under the four fundamental rules may be acquired; as want of accuracy and rapidity in mere calculations distracts the attention which should be given to the investigation and correct statement of clothed exercises. The pupil should be required to do only so many of these number-problems as are found to be necessary to give him facility and accuracy in the four fundamental operations; and he should be allowed to omit some of the harder-clothed problems until he reviews the book.

The chapter on the Metric System is put at the end of the book because many grammar-school pupils have no time for it, while those who have time can as well learn the system at this stage of their progress as earlier.

The chapter on Miscellaneous Problems is intended as a review of the subject-matter of Arithmetic and as a test of the learner's knowledge.

The author is under obligations to many teachers who have given valuable suggestions and assistance in the preparation of this work.

PHILLIPS EXETER ACADEMY, April, 1889.

G. A. WENTWORTH.

VOCABULARY.

Abstract number. This phrase is employed to designate numbers used without reference to any particular unit, as 8, 10, 21. But all numbers are in themselves abstract whether the kind of thing numbered is or is not mentioned.

Addition. The process of combining two or more numbers so as to form a single number.

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Aliquot part. A number which is contained an integral number of times in a given number. Thus, 5, 61, 12, 163, are aliquot parts of 100.

Amount. The sum of two or more numbers. In Interest, the sum of principal and interest.

Analysis. The separation of a question into parts, to be examined each by itself.

Antecedent. The first of the two terms named in a ratio.

Area of a surface. The area of a surface is the number of units of surface it contains; the unit of surface being a square whose side is a unit of length.

Arithmetic. The science that treats of numbers and the methods of using them.

Assets. All the property belonging to an estate, individual, or corporation.

Average. The mean of several unequal numbers, so that, if substituted for each, the aggregate would be the same.

Bank. An establishment for the custody, loaning, and exchange of money; and often for the issue of money.

Bank discount. An allowance received by a bank for the loan of money, paid at the time of lending as interest.

Bonds. Written contracts under seal to pay specified sums of money at specified times, issued by national governments, states, cities, and other corporations.

Cancellation. The striking out of a common factor from the dividend and divisor.

Commission. Compensation for the transaction of business, reckoned at some per cent of the money employed in the transaction. Common denominator. A denominator common to two or more fractions.

Common factor. A factor common to two or more numbers.

Common multiple. A multiple common to two or more numbers. Complex fraction. A fraction that has a fraction in one or both of its terms.

Composite number. The product of two or more integral factors, each factor being greater than unity.

Compound denominations. Several denominations used to express parts of one quantity.

Compound interest. When the interest due is left unpaid, and considered as an increase made to the principal, the whole interest, accruing in any time, is called compound interest.

Compound fraction. A fraction of another fraction.

Concrete number. A phrase used to denote numbers applied to specified things; as 6 horses, 8 desks.

Consequent. The second of the two terms named in a ratio.
Consignee. The person or firm to whom goods are sent.
Consignor. The person or firm who sends goods to another.
Corporation. An association of individuals authorized by law to
transact business as a single person.

Couplet. The two terms of a ratio taken together.

Coupon. A certificate of interest attached to a bond, to be cut off when due and presented for payment.

Creditor. A person or firm to whom money is due.

Cube root. One of the three equal factors of a number.

Customs. Duties or taxes imposed by law on merchandise imported, and sometimes on merchandise exported.

Debtor. A person who owes money to another.

Decimal fractions. Fractions of which only the numerators are written, and the denominators are ten or some power of ten. Decimal point. A dot placed after the units' figure to mark its place. Decimal system. The common system of numbers founded on their relations to ten, ten tens, etc.

Denominator. The number which shows into how many equal parts a unit is divided.

Difference. The number which, added to a given number, makes a sum equal to another given number.