authority of the teacher, or the writer of the book; and after rendering them familiar to his mind he has nothing to do but to combine and apply the rules in reading or composing the language. He follows, in short, the method of Instruction. But this is an entirely different and opposite process to that which the scholar must pursue who has received some writings in an unknown language, and is endeavoring to make out the alphabet, words, grammar, and syntax of the language. He possesses not the laws of grammar, but words and sentences obeying those laws; and he has to detect the laws if possible by observing their effects on the written language. He pursues, in short, the method of discovery consisting in a tedious comparison of letters, words, and phrases, such as shall disclose the more frequent combinations and forms in which they occur. The process would be a strictly inductive one, such as I shall partially exemplify in the Lessons on Induction; but it is far more difficult than the method of Instruction, and depends to a great extent on the happy use of conjecture and hypothesis, which demands a certain skill and inventive ability.

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Exactly the same may be said of the investigation of natural things and events. The principles of mechanics, of the lever, inclined plane, and other Mechanical Powers, or the Laws of Motion, seem comparatively simple and obvious as explained to us in books of instruction. But the early philosophers did not possess such books; they had only the Book of Nature, in

which is set forth not the laws, but the results of the laws, and it was only after the most patient and skilful investigation, and after hundreds of mistakes, that those laws were ascertained. It is very easy now to understand the Copernican system of Astronomy, which represents the planets as revolving round the sun in orbits of various magnitude. Once knowing the theory we can readily see why the planets have such various movements and positions, and why they sometimes stand still; it is easy to see, too, why in addition to their own proper motions they all go round the earth apparently every day in consequence of the earth's diurnal rotation. But all these changes were exceedingly puzzling to the ancients, who regarded the earth as standing still.

"The method of discovery thus begins with facts apparent to the senses, and has the difficult task of detecting those universal laws or general principles which can only be comprehended by intellect. It has been aptly said that the method of discovery thus proceeds from things better known to us, or our senses (nobis notiora), to those which are more simple or better known in nature (notiora naturae). The method of Instruction proceeds in the opposite direction, beginning with the things notiora naturae, and proceeding to show or explain the things nobis notiora. The difference is almost like that between hiding and seeking. He who has hidden. a thing knows where to find it; but this is not the position of a discoverer, who has no clue ex

cept such as he may meet in his own diligent and sagacious search.

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Closely corresponding to the distinction between the methods of Discovery and Instruction is that between the methods of Analysis and Synthesis. It is very important indeed that the reader should clearly apprehend the meanings of these terms in their several applications. Analysis is the process of separating a whole into its parts, and synthesis the combination of parts into a whole. The analytical chemist, who receives a piece of mineral for examination, may be able to separate completely the several chemical elements of which it is composed and ascertain their nature and comparative quantities; this is chemical analysis. În other cases the chemist mixes together carefully weighed quantities of certain simple substances and combines them into a new compound substance; this is chemical synthesis. Logical analysis and synthesis must not be confused with the physical actions, but they are nevertheless actions of mind of an analogous character.

"In logical synthesis we begin with the simplest possible notions or ideas, and combine them together. We have the best possible example in the elements of Geometry. In Euclid we begin with certain simple notions of points, straight lines, angles, right angles, circles, &c. Putting together three straight lines we make a triangle; joining to this the notion of a right angle, we form the notion of a right-angled triangle. Joining four other equal lines at right

angles to each other we gain the idea of a square, and if we then conceive such a square to be formed upon each of the sides of a rightangled triangle, and reason from the necessary qualities of these figures, we discover that the two squares upon the sides containing the right angle must together be exactly equal to the square upon the third side, as shewn in the 47th Proposition of Euclid's first book. This is a perfect instance of combining simple ideas into more complex ones.

"We have often, however, in Geometry to pursue the opposite course of Analysis. A complicated geometrical figure may be given to us, and we may have, in order to prove the properties which it possesses, to resolve it into its separate parts, and to consider the properties of those parts each distinct from the others.

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A similar distinction between the analytical and synthetic methods can be traced throughout the natural sciences. By keeping exact registers of the appearance and changes of the weather we may readily acquire an immense collection of facts, each such recorded fact implying a multitude of different circumstances occurring together. Thus in any storm or shower of rain we have to consider the direction and force of the wind; the temperature and moistness of the air; the height and forms of the clouds; the quantity of rain which falls, or the lightning and thunder which occur with it. If we proceed by analysis only to explain the changes of the weather we should have to try resolving

each storm or change of weather into its separate circumstances, and comparing each with every other to discover what circumstances usually go together. We might thus ascertain no doubt with considerable certainty what kinds of clouds, and what changes of the wind, temperature, moisture, &c., usually precede any kind of storm, and we might even in time give some imperfect explanation of what takes place in the atmosphere.

"But we might also apply with advantage the synthetical method. By previous chemical investigations we know that the atmosphere consists mainly of the two fixed gases, oxygen and nitrogen, with the vapour of water, the latter being very variable in quantity. We can try experimentally what takes place when portions. of such air of various degrees of moistness are compressed or allowed to expand, or are mixed together, as often happens in the atmosphere. It is thus discovered that whenever moist air is allowed to expand cloud is produced, and it may be drops of rain. Dr. Hutton, too, found that whenever cold moist air is mixed with warm moist air cloud is again produced. We can safely argue from such small experiments to what takes place in the atmosphere. Putting together synthetically, from the sciences of chemistry, mechanics, and electricity, all that we know of air, wind, cloud and lightning, we are able to explain what takes place in a thunderstorm far more completely than we could do by merely observing directly what happens in the