In order to discover the value of any compounded num ber it must be observed, that a mamber placed in the first place towards the right hand, ftands for no more than its real intrinsic value, but increafes in value in a tenfold proportion by every remove towards the left hand: thus, in the number 1799, the firft figure o ftands for 9 only; the fecond 9 figure being in the fecond place towards the left hand, its value is increased tenfold; thus it reprefents ninety, or ten thnes nine; which, with the foregoing 9, ftands for ninetynine. Again, the figure 7, which ftands in the third place towards the left hand, is increased to ten times as much as it would be if it flood in the next inferior place, viz, where the laft-mentioned 9 ftands: thus it reprefents feven hundred; which, with the two fore-mentioned figures, ftand for seven hundred and ninety-nine. The figure 1, which fands in the fourth place, towards the left hand, is alfo increased ten times in value to what it would be if it food in the next inferior place, where the 7 is placed; in which cafe it would reprefent one hundred; whereas, in the prefent inftance, it ftands for one thoufand; and with the other figures reprefents one thoufand, feven hundred, and ninety-nine.

This defcription of the four foregoing figures may ferve to give the uninformed au idea of the value of figures, according to the different places they occupy in a compounded number. For every remove of a figure towards the left hand increases its value to ten times as much as before; as will more fully appear by the following table, called the Numeration Table:

The

In order to read any number with facility and cafe, it is neceffary that the learner have all the names of the numbers at the head of the table perfectly in his memory, that he may apply them to any other number he may have occafion for; calling the first figure, on the right hand, units; the fecond, tens; the third, hundreds; the fourth, thoufands; &c. as in the table.

Thus, the bottom figure in the table, ftanding under the place of units, is itself an unit, or a fingle one. The next

higher number in the table confifts of two figures, 1 and 0; the first whereof, ftanding in the place of tens, ftands for ten, being only a figure one: the other figure, being a cypher, and in the place of units, ftands for nothing, or no units: these two figures, therefore, exprefs only ten. The next number confifts of the figures 432; the four being in the place of hundreds, fignifies so many hundreds; the three, as many tens; and the two, as many units; and is thus expreffed: four hundred and thirty-two. The fourth number in the table confifts of four figures, the firft whereof stands in the place of thousands; this number, therefore, is thus expreffed: eight thousand, feven hundred, and fixty-five. The fifth number has its highest figure in the place of tens of thousands, and is thus expressed: feventy-eight thousand, nine hundred, and nine; it having a cypher in the place of tens, which stands for nothing. The fixth number confifts of hundreds of thousands, and is thus expreffed: one bundred and twenty-three thoufand, four hundred, and fifty-fix. The highest place of the feventh number is that of millions: it is expreffed thus: fix million, five hundred and forty-three thousand, two hundred, and ten. The eighth number confifts of tens of millions, and is thus expreffed: fixty-feven million, eight hundred and ninety thoufand, nine hundred, and eighty-feven. The ninth number has its highest figure in hundreds of millions; it is expreffed thus: three hundred and twenty-one million, twelve thousand, three hundred, and forty-five.

The fix other numbers are expreffed as follows:-The tenth number: feven thousand, eight hundred and ninety millions, nine hundred and eighty-feven thoufand, fix hundred, and fifty-four. The eleventh number: forty-three thoufand, two hundred and ten million, one hundred and twenty-three thoufand, four hundred, and fifty-fix. The twelfth number: four hundred and fifty-fix thousand, seven hundred and eighty-nine million, ninety-eight thousand, feven hundred, and fixty-five. The thirteenth number:

nine million of millions, eight hundred and feventy-fix thoufand, five hundred and forty-three million, two hundred and ten thousand, one hundred, and twenty-three. The fourteenth number: forty-three million of millions, two hundred and ten thousand, one hundred and twenty-three millions, four hundred and fifty-fix thoufand, feven hundred, and eighty-nine. The fifteenth number: one hundred and twenty-three million of millions, four hundred and fiftyfix thousand, feven hundred and eighty-nine millions, ninetyeight thoufand, feven hundred, and fixty-five.

I have, in the table, diftinguished every three figures by a point, or comma, beginning at the right hand, as is generally done in public offices, and by men of extenfive business.

This method alfo affords an eafier way of enumerating numbers, than by the foregoing table, as every three figures may have a common furname appropriated to them (inserted in italics at the head of the table), befides their names of units, tens, and hundreds: thus, when the learner çan enumerate the first three figures in a number, and knows the proper furname to apply to each three figures, he may enumerate any number, however large. The first three figures on the right hand have no furname, as they stand simply for units, tens, and hundreds; but the next three figures have the furname of thousands; the next three have the furname of millions; the next three, thousands of millions; and the other three figures have the furname of millions of millions. Thus, to repeat the higheft number in the table, beginning at the left hand, I say, one hundred and twenty-three (to which I add its furname of) million of millions; four hundred and fifty, fix (with its furname) thoufands of millions; feven hundred and eighty-nine (with its furname) millions; ninety-eight (furname) thousands; feven hundred, and fixty-five.

I have been more particular in the defcription of the Numeration Table, as it is generally found the most difficult of all the tables in Arithmetic to a learner; and feveral perfons who have arrived to a tolerable proficiency in this science,

are,

are, nevertheless, very imperfectly acquainted with this moft effential part.

Belides the foregoing ten characters used to exprefs numbers, there are alio letters employed for the fame purpose, called Numerical Letters. This was the ancient method of expreffing numbers, and is ftill made ufe of frequently, in the title-pages of books, and in funeral monuments in Roman hiftory, to exprefs the date of the year.

I, ftands for one.

V, five.

X, ten.

L, fifty.

C, an hundred.

D, or 13, five hundred.
M, or CIO, a thoufand.
100,, five thousand,
CCIO, ten thousand,
1300, fifty thousand..
CCCC, a hundred
thousand.

ɔɔɔɔɔ, five hundred
thoutand.

CCCCC33303, ten hundred thousand, or a million.

The letters MDCCCVIII exprefs the number 1808, the date of the present yearM standing for one thousand, D for five hundred, CCC three hundred more, which is eight hundred, and VIII eight; together one thoufand, eight hundred, and eight.

If a letter or letters of inferior value follow one of fuperior value, they are to be added thereto: thus, VI fignify- fix, VII feven, VIII eight, and DCC feven hundred. But when a letter of inferior value is placed before one of fuperior value, it is then to be deducted therefrom: thus, IV fignify four, IX nine, XL forty, CD four hundred, &c.

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SECT.