If the above Improvement in the Operations of the Rule of Alligation Alternate, should prove of Service in real Bufiness; the Knowledge thereof may induce the Editor to publish some farther Thoughts upon that Subject.

The Explanation of certain Marks and Characters,

which, for the Sake of Brevity and Perfpicuity, are

frequently used in the ensuing Work. + is the Mark of Addition ; and, when it stands between two

Numbers, denotes that they are to be added together. ; is the Mark of Subtraction; and, when it stands between two Numbers, denotes that the latter is to bc taken from

the former. x is the Mark of Multiplication; and, when it stands between

two Numbers, it denotes that they are to be multiplied

together. • is the Mark of Division; and, when two Numbers are

placed in the same manner as the two Points are here, it denotes that the Number above is to be divided by

that below. = is the Mark of Equality; which, being set between two nu

merical Expressions, denotes that they are equal between

themselves. ::: : are the Marks of Proportionality; and denote that the

Numbers, between which they are placed, are proportional

Numbers.

EXAMPLES. For.4+3=7; read, the sum of 4 and 3 is equal to 7. For 4-3=1; read, when three is taken from 4; the Re

mainder is equal to 1. For 4x3=12; read, the Product of 4 and 3 is equal to 12. For 4; read, if 12 be divided by 3, the Quotient is 3

equal to 4. For 1:4:: 3: 12; read, as I is to 4, fo is 3 to 12.