has been suggested for the prevalence of this mode of communication. "We can conceive occurrences which would give us evidence that the Moon, as well as the Earth, contains geometers. If we were to see, on the face of the full moon, a figure gradually becoming visible, representing a right-angled triangle with a square constructed on each of its three sides as a base; we should regard it as the work of intelligent creatures there, who might be thus making a signal to the inhabitants of the earth, that they possessed such knowledge, and were desirous of making known to their nearest neighbours in the solar system, their existence and their speculations." Plurality of Worlds, Chapter IV.

40. In asking the beginner to give his attention to the work on Natural Philosophy now put into his hands, it will be well to remind him that the knowledge which he gains from the book should be confirmed and extended by carefully watching the phenomena which spontaneously offer themselves to his observation, and also by attending good experimental lectures if such be within his reach. Some attempt might be made to supersede the advantage of external observation and experiment by elaborate drawings, but it is difficult to make these easily intelligible without familiarity with the objects they represent, and after such familiarity they become superfluous. While it may be readily admitted that books on Natural Philosophy alone do not make a sufficient impression on the mind and memory, it is equally certain that a book in which the principles are recorded and explained, is a necessary accompaniment to the oral and visible teaching of the lecture room. It must not be forgotten that in the course of life books are always and everywhere accessible, but lectures by no means so certainly; hence too much stress cannot be laid on the importance of early acquiring the habit of learning from books. In these days of diffused knowledge it is curious to observe how many persons of respectable education are practically unable to read; though they may be fluent in conversation and quick to appreciate what is made audible or tangible, they have never accustomed themselves to apply with close attention to the silent and unobtrusive teaching of the printed page.

41. It has been the singular honour of some elementary books intended mainly for youth that they have fallen under the notice of persons of maturer power, and have thus indirectly influenced the history of science. Thus it has been stated that Mrs Marcet's Conversations on Chemistry "first opened out to Faraday's mind that field of science in which he became so illustrious, and at the height of his fame he always mentioned Mrs Marcet with deep reverence." (Mrs Somerville's Personal Recollections..., page 114.) The same book had the honour of Dr Whewell's attention; he read it and made a short analysis of it in 1817. A sentence in Mrs Somerville's Connection of the Physical Sciences incited a living astronomer to undertake the laborious investigation which finally enabled him to ascertain the existence of the planet Neptune, then unknown.

II. VARIOUS BRANCHES OF KNOWLEDGE.

42. Many eminent philosophers have turned their attention to the subject of the classification of the various branches of knowledge, and though no solution of the difficult problem has been obtained which is entirely satisfactory, yet the attempts have been interesting and instructive. We shall not give here any elaborate discussion of the subject, but a few remarks will be advantageous, as they will furnish a general idea of the range of the present work.

43. It will be sufficient for our purpose to consider that there are five main branches of knowledge; these may be called Mathematical, I hysical, Chemical, Vital and Mental.

44. The Mathematical sciences relate to number and to figure. They have as their foundation Arithmetic and Geometry. They are sometimes called abstract sciences, being to a great extent independent of all that takes place in the world around us, and derived by the human mind

from its own resources. These sciences have been cultivated from the days of the ancient Greeks to our own, and as, from their nature, whatever has been once established in them remains as a permanent truth, an enormous mass of striking and valuable results has been accumulated by the labour of successive generations. As we have already said, the amount of mathematical knowledge assumed for the purposes of the present work is very slight.

45. The Physical sciences are often called Natural Philosophy. Such sciences might have originally included the knowledge of everything which the world of Nature contains; but at present the term is somewhat restricted in its application. Natural Philosophy now may be said to include a group of sciences which has grown up round Astronomy, the oldest and most perfect of them all. Astronomy at first involved only observations of the situations of the heavenly bodies, and predictions of their future course from the records of the past; but Newton by his theory of gravity extended the subject and deduced the motions of the moon and the planets from one general law. Then the whole science of Mechanics in its widest sense was gradually formed; this treats of the connexion between force and the motion which it produces or changes or arrests, and it has different names according as it relates mainly to motion or to rest, to solid or to fluid bodies. With Astronomy is naturally connected the science which treats on Light, the medium by which so much of our knowledge of the skies is obtained; and Navigation which is closely connected with Astronomy introduces Magnetism in virtue of the Mariner's Compass. Light may be said to draw with it the kindred subject of Heat, and Magnetism all the train of sciences which in modern times have sprung from this and Electricity. The progress of every science and of every part of a science resembles that of Astronomy; it is traced back to more simple and more general principles as its origin, and carried forward to more numerous and more varied applications and extensions.

46. The Chemical sciences take their rise from the fact that there is more than one kind of substance in nature. Had there been only one kind, what is called Chemistry

would have been absorbed in Natural Philosophy. But there are more than sixty different kinds of substance, as gold, silver, charcoal, sulphur, and others, which, at least according to present knowledge, are believed to be quite distinct. Now all the Laws of Natural Philosophy hold with regard to each of these kinds of substance separately, so that no new science is introduced as yet. Moreover observation and record of the special properties of each kind of substance would be included in what is popularly known as Natural History. But it is found that when two or more of these different kinds of substance are brought together under certain circumstances, then special phenomena are seen. Thus, for example, fine sand and powdered soda exposed to heat and melted together become glass, which differs from each of its components as to its distinctive properties. Again, the metal sodium is poisonous, if swallowed, and the gas chlorine if breathed; if these are brought together they explode and burst into a flame, and the result of the combustion is common salt, which is very wholesome. Chemistry then treats of all the phenomena which are connected with the combination of two or more kinds of substance to form a new body, or with the separation of any body into the simple kinds of substance of which it may consist. The science had its origin in the attempts made by enthusiasts to convert the more common metals into gold the most valuable: these men received the name of alchemists.

47. Next we have to consider the sciences which involve the idea of Life. The bodies of men and of animals, and the vegetable structures, consist of various remarkable collections of tubes and cavities, in which fluids circulate and produce constant change. In addition to the laws which prevail and the forces which act in Natural Philosophy and Chemistry, others of a peculiar kind here present themselves; instead of the permanence which belongs more or less to the objects of the two former divisions of knowledge, we have here the changes involved in birth, growth, and decay.

48. In the last place we have sciences which relate to the mind itself, as Logic and Metaphysics. These have

been cultivated from the origin of civilization, and though they have passed through various fluctuations of influence have never lost their charm. "Even in ages the most devoted to material interests, some portion of the current of thought has been reflected inwards, and the desire to comprehend that by which all else is comprehended has only been baffled in order to be renewed." In this division we may place various studies which bear, at least indirectly, on the mind-as that of Languages which has long been held of great value as a training, History which teaches by example the lessons of duty and prudence, and Moral Philosophy which gathers these lessons into a system, and seeks to enforce them by adequate sanctions.

49. It is easy to see that the rough division which we have given of the branches of Human Knowledge is open to the objection of a failure in distinctness; some sciences may claim to appear under more than one of the five classes. Thus we make Mathematics a distinct class, and yet it must be allowed that this science enters largely into all the elaborate works on Natural Philosophy. The aid of Mathematics is absolutely necessary in order to develop fully the principles which are discovered in operation throughout nature; and not unfrequently the wish to penetrate further into the constitution of the earth and the heavens has led men to the construction of new methods in Mathematics. The sciences which we include under the title Natural Philosophy have sometimes been called Mixed Mathematics, while the title Pure Mathematics has been adopted as more strictly appropriate to the first of our five classes. Up to the present time Chemistry has not been annexed to Mathematics; but eminent men, among whom Faraday may be named, have pointed with satisfaction to that as the destiny of their science.

50. Again, some of the subjects which we have included under Natural Philosophy are closely connected with Chemistry. Thus, many of the changes which Chemistry investigates are produced by the agency of Heat; so that this subject belongs both to the third and to the second class of our arrangement. A similar remark holds with respect to Electricity and the kindred sciences. Again,