Liquid Measure, or Measure of Capacity, is used in the sale of both dry and liquid goods, although it is becoming more the fashion now to sell all dry goods by weight. The imperial gallon will hold 10 pounds of pure water, or its contents is about 277 cubic inches.

WOOL WEIGHT.

This weight is closely connected with Avoirdupois, and is expressed thus :

Time.-Every four years we have leap year. If the year will divide by 4 without a remainder it is leap year, for instance, 1876 divides by 4, and is leap year; 1878, when divided by 4, gives a remainder 2; it is the second year after leap year. The exact length of a year is 365 days 5 hours 48 minutes 47.4624 seconds. Leap year contains 366 days, while an ordinary year consists of 365. 28 days form a month of 4 weeks. The calendar months vary in length, and the number of days in each can be remembered by the following rhyme :

There are other coins in circulation in Great Britain and her Colonies, viz., the threepenny piece and fourpenny piece : the value of the old groat was 4d.

ARITHMETIC.

ARITHMETIC is the Science of Numbers, and treats of their properties. The figures, or numbers, employed in arithmetic

Any number, however large or small, may be represented by means of these ten signs. A Unit, or unity, represented by 1, means a single object or thing, as one pen, one book, one man, one table, etc.

Number means one or more than one (i.e., more than unity). In speaking of a number, it may be one pen, two books, three men, four tables, etc.

The figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, are termed the digits, although we sometimes speak of the nine digits. The first nine are called significant figures, to distinguish them from the last (0), which means nothing, and is called the zero, cypher, or nought; it has no value of itself, although it is employed to alter the value of other figures when joined to them. The digits are so called from a Latin word digitus, which means a finger, because the fingers would be the first objects used in counting. When a child is in a difficulty with regard to the summation of numbers, nothing is more natural to it than to refer to its fingers.

An Integer, or whole number, is a unit, or a collection oí units, as 1, 2, 7, 49, 513, etc.

An

Numbers are of two kinds-Abstract and Concrete. abstract number is one considered without reference to a particular object or kind of unit, as five, nine, twenty, etc.

A concrete number is one that has reference to some particular kind of unit, as one candle, two apples, nine brushes, two hundred fish, etc.

An even number is one that can be separated into two equal parts, both forming whole numbers by themselves, as 2, 8, 40, 96, 106.

An odd number is one that cannot be separated into two equal parts, both forming whole numbers by themselves, as 3, 9, 41, 97, etc.

A Simple Quantity consists of one denomination only, as 1 inch, 12 pints, 45 shillings.

A Compound Quantity consists of more than one denomination, as 4 yds. 3 ft. 11 in., £21, 10s. 6d.

Notation is the art of expressing numbers by means of symbols. We express the number "five hundred and sixteen" thus-516.

Numeration is the art of expressing the signs and symbols indicating numbers in words. We express the symbols or signs 4523 by the words "four thousand five hundred and twenty-three." Hence numeration is the opposite to notation.

The digits have a local value and an intrinsic value. The local value of a figure depends upon the place it occupies when placed in connection with others or with itself. Take the number 5433-the 3 on the right denotes simply 3 units, or it has its intrinsic value of 3 only; the next 3, or the one to the left, denotes ten times 3, or thirty, this is its local value, or by placing a figure one remove to the left we increase its intrinsic value tenfold; the figure 4 indicates four hundred, we may say its simple value is 4, but it here represents 4 hundreds, so that its intrinsic value is increased one hundred-fold what it would have been had it been placed as the first figure on the right hand; the 5 has a local value called five thousand, being increased a thousand-fold.

The cypher, O, has no value of itself, but by placing it to the right of a figure or number it increases the value of the figure or number tenfold; because it affects the local position of the other figures. Each of the digits has the same effect on the others when joined to them. We can indicate numbers up to nine with one figure only. All numbers from ten to ninety-nine, inclusive, are indicated by the combination of two figures; and no higher number than ninety-nine can be expressed with two figures.

All numbers from one hundred to nine hundred and ninetynine are expressed by combining three figures. Thousands are expressed by the combination of four figures, ten thousand by five, etc., etc.

Numbers are enumerated on the following system:

When enumerating we read from left to right. The first figure on the right hand occupies the units' place, and represents 9 units.

The second figure, 8, occupies the tens' place, and represents eight tens or eighty.

The third figure, 7, occupies the hundreds' place, and represents seven hundred.

The fourth figure, 6, occupies the thousands' place, and represents six thousand; the 5 represents fifty thousand; the 4, four hundred thousand, etc., the whole number being read thus:

Seven hundred and eighty-nine billions, one hundred and twenty-three millions, four hundred and fifty-six thousands, seven hundred and eighty-nine.

It is a difficult matter to form an idea of what number a million really consists, or to give children a definite idea of the same. A halfpenny measures an inch in diameter. If the floor of a schoolroom 30 feet wide were covered with a million halfpennies touching each other, each would occupy or cover a space of one square inch; the room 30 feet wide to have a million halfpennies lying on their faces on the floor must be 231 feet long-five or six times the length of an ordinary schoolroom.

When large numbers have to be expressed, they are divided into groups of three figures, and taking them from right to left the first group consists of hundreds, the second of thousands,