Second Stage.

Simple equations involving one unknown quantity. Simple equations involving two unknown quantities. Easy quadratic equations.

Third Stage.

Equations solved like quadratic.

Quadratic involving simul

Fourth Stage.

taneous equations. Involution. Evolution. Indices and surds.

Ratio, proportion, variation and the progressions.

GEOMETRY.

First Stage.

Euclid, Book I. to Proposition 26.

Second Stage.

Euclid, Books I. and II. Elements of Mensuration.

Third Stage.

Euclid, Books I., II. and III.

More advanced Mensuration.

Fourth Stage.

Euclid, Books IV. and VI. and the definitions in Book V.

TRIGONOMETRY.
First Stage.

The different measurements of angles, and the ordinary relations of their trigonometrical ratios.

Second Stage.

The elementary formulæ connecting the trigonometrical ratios of two or more angles. The theory and application of logarithms.

Third Stage.

Solution of triangles, including the determination of their areas. The determination of heights and distances of inaccessible objects.

MECHANICS.
First Stage.

Bodies at rest (Statics). Definitions. Parallelogram of forces. Centre of gravity. Mechanical powers.

Second Stage.

Matter in motion (Dynamics). Definitions. Laws of motion. Parallelogram of velocities. Direct impact of two spheres.

Third Stage.

Fluids (Hydrostatics and Pneumatics). Definitions. Law of equilibrium of floating bodies. Hydrostatic press. Boyle's law. Air-pump. Common pump. Barometer.

SOUND, LIGHT AND HEAT.

First Stage.

Propagation of sound. Elementary notions of vibrations and waves. Reflection of sound, echoes. Musical notes, simple instruments. Simple explanations of beats and modes.

Second Stage.

Sources and propagation of light. Intensity, shadows, and shadow photometer. Reflection, mirrors, refraction, lenses, elementary explanations of the microscope, camera obscura and magic lantern. Dispersion, prisms. The rainbow, reflecting and refracting telescopes.

Third Stage.

The three modes in which heat may be conveyed from place to place. Effects of heat on solids, liquids and gases. Expansion by heat. Elementary notions of specific heat. Heat produced by mechanical, chemical and vital action.

MAGNETISM AND ELECTRICITY.

First Stage.

Attraction, repulsion and polarity, as illustrated by the magnet. Terrestrial magnetism and the mariner's compass.

Second Stage.

Attraction of light bodies by rubbed sealing-wax and glass. Experimental proof that there are two forms of electricity. Attraction and repulsion. Gold-leaf electroscope. Construction of electrophorus, electrical machine and Leyden jar. Explanation of atmospheric electricity.

Third Stage.

Voltaic or chemical electricity. The voltaic battery and motions of a current.

ANIMAL PHYSIOLOGY.

First Stage.

The build of the human body. Names and positions of the internal organs. The properties of muscle.

Second Stage.

The mechanism of the principal movements of the limbs and of the body as a whole. The organs and functions of alimentation, circulation and respiration.

Third Stage.

The general arrangement of the nervous system. The properties of nerve. Reflex action. Sensation. The organs and functions of touch, taste, smell, hearing and sight.

BOTANY.

First Stage.

Characters of the root, stem, leaves and parts of the flower, illustrated by specimens of common flowering plants.

Second Stage.

Structure of wood, bark and pith. Cells and vessels. Food of plants, and manner in which a plant grows. Functions of the root, leaves and different parts of the flower.

Third Stage.

The comparison of a fern and a moss with a flowering plant. The formation of different kinds of fruits. The structure of a

bean and of a grain of rice or corn. The phenomena of germina

tion.

CHEMISTRY.

First Stage.

Elementary and compound matter. Illustrations of combination and decomposition in such bodies as hydrochloric acid, water, oxide of mercury and rust of iron.

Second Stage.

Preparation and properties of the common gases, such as oxygen, hydrogen, nitrogen and chlorine. The chemical character and constituents of pure air and pure water, and the nature of the impurities sometimes found in both.

Third Stage.

The properties of carbon and its chief inorganic compounds. Differences between metallic and non-metallic bodies. Combination by weight and volume. The use of symbols and chemical formula.

TECHNICAL AGRICULTURE.

First Stage.

The principles influencing the supply of plant food in the soil, the necessity for cultivation, and the circumstances making tillage more or less effective.

Second Stage.

The principles regulating the more or less perfect supply of plant food. Manures as supplemental sources of plant food.

Third Stage.

The principles regulating the growth of crops, and the variations in their yield and quantity.

PHYSICAL GEOGRAPHY.

First Stage.

The nature of a river or stream, whence it is supplied, and what becomes of it. Evaporation and condensation. Rain, snow, hail, dew and mist. The atmosphere and its composition. Winds. An explanation of the terms "river-basin" and "water-shed."

:

Second Stage.

The ocean its extent, divisions, depth, saltness and currents. Action of waves, sea beaches. The phenomena of the tides.

Third Stage.

Form and size of the earth and its motions. Day and night. The seasons of the year; how they depend upon the relative positions of the earth and sun. Moon's dimensions and distance. Explanation of her phases. General arrangement of planetary system.

AFRICAN MATTERS.

First Stage.

An acquaintance with the history and geography of the West Coast of Africa.

Second Stage.

An acquaintance with the history and geography of the interior lands of West Africa, and with the institutions, religions, traditions and customs of the various tribes.

Third Stage.

An acquaintance with the history and geography of Africa, particularly of Eastern and Equatorial Africa, and with the institutions, religions, traditions and customs of the various tribes.

LOGIC.
First Stage.

Terms and their various kinds. The twofold meaning of Terms -in Extension and Intention. Classification. Propositions and Conversions of Propositions. Rules of the Syllogism. Hypothetical Syllogisms. Fallacies in Deductive Reasoning.

Second Stage.

Inductive Reasoning. Observation and Experiment. Antecedents and Causes of Events. Methods of Agreement, Difference and Variation. Reasoning by Analogy. Fallacies in Inductive Reasoning.

SHORTHAND.

First Stage.

To show an acquaintance with the first fifty exercises of Pitman's Phonographic Teacher and to be able to read and write any piece with ease in the learner's style.

Second Stage.

To show an acquaintance with Pitman's Phonographic Teacher and to be able to read and write with tolerable ease any piece in the corresponding style.

Third Stage.

To be able to read any portion of "Self-Culture," to know "The Manual" and to be able to write from dictation in the reporting style.

Simple crochet. Cross-stitch samplers. Outlining in crewels.

Second Stage.

Advanced crochet. Crewel work. Wool work. Braiding. Knitting simple.

Third Stage.

Advanced kinds of all the matters included in Stage II. Embroidery of all kinds. Lace work. Knitting socks or stockings.

* For female pupils only.