, or 3 shillings ^469 3 5| 

 and 5 pence ; we take the shillings, 

 and add them to the shillings ; and this we find 

 gives 63, or ^3 and 3 shillings. We write the 3 

 shillings under the shillings, and carry the 3 

 pounds, and add them along with the pounds ; 

 this makes the sum of the pounds 469. So that 

 the whole sum is .469, 35. 5^d. 



Again, let it be required to subtract ,27, 125. 

 8|d. from ;ii2, 23. 6|d. We begin by subtract- 

 ing the farthings in the under line 

 from those in the upper ; but we 

 cannot take 3 from 2, and there- 

 fore we add to both i penny ; we 

 add this penny to the upper line 

 as 4 farthings, and to the under as 

 i penny. We will then have six farthings above, 

 from which we can take 3 farthings ; there there- 

 fore remain 3 farthings. We have now 9 pence 

 to take from 6 pence ; this we cannot do, and we 

 add to both i shilling, to the upper line we add 

 this as 12 pence, and to the under as i shilling; 

 we then take 9 from 18, and get a remainder of 9. 

 There are now 13 shillings in the under line ; but 

 this we cannot take from 2 ; so to both we add i 

 pound, and this we add to the upper line as 20 

 shillings, and to the other as I pound. We then 

 take 13 from 22, and find a remainder 9. We 

 now have 28 pounds to take from 112 pounds, and 

 the remainder is found to be 84 pounds ; so that 

 the whole remainder is .84, 95. gfd. In the above 

 operation, we have not found the difference be- 

 tween the given quantities of money, but between 

 these, after i, is. id. has been added to both, 

 and, as we have seen, the addition of this to both 

 does not alter the difference between the original 

 quantities. 



Multiplication of Compound Quantities Practice. 



Let it be required to multiply ^25, 123. 4|rd. by 

 53. We might begin by multiply- 

 ing first the farthings by 53 ; this /2? 12 4i 

 gives 53 farthings, or 13 pence 

 and i farthing ; then 53 times 4 

 pence is 212 pence, and 13 added ;i357 J 4 9i 

 makes 225 pence, or 18 shillings 

 and 9 pence; 53 times 12 shillings with 18 added 



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