symbols would obviate, but if we should suppose that the difference between a and b was less than any assignable quantity, that is, an infinitesimal, the trouble would disappear and a-b would equal ±0 in the sense attributed to it in the original discussion of "Anomalous Forms." This would logically answer the demands of the algebraic forms, the interpretation would be satisfactory and the comparison of the results with the facts of the case would afford a reasonable opportunity to drop the distinction between the values of 0, for practically they are the same. Another inaccuracy in the usual discussions is the omission of the negative values of 0 and ∞ which cannot properly be omitted if the modifications here suggested be adopted. Let us discuss a single hypothesis in the "problem of the couriers," in view of these hints. (q standing for the numerical difference between a and b); this result indicates that the couriers were together the least possible time after 12 o'clock, when a>b, and before 12 o'clock when a<b, and at no other time, which is a true result, and shows that the couriers were practically together at 12 o'clock; for if A be the more rapid courier and is an insensible distance behind B at 12 o'clock, the next instant he must overtake him, but if A be the less rapid courier he must have been overtaken by B the last previous instant; but practically, both instants are one and the same with 12 o'clock, and traveling at unequal rates they were never together before or after 12 o'clock. It is possible the foregoing is only an explicit statement of the meaning of the usual discussion, and perhaps such explicitness is more nice than wise;" but, however it may be, I see no other way to secure an entire satisfaction of the thought. USE THE DICTIONARY. The cost to the state of putting a copy of Webster's Unabridged Dictionary into every school has been enormous, Few teachers among the great multitude who look upon the familiar pages (or we might say cover more correctly in many cases), from day to day, have ever taken the trouble to reflect upon the munificence that has placed so valuable an auxillary to the work of teaching, within the reach of both instructors and pupils. Careful observation reveals the fact that this book which might be made of the highest utility in the study of the English language,—that department of our common school course which is first in importance,—often serves no better purpose than to ornament (?) the teacher's desk, or to gratify the desires of the smaller boys and girls who like to look at the pictures. Indeed, instances have been known in which it has served a very bad purpose, by affording to pupils with large "destructiveness," an object upon which to gratify their propensity. The use, or lack of use, that is made of the dictionary in the majority of schools, creates the suspicion that our law-makers who were instrumental in securing its introduction into the schools, were not well informed as to the character and abilities of the average teacher. It would be a most gratifying symptom were the idea that is entertained by a few, found to be universal among teachers, viz: that the dictionary is placed in the schoolroom for the special benefit of the teacher. Much better have it used with this understanding than not all. Now a few words as to its proper use, not, however, with the design of exhausting the subject: First, see that it is preserved from injury. If possible, have some desk, table or stand that is to be devoted exclusively to it, and never allow it to be taken therefrom. Let all pupils or others who consult it use it in its place. The great weight of the volume makes it incapable of sustaining the handling necessary to meet the wants of all in the school, if they are to use it at their seats. Second, require of all the pupils who are able to pronounce words of two syllables readily the ability to find any word in the language. Do this, not arbitrarily, not as a result of a command, but after having given all necessary instruction and drill. Devote the time of "general exercise " to this for several days, or long enough to secure the desired facility in its use. This advice seems unnecessarily minute, but the fact that whole schools are found, and those too in which the pupils are not all primary, in which not a single student can readily find in the dictionary the words of his reading lessons justifies all the minuteness of directions that it is possible to employ. Third, drill upon the orthoepy. Let the teacher himself study carefully the principles of pronunciation as set forth in the introductory part of the work. Then secure a thorough acquaintance on the part of the pupils with the key to the pronunciation, so that any indicated sound can be given instantly and correctly. Attend to accent also. In cases where careful pronunciation has been neglected during the years of childhood, much time and patience will be necessary to make a discrimination possible between sounds that are in the least similar. Lastly, drill in definition; not so much in words as in ideas. Use the text of the books to furnish the material for this exercise. Test pupil's understanding of the meaning of words by the use he can make of them in sentences of his own construction. Conservatism opposes the prevailing tendency, which it regards as "new-fangled," to circumscribe the use of books in teaching. Here is the place for conservatism. Whatever notions we may hold in reference to the use of the text-book in arithmetic, geography and grammar, we are heart and soul with the conservatives in regard to the use of the book when it comes to the dictionary. Let it by all means be most thoroughly conned by both teacher and pupil.-J. H. TERRY, in the Baraboo Republic. WORKING OF THE TOWNSHIP SYSTEM. EAGLE POINT, March 19th, 1873. Editors of Wisconsin Journal of Education, Madison, Wis, SIRS I observe that there is doubt expressed by some in the state, who seem to be interested in the cause of education, of the propriety of the township system of school government. Allow me to say to all, who may feel any interest in the system, that this town has tried the efficacy of the township system for four years, and although it met with some opposition at first, it is now supported and sustained by all parties and factions; and I do not know of a single individual in town, desirous of changing to the old system again. The advantages to be derived from the township system have often been enumerated in your journal; but if not trespassing too much on your space, let me call the attention of your readers to some things which are being done here, which can be done to a better advantage than under the single district system. Each school house in town is furnished with a complete set of out-line maps, (GuYor's) writing chart, globe, cube root blocks, geometrical forms, numeral frame, programme clock, etc.; besides an extensive library, which is divided into as many parts as there are sub-districts, with one surplus part, which is alway in the hands of the librarian, giving each clerk a chance to exchange as often as the part in his district may be read. School books are obtained by the board, at wholesale price, and distributed to each sub-district according to their wants; thus making a uniformity of text books, and supplying every scholar with just what they require. Every teacher will perceive the great advantage of this method. We have also found, that by economy and efficient management, we are enabled to pay higher wages, procure better teachers, and have longer terms, on the same tax, than could be done under the old system. If any one whishes to know why, let him go to the town records of his own town, and review the financial reports of the school district clerks for the past five years. Not with criticism, but for information. And bear in mind that these clerks are not paid for their services, and as a general rule have endeavored to make an honest and truthful report. Under the township system, the records are all in the hands of the secretary, who makes the financial report, who is paid for his services. He is selected on account of his efficiency and what a man is paid for doing, and competent to do, he has no excuse for not doing well. W. HOPKINS. Yours truly, JUDGMENT. BY S. D. FORBES. There is a faculty which mental philosophers call judgment, that stands first and foremost among the essential requisites to success in teaching. It consists in a sense of the fitness of things; the art of adaptation, of putting the right thing in the right place. It is a power not always possessed by the learned, nor always denied to the ignorant. It may, perhaps, be considered more as a natural endowment than as an acquisition; at least it is scarcely in the gift of profes sional training, only so far as such training includes the developement and discipline of the whole range of mental faculties. Teachers of extensive acquirements, both scholastic and professional, often fail from lack of skill in adjusting means to ends, under given circumstances. They have learned a system or set of principles in teaching, embracing the whole professional "kit," all perfectly adapted to the work, when judiciously applied. But in their hands it proves rigid and unadjustable. The normal graduate goes out to begin his chosen work, his profes sional repertory crammed with theories, methods and systems of teaching. He installs himself in a mixed country school, fully convinced that he knows all about the business. Without previous study of the peculiarities or circumstances of the work he has undertaken, he lays out his plans, draws up his specifications, and enters, in full faith, upon their execution; and is surprised to find that they do not work so charmingly as in the imaginary classes of the institute. The plan of his campaign is faultless, and his manouvering skillful. In all reason he expects to win a Waterloo victory over the gathered hosts of ignorance. But he soon discovers that there is a defect somewhere. The tactics that he has seen prevail elsewhere, fail here, and all because he has not reconnoitered the position of the enemy, and directed his movements accordingly. Like many a good tactician, but weak general, he rushes to battle before knowing the exact location of the main body, discharges his heavy ordinance at random, attacks the picket line with his whole force, and the main body with his skirmishers; and often exhausting his strength in a series of brilliant manouvers, retires from the contest astonished that such masterly tactics have produced so little effect. So our theoretical teacher, fully armed with plans and familiar with all the evolutions of the schoolroom, utterly fails as a practical teacher, because he does not know how to cut and fit his system to the particular case in hand. He may be likened to the tailor who has learned to sew but not to fit. Give him a suit ready cut and he will do a perfect job, but put him to fitting as well, and his skill with the needle will not save his reputation as a tailor. The teacher must have the power to adapt his system to his particular school. His plans should neither be too large nor too small for the occasion. The same system will not suit every school. The professional graduate is not unfrequently mortified to see unprofessional "quacks" accomplishing, without normal training, what he fails to do with all the equipments of a full technical course. So long as normal schools aim only to supply students with ready-made plans and systems, their products will be practical failures, except those by nature gifted with judgment that will enable them to reduce their theories to successful practice. Give them whole cloth and the art of fitting, and success will be assured to all. UNABRIDGED. BY CHARLES T. POOLER. Oft, as listless you've sat humming o'er the keys of mem'ry, thrumming and store, |