made some remarkable advances soon afterwards. Optics and Harmonics were also cultivated as mathematical sciences among the Greeks. And these sciences, especially Astronomy, were employed as portions of the Higher Education. Such sciences derive their fundamental principles from observation of the material world; and deduce results from these principles by mathematical processes. Besides these portions of knowledge, thus obtained in various ways, the Greeks employed themselves in speculating concerning the nature of knowledge in general, and the mode in which man may and must acquire it. Such speculations formed a large portion of their Philosophy; and such Philosophy has occupied every succeeding generation up to the present time; and most, the generations of greatest intellectual activity.

20 In this portion of human knowledge, which has thus been progressive, it naturally follows that the subjects are expanded, transformed, and multiplied by the successive steps of progress. The Science and Philosophy of modern times differ from, or at least extend beyond, those of the ancient world. Even those Sciences which had begun to exist among them, have so changed their aspect and enlarged their boundaries, that the ancient portion is the smallest part of them. Our Mechanics, and our Hydrostatics, are much more extensive and profound than those of the Greeks. Our Astronomy has undergone revolutions which have made it belong eminently to modern times, although the ancient foundations laid by the Greek geometers have not even at this day lost their validity or importance. But in addition to these ancient sciences, others have sprung up, which did not exist at all, or at least in any scientific form, among the Greeks and Romans. Such are the Classificatory Sciences, Botany and Zoology. Such are those Sciences which

I have elsewhere* termed Palætiological, and which explore the past history of the world by studying the causes of change; among which we may especially notice Geology, the History of the Material Earth, and Ethnography, or Glossology, the History of Languages. Such, again, are the Sciences which consider bodies according to the elements of which they are composed: Chemistry, which analyses them, and Mineralogy, which classifies them with a view to their analysis. Such sciences, finally, are those which attend to the structure, the symmetry, and the functions of living beings; Anatomy, Comparative Anatomy, Morphology, Biology. On these subjects, whatever sparks and gleams of intelligence we may discover in ancient authors, the broad light of science was not shed, till the human mind, in the course of its movements, arrived at its modern period of activity. These are the subjects with which a person must acquaint himself, who wishes fully to appreciate the progress which man has made and is making in the pursuit of truth. And though it may not be possible for any one to give his attention to the whole of these; and though it is not necessary, for educational purposes, that a man should attempt to acquaint himself with any large portion of them; yet it is requisite, as a part of a Liberal Education, that a person should so far become acquainted with some portion of this body of accumulated and imperishable knowledge, as to know of what nature it is, what is the evidence of its reality, by what means additions to it are made from time to time, and what are the prospects which it opens to the present generation of mankind. The Progressive Sciences, to this extent, ought to enter into the scheme of a Liberal Education.

History of the Inductive Sciences, Book xvIII. Intro

[PT. I.]

duction.

3

21 The Sciences just mentioned derive their new truths in part from experiment and observation, and are progressive in virtue of new facts, as well as new reasonings, which they incorporate into their texture. But even those sciences which consist altogether of reasonings are progressive, and require to be noticed under this aspect. Mathematics must be studied in the character of a Progressive, as well as of a Permanent Science. For the Mathematics of modern times involves processes unknown to the ancients. Results are now deduced from principles by combinations of symbols of number and quantity, rather than by reasoning upon the relations of space. And thus, in addition to the Elementary Geometry and Conic Sections of the Greeks, and the calculation of numerical questions directly; we have the calculation of such questions by symbols (Algebra), and the calculation of the properties of curves by the symbols of their coordinates (the Algebra of Curves), and by the symbols of the changes of such quantities (the Differential Calculus); and these modes of calculation form additions to the body of mathematics, which may overlay, and almost put out of sight, the original form of mathematical sciences.

22 Again, as the study of the exact reasoning of the ancients pointed to Logic, which defines the methods of strict reasoning; so the sciences which are, as we have said, derived from facts, direct us to the study of those processes which determine the methods of obtaining truth from facts. To obtain consequences from principles is Deduction; to obtain general truths from particular facts is Induction. The Logic of Induction, or at least a Philosophy which includes Induction within its scope, is a necessary accompaniment of the progressive sciences; and such a Philosophy ought also to make a part of our Liberal Education.

23 I have said that a portion of the Sciences

which have come into existence in modern times, and which are still in progress, should be introduced into a Liberal Education, to such an extent as to acquaint the student with their nature and principles. It is an important inquiry, in determining the proper scheme of a Liberal Education, what portion of science is best fitted for this purpose. I have already remarked elsewhere*, that among the sciences, Natural History affords very valuable lessons which may beneficially be made a portion of Education: the more so, inasmuch as this study may serve to correct prejudices and mental habits which have often been cherished by making pure mathematics the main instrument of intellectual education. The study of Natural History teaches the student that there may be an exact use of names, and an accumulated store of indisputable truths, in a subject in which names are not appropriated by definitions, but by the condition that they shall serve for the expression of truth. These sciences show also that there may exist a system of descriptive terms which shall convey a conception of objects almost as distinct as the senses themselves can acquire for us; at least when the senses have been educated to respond to such a terminology. Botany, in particular, is a beautiful and almost perfect example of these scientific merits and an acquaintance with the Philosophy of Botany will supply the student with a portion of the Philosophy of the Progressive Sciences, highly important, but for the most part hitherto omitted in the usual plans of a Liberal Education. But the Philosophy of Botany cannot be really understood without an acquaintance with a considerable portion, at least, of

* Philosophy of the Inductive Sciences, Book XIII. Chap. 3. Intellectual Education.

+ Philosophy of the Inductive Sciences, Book XIII. Chap. 2. The Education of the Senses.

the details of Systematic Botany. On these grounds, I should much desire to see Botany, or some other branch of Natural History, or Natural History in general, introduced as a common element into our Higher Education, and recommended to the study of those who desire to have any clear view of the nature of the Progressive Sciences; since it is, in fact, the key and ground-work of a large portion of those

sciences.

24 I have ventured to give reasons* why the Chemical Sciences (Chemistry, Mineralogy, ElectroChemistry) are not, at the present time, in a condition which makes them important general elements of a Liberal Education. But there is another class of sciences, the Palætiological Sciences, which, from the largeness of their views and the exactness of the best portions of their reasonings, are well fitted to form part of that philosophical discipline which a Liberal Education ought to include. Of these sciences, I have mentioned two, one depending mainly upon the study of Language, and the other upon the sciences which deal with the material world. These two sciences, Ethnography, or Comparative Philology, and Geology, are among those Progressive Sciences which may be most properly taken into a Liberal Education, as instructive instances of the wide and rich field of facts and rea

* Philosophy of the Inductive Sciences, Book xi. Chap. 3. Intellectual Education. Of course it is not here intended to imply that Chemistry and the Sciences connected with it are not studies highly philosophical and important, and very suitable and instructive parts of a Liberal Education; but only, that if we select some of the progressive sciences as necessary portions of our educational scheme, there are much stronger reasons in favour of taking Natural History than Chemistry, for this purpose. It is further to be recollected, that a knowledge of Chemistry is quite essential as a part of the professional education in medicine.