In compliance with the resolution passed by the Honorable Board of Trustees on the 26th of June, I beg to lay before you the following divisions of labour to be performed by the Professors and Tutors.

Dr. Caldwell	3
Prof. Anderson	6
Prof. Mitchell	8
Prof. Hooper	8
Prof. Phillips	8
3 Tutors 9 each	27
Total	60

This statement, it will be seen, differs from Dr Caldwell's only in assigning 8 instead of 7 to Wm Hooper , who is perfectly willing to take with his colleagues an equal share of labor whatever that may be.

I avail myself of the present opportunity of making the following statement for the information of the Board, and hope that the facts which it discloses may be found of sufficient importance to render any apology unnecessary. I have been devoted to the business of instruction for the last 25 years, the last eight of which have been spent at Chapel Hill, and tho' I have met with many discouragements from the waywardness and incapacity of individuals, yet I cannot recollect a single case of an entire failure. It is therefore with no little mortification that after an impartial review of what has been affected here I am compelled to say I have utterly failed of my object, the extremely meager minorities of the successful students being a confirmation of my assertion. The causes which have operated to produce this result one no doubt various and some perhaps beyond our control; but it is believed however that some may be traced to the following sources. 1. The imperfect, superficial and inaccurate methods adopted by too many teachers of the elements of Arithmetic & Algebra in our schools, the consequences of which are lamentably injurious, as they are felt thro' the entire collegiate course of study, page torn produce results humiliating to the Professor and affecting the credit of the Institution. 2. The inexperience and incompetency of our Tutors, to whom the instruction generally of the two inferior classes has been committed. 3. The estimation in which the mathematical sciences are held not only here but too generally the state. Little progress can be expected to be made by those who, blinded by ignorance and prejudice, have constituted themselves judges of what is and what is not adapted to train the mind to vigorous exertion to develope the intellectual faculties, and to prepare for profound meditation and accurate discussions. 4. An obstinate determination on the part of some to do as little as possible, and to considerthe time allotted to preparation better employed in wading thro' trashy productions or consuming it in enervating indolence. It is presumed that the withholding of the usual collegiate honors from all such would check this growing evil. 5. The present mode of examination is not sufficiently regarded as a test of scholarship, nor does it afford to the examiner any means of comparing with precision the students with each other. The time necessary for this purpose on the present plan is too short. The multitude and variety of questions necessarily proposed by the examiner in a very short interval of time is embarrassing. To these may be added the effects resulting from timidity in oral examinations. I would therefore respectfully propose to substitute, for the present mode, an examination in writing, which gives the student more time to collect his ideas, diminishes the disadvantages of timidity, and while, being simultaneous for all, allows us to propose the same questions to each and renders the replies more easy to be compared. I think the attention is more easily arrested by the eye than the ear; that the student finds it often necessary either to recal analytical artifices, or intricate constructions which are not always readily presented to the mind especially in a state of embarrassment. To regain what is entirely lost is to invent, and we cannot do in an instant what has often cost an abler person much labour in the silence of his study. Perhaps shorter intervals between the periods of examinations would have a happy effect; but I am not prepared to recommend at present any further alteration.

As a proposition has been made to raise the standards of education higher, by demanding the matriculate an acquaintance with Algebra, and introducing new subjects of instruction into our course, I beg to present the following remarks.

That system of education which embraces the synthetic to the exclusion of the analytical mode of mathematical instruction is essentially defective. First, because the analytic being more concise it admits of the introduction of a greater amount and variety of information in a given time. Secondly, it is more uniform, general and comprehensive. There is a very great similarity in all analytical processes; all are conducted by the same general rules, and commonly lead to universal results, whence particular consequences are deducible at pleasure. Thirdly, it is the easiest. Its processes are simple, its necessary modifications natural and obvious, and its operation being general and elements few, it imposes no unnecessary load to the memory. La Croix advises us "always to choose the most general methods" and La Place in the "Journal des Séances de l' Ećole Normal" says, "Próférez dans l'énseignment les méthods générales, attachez-vous à les présenter de la manière la plus simple, et vous verrez au même temps qu'elles soul presque toujours les plus faciles." Fourthly, the best treatises on Statics, Dynamics, and Physical Astronomy abound with analyticalformula which would be unintelligible to those who had not formed a previous acquaintance with analysis. There is no doubt amongst those who have gone a little below the surface, that the "Mécanique analytique" and the "Mécanique céleste" are the true sources from which we can acquire a complete and methodical knowledge of all the properties of the equilibrium and motion of bodies, and therefore it is important that the student understand the analytical method. Fifthly and lastly, it has a direct tendency to communicate a habit of investigation and compels the student to think for himself. If it be objected that our present course has been found to present insurmountable difficulties to the majority of the members of the different classes, and that a reduction rather than an elevation of our standard seems to be demanded; it may be answered that no increase of difficulty is intended by such an arrangement; that the University of N. Carolina ought to enter into honorable competition with similar institutions in our country which have introduced analytical Trigonometry & Geometry into their course of instruction, and that the interests of society and not that of individuals ought to regulate not only the quantity but the quality of instruction.

I recommend therefore the candidates for the Freshman class be required to stand an examination on the whole of Arithmetic, practical & theoretical, and Algebra as far as Irrational and Imaginary qualities in Young's Algebra or a fair equivalent on the same subjects in any other treatise, as are found in Young . This small increase of qualifications for matriculation will enable us to introduce a system of Analytical Trigonometry and Geometry, which would place our University on a level with the most respectable Institutions in our country.