Elementary arithmetic, with brief notices of its history... by Robert Potts.

in 1 clay. In such cases the efective cause is the product of the units
of agent and the units of time for producing the given effect.
In all questions involving these three elements there will be found
given; one cause, its effect and the time in which it was produced; and
the requirement will be; to find what efect another given cause will
produce in another given time; or what cause will be necessary to
produce another given effect in another given time; or in what time
tanother given cause will produce another given effect.'
5. Proportion is employed in calculating the interest of money,
which is a payment agreed upon between the borrower and the
lender for the loan of a sum of money, called the Principal. This
payment is generally a fixed sum for every ~100 during a year, and
is called the rate per cent. The sum of the Principal and the Interest
together is called the Amount.
Interest is called simple, when it is paid at regular periods, as
yearly or half-yearly, or at the end of the time for which the Principal
was lent. It is obvious that the simple interest of any sum for one
year can be found by a proportion when the interest of ~100 for one.year is given; and the interest for any number of years will be
*determined by multiplying the interest for one year by the given
number of years.
The result, however, is more readily obtained, by dividing by 100,
the product of the principal, the rate per cent., and the number of
years.
The interest for months, for weeks, or for days, of any sum will:also be found by means of a proportion, from the interest for a year,
which may be considered as consisting of 12 months, 52 weeks, or 365
days.
If the amount and the principal be given, the interest is the
difference between them. Also of the principal, amount, rate per
cent., and time; if any three be given, the fourth can be found by
means of a proportion.
Interest is called com2pounld when the interest of the principal for
the first year is not paid at the end of the year (or of the period)
1 The following question may be taken as an example:If 120 men in 15 days of 12 hours long can dig a trench 50 yards in length, 2
in breadth, and 4 deep; how many men will be required to dig a trench 72 yards
long, 6 broad, and 5 deep, in 9 days of 10 hours long?
Here, the first cause, 120 men;
effect, 50 X 2 X 4 cubic yards;
time, 15X]12 hours.
The second cause, Men required;
effect, 72 x 65 cubic yards;
time, 9 X 10 hours.
Taking the effects proportional to the effective causes, the number of men
required will be found to be 324.
The requirement may be varied to find the days, the hours, or the effects.