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Decimal Tables of Coin, Weight, and Measure.

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TABLE V. AVOIRDUPOISE WT,

Tlb. the. Integer.
Ounces. Decimals.

8 ,5
7 ,4375
6 ,375
5 ,3125
4 ,25
3

,1875
2 ,125

,0625

80
,317460

Pints. Decimals. 70 ,27

3 ,005952 60 ,238095 2 ,003968 50 ,198412 1 ,001984 40 ,158730 30 ,119047

TABLE VII. 20 ,079365

MEASURE. 10 039682

Liquid. Dry. 9

035714 8 031746

1 Gullon, 1 Quarter, 7 ,027

Integer.

Pints. Decim. Bush. 6 ,023809 5 ,019841

4, 1,5 4

3 4 2015873

,375

2 3 ,011904

,25

1 2 ,007936

,125 1 ,003968

Qt. pt. Decim. Peck.

3 1,09375 3

2 Pints. Decimals.

,0625 2

1 4 ,001984

,03125 3 ,001488

Decimals. IQ. Pks. 2 ,000992

,0234375 1

3 ,000496

,015625 2

,0078125 A Hogshead the Integer. Decimals. Pints.

,005859 Gallons.

,003906
Decimals.

,001953
30 ,476190
20 ,317460
10
,158730

TABLE VIII.
9 ,142857 LONG MEASURES
8 ,126984 1 Mile the Integer.
77 lunu
6 ,095238 Yards. Decimals.
5 ,079365 1000 ,568182
4 ,063492 900 ,511364
3 ,047619 800 ,154545

,031746 700 ,397727 1 015873 600 ,340909

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Decimal Tables of Coin. Weight, and Measure. 500 ,284091

80

,219178 TABLE X. 400 ,227272 70 ,191781

CLOTH MEASURE. 300

,170454 60 ,164383 200 113636 50

1 Yard the Integer.

,136986 100 ,056818 40 ,109589

Qrs. the same as 90 ,051136 30 ,082192 Table 4. 80 ,045454 20 ,054794 70

Nails, ,039773

Decimals. 10 ,027397 60

2 ,034091 9 ,02465

,125
50

f
,028409 8
,021918

,0625 40 ,022727 7

,019178 30 ,017045 6

,016-38 TABLE XI. ,011364 5 1,013698

LEAD WEIGHT. 10 ,005682

,010959 9 ,005114

A Fother the Integer.

,008219 ,004545 2

,005479 Hund. Decimals. ,003977

1 ,002739 10 ,512820 ,003409 1 Day the Integer.

,461538 ,002841 Hours, | Decimals.

8 ,410256 ,002273 12

7. ,5

,358974 ,,001704 11

6 ,4583

,307692 ,001136 10 ,416

, 256410 ,000568 9

4 ,375

,205128 Feet. Decimals, 8 ,s

,153846 2 0003787 7 ,2916

,102564 1 0001894 6 ,25

,051282 Inches. Decimals,

Qrs. Decimals. 6 ,0000947

,16

2 ,025641 3 ,0000474

1

,012820 1 ,0000158

-,083, Pounds. Decimals. 1 ,0416

14 ,0064102 TABLE IX.

Min. Decimal 13 ,0059523 TIME.

30 ,02083 12 ,0054945 1 Year the Integer.

20
,013888

11 ,0050366 Months the same a

10

,006944 10 ,0045787 Pence in the second

,00625 9 ,0041208 Table.

8 ,005555 8 ,0036630

,004861 7 ,0032051 Days. | Decimals. 6

,004166 6 ,0027472 365 1,000000 5 ,003472 5 ,0022893 300

,821918 4 ,002777 4 ,0018315 200 ,547945

,002083 3 ,0013736 100

,273972 2 ,001388 2 ,0009157 90 ,2465751

,000694

,0004578

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CA O VOC

EXTRACTION OF THE SQUARE ROOT. EXTRACTING the Square Root :s to find out such a num,

ber as being multiplicd into itself, the product will be equal to the given number.

Rule. First, Point the given number, beginning at the unit's place, then to the hundreds, and so upon every second figure throughout.

Secondly, Seek the greatest square number in the first point towards the left hand, placing the square number under the first point, and the root thereof in the quotient; subtract the square number from the first point, and to the remainder bring down the next point, and call that the resolvend.

Thirdly, Double the quotient, and puce it for a divisor on the left hand of the resolvend; seek how often the divisor is contained in the resolvend (preserving always the unit's place,) and put the answer in the quotient, and also on the right hand side of the divisor ; then multiply by the figure last put in the .quotient, and subtract the product from the resolvend; bring down the next point to the remainder (if there be any more) and proceed before. Roots. 2. 3. 4. 5.

9. SQUARES.

1. 4. 9. 16. 25. 36. 49. 64. 81.

t.

7.

8.

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685)3425

3425 2. What is the square root of 1069 29 :

Ans. 327. 3. What is the square root of 2208741 ? Ans, 1506,23+ 4. What is the square root of 7590796 ? Ans. 2756,228+. 5. What is the square root of 36372961? Ans, 6031. 5. What is the square root of 22071204? Ans. 4698.

When the given number consists of a whole number, and decimals together, make the number of decimals even by adding cyphers to them ; so that there may be a point fall on the unit's place of the whole number.

7. What is the square root of 3271,4007 ? Ans. 57,19+ 8. What is the square root of 4795,25731! Ans. 69,867 + 9. What is the square root of 4,372594 ? Ans. 2,091+:

10. What is the square root of 2,2710957 ? Ans. 1,50701+. 11. What is the square root of ,00032754 ? Ans. ,01809+ 12. What is the square root of 1,270054 ?

Ans. 1,1269 +. To extract the Square Root of a Vulgar Fraction. Rule. Reduce the fraction to its lowest terms, then extract the square root of the numerator for a new numerator, and the square root of the denominator, for a new denominator.

If the fraction be a surd (i. e.) a number where a root can never be exactly found, reduce it to a decimal, and extract the root

from it.

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16. What is the square root of 175 ?

Ans. ,89802+: 17. What is the square root of 3577

Ans. ,86602+. 18. What is the square root of 375 ?

Ans. ,933099+ To extract the Square Root of a Mixed NUMBER. Rule 1. Reduce the fractional part of the mixed number to its lowest terin, and then the mixed number to an improper fraction.

2. Extract the root of the numerator and denominator for a view numerator and denominator.

If the mixed number given be a surd, reduce the fractional part to a decimul, anncx it to the whole number, and extract the square root therefrom.

EXAMPLES 19. What is the square root of 513

Ans. 7. 20. What is the square root of 27% 21. What is the square root of my

Ans. 51 Ans. Ss

SURDS.

22. What is the square root of 854 ?

Ans. 9,27 +: 23. What is the square root of 837

Ans. 2,9519-+. 24. What is the square root of 6; ?

Ans. 2,5819+ To find a mean proportional between any two given numbers. Rule. The square root of the product of the given numbers is the mean proportional sought.

EXAMPLES.

27. What is the mean proportional between 3 and 12 ?

Ans. 3x12=36 then N 36=6 the mean proportional. 38. What is the mean proportional between 1276 and 8497

Ans, 1897,47. To find the side of a square equal in area to any given superficies. RULB. The square root of the content of any given supersia cies, is the square equal sought

EXAMPLES.

29. If the content of a given circle be 160, what is the side of the square ?

Ans. 12,&1911. 30. If the area of a circle is 750, what is the side of the square equal ?

Ans, 27,38612. The Area of a Circle given to find the Diameter. Rule. As 355 : 452, or, as 1 : 1,273239 :: so is the area : to the square of the diameter :-or, multiply the square root of the area, bý 1,12837, and the product will be the diameter.

EXAMPLES.

31. What length of cord will be fit to tie to a cow's tail, the other end fixed in the ground, to let her have liberty of eating an acre of grass and no more, supposing the cow and tail to be 5 yards ?

Ans. 6,136 perches. The Area of a Circle given to find the Periphery or Circumference.

Rule. As 113: 1420, or, as 1 : 12,56637 :: the area to the square of the periphery,–or, multiply the square root of the area by 3,5449, and the product is the circumference.

EXAMPLES.

32. When the area is 12, what is the circumference ?

Ans. 12,2798. 33. When the area is 160, what is the periphery ? Ans. 44839.

Any two sides of a right angled triangle given to find the third side..

1. The Base and Perpendicular given to find the Hypothenuse. Rule. The square root of the sum of the squares of the base and perpendicular is the length of the hypothenuse

.

EXAMPLES

34. The top of a castle from the ground is 45 yards high, and surronie into an ethicha din yuris broad; what length must a fareler be iu rtaci from the outside of the ditch to the top of the cásile.

Ans. 75 yaris.

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