that we reach the height of confusion. Rival theories contend for dominion in the mind of the author, and his work by its fragmentary nature reveals at once his incompetence and his total ignorance of all the prerequisites for the task. Although there is a school of analytical mathematics now dominant in the scientific world; which had for its apostles GAUSS, CAUCHY, ABEL, DIRICHLET, and all the famous geometers of our century which numbers among its adherents the schools of Great Britain, France, Germany, Italy, and in short of all Europe; whose methods and definitions and notations are by common consent of mathematicians irrevocably established: yet these compilers ignore its very existence, discard its methods for others that are false and obsolete, reject its notations and replace its definitions by the vagaries of their undisciplined brains.

Happily for the the repute of this and similar Associations throughout our country, the rapid advances of the past few years in the arts and implements of teaching encourages us to hope that the work necessary to remove this stigma will soon be done. In the opinion of the reader it would be easy for an author who possessed the gift of incisive expression and judicious condensation to compress within two volumes (one devoted to analysis, the other to geometry) the whole of our course of mathematics. And this done it would be possible for a student of average intelligence and the maturity of mind necessary for mathematical studies, to complete this course in three, or at most four years. The abundant materials for this course are already at hand in the classical writings of those illustrious geometers who have adorned the science, and the famous journals which have been the repositories of scientific discoveries.

When he has led the student thus far the teacher's work is at an end; and perhaps it is beyond the province of this paper and of this body to go further. But the Association will pardon me if I go on to say, in view of the recent establishment in this city of a University of higher aim and wider scope, that here we find the beginnings of the true work of the University. The study of the Elements having equipped the student with all the tools of the geometer, he will find abundant material to exercise them on in the manifold branches of the higher analysis, of the higher analytical geometry, the delicate investigations in the theory of Number and the theory of Quaternions. The same course also which has prepared the student for the higher investigations of pure mathematics has equipped him to pursue the various theories of mathematical physics, of theoretical mechanics, and of physical astronomy. It is in all these subjects that the modern mathematician finds the incentives to original research and the materials on which to work.

Prof. W. C. SAWYER then presented a

REPORT ON ORTHOEPY.

Your committee has found the field upon which they were desired to report, so wide and full of interest as to compel the entire omission of some topics of great orthoëpic prominence among the philologists of our day.

We have chosen, therefore, to notice only those subjects which are of the highest practical interest to us as educators. In this relation we regard the Orthoëpy of our English speech of unquestionably the highest importance; that of the modern European languages, with their living literatures and their moving millions, we estimate as second. The classical and oriental languages are of less vital importance either in the common or the higher education though all languages are dependent upon the science upon which we are now engaged.

The correct pronunciation of words is a matter of prime importance to the culture of any people and may serve as a measure and index of refinement. In Europe we find many dialects of the same language, varying with the rank and culture of the people as well as with the locality. In the United States no such strangely-marked dialects prevail anywhere. The conditions favorable to the growth of dialects are wanting among us. We have no caste to divide us and there is so much communication between different parts of the country that local peculiarities of utterance become almost impossible. This National Educational Association and the various other means of bringing together teachers and other educated men, for consultation, and of calling them from one section of the country to another, are forces against which provincialisms can make but little progress. The peculiarities of speech often met with in this country are usually the characteristics of families and of foreign nationalities rather than of communities or states; and they never occasion any difficulty of understanding even the most uneducated people, except foreigners like the Pennsylvania Dutch who have not yet fairly learned the language of the country. But no familiarity with the best Parisian French, or Hannoverian German will enable one to converse with the average citizen in all parts of England, France, or Germany.

Mr. ALEXANDER J. ELLIS, in speaking of American pronunciation, does not pretend to decide whether we speak better or worse than the English, but declares that we reveal our home, even the most English of us, by some chance words, as, for instance, the word trait, of which the English still retain very nearly the French pronunciation. Nevertheless he maintains that our American pronunciation as compared with the English is archaic. We have no other present interest, however, in this comparison than to show that good "English" is not altogether the same thing in England and America, and, for the sake of avoiding confusion to impress the necessity of confining our research for the actual orthoëpy of our own speech to the best usage of American scholars. It is, of course, very desirable that American and English usage should coincide, but the, fact remains all the same that if an American orator should speak of a "trā" of character, affectation would be set down as the most conspicuous trait of his own.

We may seem to take very little interest in Orthoëpy since we teach it so little in classes formed for that purpose; but it should not be overlooked that we have no classes formed for any purpose, in which we are not constantly impressing a correct or false utterance of some language; and in the present state of orthoëpic science who can be sure that either his example or his precept can be safely followed?

Just here we find the chief claim of this subject upon our attention. A great obstacle, insurmountable to the individual, lies in the way of correct and assured utterance in almost every language living and dead. Careful scholars feel this embarrassment even more than the careless. They may consult and compare authorities, but they find evident discrepancies on the one hand, and on the other an ever-present uncertainty of the meaning of the orthoëpist, except in presence of his living voice. Philology suffers no other disability at this time to be compared with this lack of all means of definitely representing sounds upon paper. The most popular way of showing the pronunciation of words is by saying that the sounds of certain doubtful letters are like the sounds given to the same or different letters in other words which are supposed to be better known. But, as Mr. ELLIS justly remarks, this "involves the very riddle which we have to solve. Any improper pronunciation in the key-word will of course be perpetuated in the word to be explained. Thus the a in calf would not serve any good purpose as a standard sound in any orthoëpy because it would be variously interpreted. Mr. ELLIS has also shown what we have all doubtless felt, that the description of sounds as hard, soft, thick, thin, full, broad, etc., is of little value on account of the variable use of these terms in their abnormal or secondary applications. It is impossible therefore at present for us to learn Orthoëpy without the living teacher. But there are no living teachers who can speak with much authority, themselves all having lacked competent teaching, especially in the dead languages. We can hardly guess how Cicero's orations sounded in the ears of the Romans. Modern European languages we can study from the liv ing tongues if we will go far enough for the privilege. It is not a rare thing for American scholars to study French and German several years in this country till they can read and translate them very easily, and then discover that they can neither understand a single sentence of those languages as pronounced by the natives, nor make the natives understand a sentence of their pronouncing. It is a remarkable result of a similar cause that at Pekin they understand the writing but not the speech of Canton. Who can estimate the burden of such disabilities imposed upon Philology either by a cruel fate or by a stolid indifference on our own part? This difficulty of recording any speech, our own or foreign, is a great hindrance to all intellectual growth. The natural expression of thought is by the sounds of the voice, but we learn much more through the eye than through the ear. What we read is only the sign of language proper, and is two removes from the thought itself. Whatever complicates, therefore, or confuses the immediate suggestiveness of this sign, cumbers the thought by so much and makes writing so much weaker than speech.

We now come to the inquiry for the root of this evil. If the elements of writing had definite significance their combinations would be equally significant. The ultimate elements of writing are the letters of the alphabet. We cannot now dwell upon the defects of this wonderful instrument. Merits it has none that are noticeable among its conspicuous blemishes. A sentimental English writer says, "the uses of the alphabet are sweet and marvellous." The marvellousness is only too ap

parent, but we suspect there is some mistake about the sweetness. In short the alphabet consists of twenty-six letters, which signify nothing in particular and sometimes nothing at all as individual elements; but which in capricious groups represent the words of our speech. It contains nothing systematic and nothing exact. It was barbarous in its origin and is barbarous in its character. Before printing was invented it is supposed that men represented as well as they could with such an alphabet the words which they heard or would themselves utter, but that the inadequacy of the instrument made the representation necessarily very incorrect and incomplete.

*

With printing came fixed orthographies into use, and now the letters and their grouping have acquired a sacred character in the eyes of many, who dare not violate them, at least when they know what they are. According to Mr. ELLIS, printed books generally represent not the orthography of the man of education, who writes, but only of the man of routine, who prints. "Our present standard orthography," he assures us, "is simply typographical. * It is a tyrant in possession. It has an army of compositors who live by it, an army of pedagogues who teach by it, an army of officials who swear by it and denounce any deviation as treason. An army, yea, a vast host, who having painfully learned it as children cling to it as adults, in dread of having to go through the awful process once more, and care not for sacrificing their children to that Moloch, through whose fires they themselves had to pass, and which ignorance makes the countersign of respectability." "Our present standard typographical spelling," he adds, "is a monstrous misshapen changeling, a standing disgrace to our literature."

Professor F. J. CHILD very justly remarks that "Nothing can be more absurd than the veneration felt and paid to the actual spelling of English, as if it had been shaped by the national mind, and were not really imposed upon us by the foremen of some printing-offices." If, therefore, any remedy for these great orthoëpic and orthographic embarrassments can possibly be found, there is no good reason why we should not avail ourselves of it.

Is there, then, any remedy? This question cannot be fully answered, and the demonstration made satisfactory to all in any hasty and brief examination of the subject. Enough, however, can perhaps be said to indicate the direction of the solution. We have shown that the chief obstacle to the progress of Orthoëpy and Philology generally lies in the want of any exact symbols with which to record the sounds of the human voice. Can the lacking symbols be provided? The conditions of the case demand that they should be phonetic, and represent definite sounds without variation.

In 1843, Mr. ISAAC PITMAN suggested the introduction of phonetic writing and printing into general use. Very soon thereafter he was joined by Mr. A. J. ELLIS, whose phonetic studies have since been very fruitful, and, in 1846, they together published a phonetic alphabet consisting of forty characters composed of Latin letters and their modifications. These letters were systematized and certainly were a great improvement on the old alphabet. More recently Mr. PITMAN has made some modifications

in the forms of his letters, and Mr. ELLIS has invented an excellent method of representing all the sounds of the voice by the use of the old letters with fixed powers, using to make up the number to about three hundred, such combinations and inventions as would be most suggestive. With these all the languages taught in our schools can be very accurately represented to any person who is acquainted with the powers which Mr. ELLIS would have his symbols represent. This alphabet, however, was never designed for general use, and is clearly unfit for it though serving very well the purposes of science. But why cling to the old alphabet if anything exact is required? Dr. BRÜCKE, who has carefully studied the physiology of speech, finds no reason for attempting to repair the defects of the old alphabet rather than produce one altogether new, except simply to save labor at the start, if even that is possible, and he thinks we ought not to be frightened at the cost of a luxury which is destined to be of incalcuable advantage for centuries. Moreover, letters fashioned after the old, but with new powers, are not received with favor, and their abandoned uses must occasion some confusion till new habits have been formed.

The invention of talking-machines has exposed some phonetic fallacies, and confirmed or suggested some scientific facts. KEMPELEN and WILLIS have discovered, by mechanical experiments, so many of the conditions of the various tones of the voice as to be able to counterfeit them with remarkable success through artificial appliances. All our tones are produced by an equally-exact adjustment of the various parts of the talkingmachine of nature. The adjustment is in part voluntary and in part unconscious except as we know it by the phonetic products. There is good reason to hope that we may soon know how we talk, and that the query ridiculed by MOLIÈRE may be proudly answered, and that we may learn at last what he could not guess nor see the use of knowing, viz: "what we do when we say o."

Dr. BRÜCKE suggests that the new characters shall indicate the position and action of the organs of speech, and thus acquire absolute and unvarying significance; but he does not propose any specific characters, for the conscious lack of typographical, artistic, and philological skill. Dr. BRÜCKE's work was published in Vienna, in 1856. In 1864 Mr. A. MELVILLE BELL, a professor of vocal physiology in England, claimed to have discovered the organic relations of speech sounds, and published a universal alphabet called "Visible Speech," based upon the discovered principles. These symbols show the part taken by the lips, the tongue, the uvula, and the vocal chords in each sound. Mr. ELLIS speaks in the highest terms of this system, and compares his Paleotype and his Glossotype to it in order to fix the powers of his letters. Professor S. S. HALDEMAN is also among the endorsers of Mr. BELL'S system.

The practical value for common use of the physical basis of voice symbols may easily be overestimated. We have seen the worthlessness of keywords to describe the pronunciation even of our own day, but after the language has passed through several transformations they are still less available. Mr. ELLIS appreciates Visible Speech, the more highly because it not only records for present use a complete description of every sound we utter, but leaves in every written word a permanent record for all