Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

The sun appears to pass completely around the earth in 24 hours, that is, it appears to move westward over 360° of longitude in 24 hours. Consequently, in one hour it will move over of 360° 15° of longitude. Hence, if the difference in the longitudes of two places is 150, it will be noon at the more easterly place, just one hour before it is noon at the other place. And in all cases, the difference in time of any two places will be at the rate of one hour for every 150 of longitude between the two places. As an example, suppose the city of Washington to be 770 west of Greenwich: it is required to find what time it is at Washington, when it is noon at Greenwich.

Dividing 770 by 15° we have 5

for the number of hours difference in time, that is, 5h. 8m. And as the apparent motion of the sun is westward, it must be earlier at Washington than at Greenwich. Therefore, when it is noon at Greenwich, 15h. m. before noon at WashWasni..gton 6h. 52m. A. M.

ington; that is, it is

What use is made of Circular Motion? Into how many degrees are all circles supposed to be divided? Repeat the Table. Over how many degrees of longitude does the sun appear to move in 24 hours? Over how many degrees in 1 hour? What is the difference of time corresponding to 770? When it is noon at Greenwich, what time is it at Washington, 770 west of Greenwich?

78. Measures, &c., not included in the foregoing tables.

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
[merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small]

79. A sheet folded into two leaves is called a folio. " folded into four leaves is called a quarto,

or 4to.

66 folded into eight leaves is called an oc

[ocr errors]

tavo, or 8vo.

folded into twelve leaves is called a duo

decimo, or 12mo.

folded into eighteen leaves is called an 18mo.

When a sheet is folded into two leaves what is it called? How called when folded into four leaves? How, when folded into eight leaves? How, when folded into welve leaves? How, when folded into eighteen leaves?

REDUCTION.

80. REDUCTION is the changing of numbers from one name or denomination to another, without altering their value.

When the denominations are to be reduced from a higher denomination to a lower, it is called Reduction Descending; but when they are to be reduced from a lower to a higher denomination, it is called Reduction Ascending.

REDUCTION DESCENDING.

Let it be required to reduce £7 5s. 10d. 3 far. to farthings

OPERATION.

7 the number of pounds.

Multiply by 20, the number of shillings in one pound. 140 product in shillings.

[blocks in formation]

145 the number of shillings.

Multiply by 12, the number of pence in one shilling.

290

145

1740 product in pence.

Add 10 pence.

1750 the number of pence.

Multiply by

4, the number of farthings in one penny.

Add

7000 product in farthings.

3 farthings.

7003 the number of farthings sought.

From the above operation, we readily deduce this general

RULE.

Multiply the number in the highest denomination by the number indicating how many of the next lower make one in

that higher; to this product add the number, if any, belonging to this lower denomination; we shall thus obtain an equiva lent value in the next lower denomination.

II. Proceed in a similar way for all the successive de nominations; the last result will be the number sought.

What is Reduction? When is it called Descending? And when Ascending Repeat the rule for Reduction Descending.

REDUCTION ASCENDING.

81. Let it be required to reverse the last example, that is, to find the number of pounds, shillings, pence, and farthings, in 7003 farthings.

We must obviously perform a reverse operation to that performed under Reduction Descending.

[blocks in formation]

Collecting results, we have 7003 farthings, equivalent

to £7 5s. 10d. 3 far.

EXPLANATION.

First, we divide the number of farthings, 7003, by 4, because 4 farthings make one penny; the quotient is 1750 pence, and 3 farthings remaining.

Secondly, we divide the number of pence, 1750, by 12, because 12 pence make one shilling; the work being performed by Long Division, we get for the quotient 145 shillings, and 10 pence remaining.

Thirdly, we divide the number of shillings, 145, by 20, because 20 shillings make one pound; cutting off the cipher from the right of 20, and the right-hand figure from the dividend, (ART. 30,) we perform the work by Short Division, and obtain the quotient, 7 pour ls, and 5 shillings remaining.

We may, therefore, deduce this general

RULE.

I. Divide the given number by as many of its denomination as make one of the next higher; write down the quotient and remainder, if any.

II. Divide the quotient by as many of its denomination as make one of the next higher; write this new quotient and the remainder as before.

III. Proceed in this way through all the denominations to the highest, and the quotient last found, together with the several remainders, if any, will give the value sought.

Repeat the Rule for Reduction Ascending.

« ΠροηγούμενηΣυνέχεια »