The teacher who teaches square root, teaches his geometry first, and the teacher who has made cube root intelligible to his scholars in America, has been appealing to geometry before algebra. It is so all the way through. I do not believe that the world's pyramids can be bettered by putting them on their points, but if we find any world's pyramid standing upon its point, we can do better by putting it upon its base. I think it in my own mathematical teaching as I look out and study the boys who come to me from the academies prepared for the college; as I consider their preparations for college and their aptitude for mathematics, it is my conviction that it would be well if what we call elementary geometry should come in our course of study earlier than what is called elementary algebra.

XII.

COLLEGE ELECTIVES.

By President JAMES MCCOSH, College of New Jersey, Princeton.

The two grand college questions of the present day are, what place should religion have in the college, and what liberty should be allowed in the choice of electives. Both of these will engage the minds of thinking people for years to come. I have a very decided opinion on the first of these questions, in its bearing on what should be the highest end of all education, the elevation of the mind and the formation of character. In this paper I am to discuss the second of these questions.

At the opening I lay down the principle that a college, at least a university should, so far as the funds placed at its disposal admit, give instruction in every branch of high learning and science, taking care to exclude all that is spurious, or merely showy, all that is not established as true knowledge. This principle is adopted on the ground that all knowledge tends to educate and enlarge the mind, and may be made to promote useful, practical ends.

I.

Modern education may be regarded as starting in the seventh century when scholae were established in connection with cathedrals and monasteries. The branches taught were divided into a trivium and a quadrivium. The trivium embraced grammar, dialectics and rhetoric. The quadrivium consisted of geometry, arithmetic, music and astrology, that is, astronomy as then understood. These branches constituted the seven liberal arts. They were taught in a narrow spirit, but created a deep interest in the minds of young men, rich and poor. In the ninth century universities were established by Charlemagne and other enlightened monarchs, and these came to be divided into separate faculties such as those of theology, of arts, of law and of medicine, always under one head and government. I am now to confine my attention to the faculty

of arts.

At that time there was no need of elective studies, no possibility of having them. In a four years' course a university could teach all that was then known of literature, science and philosophy. We moderns are apt to speak with contempt of the education of the scholastic ages. No true scholar will permit himself to do so. The studies with the attached disputations whetted the intellect, created a taste for learning and often excited great enthusiasm. In 1201 there were 3,000 scholars at Oxford, and in the time of Henry III

there are said to have been 30,000 there, "an exaggeration" says Hallam" which seems to imply that the real number was very great. A respectable contemporary asserts that there were full 10,000 at Bologna about the same time." Paris in 1453 contained 25,000 students. I maintain that a student who passed through Oxford or Paris at that time had a higher education than one in these days who chooses as his electives in the senior year a century of history, art, music and French plays.

A new era appears in the higher education in the fifteenth century. On the fall of Constantinople Greek scholars and Greek books were scattered all over Europe as seed, yielding rich fruits, and the Greek Testament and Greek literature and philosophy were introduced into the universities and were taught as humanities, an impulse to study being given by such men as Melancthon and Erasmus. In the seventeenth century the subjects of study were greatly widened by the introduction of the new mathematics by Descartes, Newton and Leibnitz. During all this century a very solid education was imparted, especially in logic, in philosophy and in law; and a number of the great men of the world had their characters formed by it. All this time there were no electives in our colleges, and young men did not betake themselves to specialties till after they had received a comprehensive training in universal learning as then available.

But there is a great change in the eighteenth century when Newton's great discovery was made known and the Royal Society of London and the Academy of Science in Berlin, and the French Academy were instituted, and chemistry and botany and zoology were cultivated. After a struggle these were admitted into the curriculum of our colleges and added immensely to the bulk of the body of knowledge and a difficulty was felt in requiring every student to eat and digest the whole.

It is in this century and especially in the last age that the need of electives was felt, and is pressing every year more heavily upon us. The physical sciences have multiplied immensely, so that it is now difficult to name or number them. They now run over the whole of nature and penetrate into the most minute departments. There are men who devote their whole lives to the study of some one branch which the great body of mankind reckon a very insignificant one. In former ages it was thought that the earth was created six thousand years ago, now it is shown that it has had an existence for millions of years, and savans are eagerly bent on unearthing the rocks and fossils which disclose its history during that long period. It was thought in ages past that the heavens were of a higher nature than the earth, now it is proved that they are composed of the same elementary bodies and there is a conservation of energy throughout them all. While the telescope is showing the infinitely great and distant the microscope is disclosing equal wonders in the small and the near.

Fortunately, providentially as I think, while there has been in this way an advance as great and wonderful in other branches of learning, philology is now an important science, and it has numerous or rather innumerable subdivisions. We know more of the classical tongues than the Greeks or Romans. The origin and history of our own tongue has been carefully investigated. There is a careful study of the Shemitic tongues, and the beginning of a scientific investigation of the languages found by missionaries in the rudest countries. History now takes in countries, the very existence of which was unknown to our tathers. The aesthetic principles involved can be investigated now that we have before ns the literature and art of all countries rude and enltivated. Archæology now comes in to combine history, art and literature. We have the means of knowing the reflective thought, that is the philosophy of not merely one individual and one country, but of all people, and can lay hold of the truth and avoid the errors which these systems

contain.

II.

It is impossible, in these circumstances for any student to master all the branches of real knowledge. The age of universal scholars, such as the world had in Aristotle, Scaliger and Leibnitz in former ages, is past and can never return. I remember that when I became a professor in the Queen's University in Ireland, then newly established, thirty-four years ago, an attempt was made to embrace all knowledge, ancient and modern, scientific and literary, in our curriculum and to impose it upon the brains of the students. The attempt utterly failed. Some of the professors in the Queen's College turned nearly every student as no one could master any one branch of learning when they had so many forced upon them. Other professors allowed nearly all to pass, as they saw that no brain could possibly contain the whole. So we had to abandon the plan of universal knowledge and to adopt an elective system, which was found to work advantageously.

It is a curious circumstance that the elective system has, as yet, very little place in the older and larger universities of Europe which, as a general rule, have one prescribed course for the whole students for their whole four years' course. The secret cause of this opposition to elective courses in the higher universities of Europe is to be found in the circumstance that the professors get a portion of their incomes from the fees of the students whom they have individually under them, and the division of these branches of study and the institution of a new department drawing away their students would lessen their income. In this country the professors are paid out of the general funds of the college, and they have no pecuniary motive to lead them to oppose the introduction of electives which are now found in one form or other in all our higher colleges and are excluded only in those institutions which have not sufficient funds to enable them to provide the requisite

teachers. The consequence is that the American universities are, in this respect, in a better position than most of the European ones for admitting new branches of learning, and for widening indefinitely the curriculum of study, and they should eagerly embrace their opportunities and not make themselves dependent on foreign universities, where they may get evil with the good. America should now aim at nothing less than having every branch of true learning taught in its universities. I believe it might

accomplish this high end in a very few years from this date in several of our universities. I wish I were ten years younger and I would attempt it at Princeton But the probability, the possibility of all this depends on the way in which electives are regulated and conducted in this country. If they are conducted in an injudicious manner; if young men in the freshmen class and upward are allowed an unrestrained and unguided choice, to choose, if they are lazy, the easiest subjects, and the lower subjects requiring little or no thought or application, then nothing but evil will follow, and the old universities of Europe will continue to realize a higher standard of scholarship than we do. The mode of regulating these electives is the subject I am to consider in the remainder of this paper.

III.

Electives are now a necessity in all the higher American colleges. The all important question is how are they to be regulated. Are we to allow students in every class, from the freshmen upward, to choose what they please or are we to impose some restrictions? and if so, what? This, next to the religious question, is the most important college question in these times.

In entering on this discussion I wish it to be understood that I am to refer mainly to what should be required of those who are seeking the A. B. and, its consequent, the A. M. degree. These degrees are given in all the colleges of the English speaking nations. In too many cases they have been given without the proper qualifications being required. But the degrees have a meaning, they imply a certain amount of general scholarship and culture. They have a prestige which should be carefully preserved by the colleges. The expectation of receiving the degree at the close of a certain course of study has been a powerful incentive to diligence. We must carefully watch in order to see that this incentive to learning be not lost, and, further, that the requirement for obtaining it be not lowered. If this is not done, the reputation of the country in scholarship, which is not so high as that of some other countries, will be diminished; and we would be esteemed a practical and not a learned or scientific people; and our very power of practical invention would be lessened, as success in work depends so much on a previous scientific investigation, as seen, for instance, in the steam engine, in the telegraph and the telephone, all of which were the outcome of deep scientific research. A