principles upon which they are founded. This will serve as a sort of connecting chain, and enable the learner easily to review the whole of the problems contained in the work. Problem I. is given only as an example of the advantageous manner in which young persons may be exercised in drawing up for themselves an account of the names and situations of the principal countries, islands, &c. The method of performing most of the problems, by maps and calculation, is added. This, it is hoped, will be a great advantage: for performing the same problems, by two or three different methods, will make them more fully understood.

In those problems that require numerical calculations, it is adviseable to accustom the pupils to mental arithmetic ; and it will be found that even children can add, subtract, and multiply without the aid of a pencil. A little accuracy may be sacrificed to facility; as in multiplying by 70 instead of 69, to bring degrees to English miles.

Brevity being aimed at in giving the general rules, explanatory notes have sometimes been added, printed in a smaller type. It will also be seen that, in some of the sections, the examples have been so arranged as to illustrate the general observations placed at the beginning of the section. The method of performing the problems by Adams's globes is given, when that is different from the common method.

Part III. treats of the celestial globe: it is divided into four sections, and contains thirty problems.-The first section contains problems relating to the stars; the second to the sun; the third to the planets; and the fourth to the moon. The above arrangement was adopted on account

of the stars being laid down upon the celestial globes, whilst the other heavenly bodies are not. Each section is preceded by a short account of those bodies, not indeed enough to satisfy curiosity, but it is hoped sufficient to excite it,

In performing the problems of the first section, the pupils will be familiarised with the names and characters of the principal fixed stars; but it is not enough to know them on the globe, they ought to be able to distinguish them in the heavens. Problem XII. will be of the greatest assistance to the pupils in doing this, as the authors have found from experience.

The planets which, from their size and colour, may easily be distinguished, should also be pointed out to them; and from noticing near which of the fixed stars they are at any time situated, their apparent motion in the heavens may easily be discovered. They may be taught to find the amplitude of the sun at rising or setting, and its meridian altitude at different times of the year. By directing them to view Nature herself, instead of referring them to imperfect delineations of her works, they will form more correct and sublime ideas of the universe.

The method of constructing maps is given at the end: this will be of great use in assisting young persons to draw maps for themselves, which is one of the most effectual ways of learning geography.-There is also a list of the latitudes and longitudes of all the places mentioned in the examples, to enable the learner to find them more readily upon the globe or maps.

As the work was not originally intended for the use of mathématical students, none of the examples have been

calculated by spherical trigonometry.* In some problems, such as to find the places that have the same latitude, &c. several places are inserted that have only nearly the same latitude. This observation must also be extended to the problems for finding the antoeci, perioeci, &c.

In compiling this little treatise, unlimited use has been made of the works of former writers on the subject; and as the greater part of it was drawn up at a time when there was no intention of publishing it, care has not always been taken to make the proper acknowledgements. This defect can now no otherwise be remedied than by stating, that to Varenius's Geography, Martin and Brandsby on the Globes, Dr. Hutton's Mathematical Dictionary and Translations of Montucla's Mathematical Recreations, the Companion to Arrowsmith's Map of the World, Pinkerton's Geography, and the Scientific Dialogues, this work is much indebted.

Conscious that this little treatise must possess many imperfections, it is not without great diffidence now delivered into the hands of the public: but those who are the most capable of distinguishing its faults, will be the most ready to pardon them.

Newcastle, May 15, 1805.

* The mathematical student is referred to Kelly's Spherics, or to Dr. Olinthus Gregory's Trigonometry, lately published for the use of

schools.

ADVERTISEMENT

TO THE

FIFTH EDITION.

IN preparing this edition, it has been the chief object of the editor to render this work still more worthy of the public approbation, by inserting every thing in it, which he thinks necessary for the pupil to attend to, on beginning to study Geography; and it is hoped those teachers who have already done it the honour to introduce it into their academies, or those who may in future adopt it as a Class Book, in teaching Geography, will find it sufficient to answer all the purposes of an introductory work on that subject. The additions occupy nearly a hundred pages, and are,..a catalogue of the chief towns in England and Wales, the rivers on which they stand, their population, and remarks on the trade of each the towns in Scotland and Ireland :—a minute account of the different states in Europe, so arranged as to correspond to a series of questions applicable to each state :—a very full catalogue of the sea-ports in Europe, their situation, and (as far as could be obtained) their imports and exports, with their latitude and longitude.

:

The population of the British towns is taken from the Abstracts of Returns made in 1811, and laid before parliament. In drawing up the list of the sea-ports of Europe, Oddy's European Commerce was chiefly consulted; where that failed, the new edition of Crutwell's Gazetteer was applied to.

The editor, without attempting to dictate to others, as to the method of teaching Geography, suggests the following plan, as one which he has found useful. To commit to memory the definitions, page 1,-situation of Europe, p. 4,-states in Europe― oceans and seas—bays, gulfs, and straits-lakes and mountainsvolcanoes (the rivers to be omitted)-proceed to islands, page

10th, isthmuses-capes-British Islands-England-counties with chief towns and rivers on which they stand-(general description of English rivers and canals, to be omitted, and also the towns in Enland and Wales.) To proceed in the same manner with Scotland and Ireland, viz. :—to learn the general situation and counties, (omitting the rivers and towns,) then proceed to the general survey of Europe, page 72, and either direct the whole to be committed to memory, or a selection of the questions as may be most suitable to the abilities of the learner. Having finished Europe, (omitting the sea-ports) it may then be proper to go over the whole again, and to learn those parts which were before omitted, viz, the rivers, towns, sea-ports, &c. Then to proceed in a similar manner with the other quarters of the globe.

Care must be taken, however, to furnish the pupil with good maps, on which to point out every thing which they commit to memory; and, also, blank maps of Europe, England, Scotland, Ireland, &c. on which to trace out the various divisions and boundaries. These blank maps the pupils may casily draw for themselves.

The catalogues of towns will form some useful and amusing exercises for young people. Let them first find out all the English towns on the map; then let it be an exercise to write out an arrangement of the towns according to their population, noticing at the same time the rivers on which they stand, and the remarks on each. The exercise may also be varied, by making them arrange the towns in the order of the counties; and, by referring constantly to the map, they will, without much labour, gain a general knowledge of all the chief towns in England, and of the importance of each. A similar use may be made of the Scotch and Irish towns.

In the sea-ports of Europe, let them be required to write out a list of those that are situated on a particular sea, as on the Baltic, the Mediterranean, &c. or of those belonging to particular countries, as Russian sea-ports, French sea-ports, &c. remarking the particular trade of each port.-They may also point out those from which particular goods are exported, as timber, hemp, &c.

Whilst the pupils are committing Part I. to memory, they may begin to perform the problems in Part II. But as the