those South of it are negative. If a particular epoch is agreed upon for the estimation of time and time forward from thence is called positive, time backward from it is negative. If a business man making up his accounts for a certain time calls his earnings and other gains positive, he must call his expenses and losses negative, the value of his property or stock at the commencement of that time being his starting point. 3. It is sometimes said, a negative quantity is less than nothing. This is plainly absurd. How can anything be less than nothing, since this expresses the absolute absence of anything whatever? This absurdity however has its origin in the mistaken idea that 0 is only the representative of an absolute nothing. Zero can be and in some cases is, but by no means always, the representative of an absolute nothing. But it is in all cases of Numeration, Addition and Subtraction, the representative of the original starting point from which we begin to count. For instance: A traveler, starting from Boston, goes the first day 15 miles due West, the second day 12 miles due West, the third day 27 miles due East; where will he then be? We have 15 + 12 - 27 27 27 The pupil will readily understand that this 0 does not mean an absolute nothing, for it neither says that the man has not been traveling at all, which would be contradictory to the statement, nor that after his travel he was at no place whatever, which would be nonsense, but simply shows that he was again at his starting point. This example furnishes us in the meantime a good illustration of the difference of absolute and relative quantities. The man having traveled one day 15, the next 12, the third 27 miles, the absolute extent of his travel was 54 miles; but the relative distance, i. o., his distance in reference to bis starting point, is 0. And it is obvious that two quantities which are absolutely taken equal, will, if the one is positive, the other negative, balance or cancel each other. Thus +9.-9= 0; and + a - a=0. -0 a = 20. Suppose now a man starting from a certain piace goes 20 miles North, which direction we will call positive, his distance will be + 20 miles. If then he turns round and goes 40 miles South, (whereby of course he passes his starting point,) his distance will be — 20 miles, i. e., , + 20 - 40 The absolute distance from the starting point is in both cases the same, but the negative sign before the latter 20 indicates that the direction of this distance is the opposite of that of the former. We see therefore that a negative quantity is as much as the positive quantity which contains the same number of units, - 5 is as much as + 5, +5 x as much as + x, but it is to be taken in the opposite direction or sense. If upward is positive, negative is downward; if forward is positive, negative is backward ; if gain is positive, negative is loss, &c. 4. Whatever be the concrete starting point, a place, a | 11 moment of time, an amount of money or anything 10 else, its representative, the abstract starting point 9 is always 0, from which we form in one direction 8 the series of positive numbers to any extent that 7 may be required, and in the opposite direction + 6 the series of negative quantities in the same 5 manner. 4 The annexed diagram represents a part of this 3 scale. The primary starting point for every 2 computation is at 0. For every positive quan1 tity the corresponding number of steps is taken 0 upward, for every negative one downward, the 1 starting point for every quantity after the first 2 being the point last arrived at. Thus, to unite 3 the quantities +5+6–8–7+2_4+9, we have: 4 From 0,5 steps up we are at +5; from thence 5 6 steps up at +11; thence 8 steps down at 6 +3; thence 7 steps down at —4; thence 2 steps 7 up at -2; thence 4 steps down at -6, and 8 thence 9 steps up we are finally at +3; hence 9 the final result of uniting these given quantities 10 is +3. EDITORIAL DEPARTMENT. Light and Shade in Editorial Life. We have been very much gratified and encouraged by the promptness of many of our friends, in sending in the dollar for the Journal and Gleanings, the three dollars for the Atlantic Monthly, Journal and Gleanings, and the fifty cents for the remaining part of the year, from April to Jan. 1862. Will a!l such as have thus favored us, please accept our thanks. The Ladies, as usual, are among the first to avail themselves of our liberal offers. They understand that our subscribers receive all the profit to be realized from this onterprise, and are willing to encourage us by such cooperation. We are under special obligations, also, to our voluntary agents, who have made special efforts to increase our circulation. Our cause seems to have friends, and perhaps none could be found willing to be called enemies. Still, there is in the State, an alarming indifference as to the prosper- . ity of our schools, and the subject of popular education in our state. May we not regard the degree of willingness manifested, in sustaining our enterprise, as a fair test of the interest felt on this subject? If so, how does the matter stand ? . As before stated, we have distributed within the last three months, free and in every town in the state, more than 1500 copies of the Journal, still there are 75 towns in which we have not a single subscriber. From one of our largest towns, where there has been a popular Academy for more than forty years, our agent writes, “sorry I am to say it, I have concluded that it is of no use to try to get ap a club for your highly commendable journal. I have lveen over a larger part of the town, and there appears to be much less interest than I supposed there could be, in such a work.” That this estimate is correct, may be in. ferred from the fact that this agent procured only two subscribers, and even these at club prices! We ask no man to subscribe for the Journal as a personal favor. We urge his own interest, the interest of his family, his district, and the interests and honor of the state. The cause of popular education in the 19th century, must be sustained; and shall Vermont falter, or refuse to share this responsibility? Is there a live teacher in the state who has not interest enough in the cause, to take the Journal ! If so, what are the symptoms by which we may distinguish the living from the dead? Our table is loaded with excel. lent educational journals, from every part of our country; from New England, from the great West, and the Sunny South. And shall Vermont fail to sustain such a Journal as her character and reputation demands? We repeat it, the Vermont School Journal must be sustained. Upon whom may we rely for aid and encouragement, not only to sustain, but to make it better? Friends, we ask you again, to lend us your assistance. Canvass your respect. ive neighborhoods for new subscribers ; continue to send us brief and carefully written articles upon practical topics connected with the school-room and the family. We are not unmindful of the favors we have already received by way of valuable contributions for the Journal. 0. а MISCELLANY. SPECIAL OFFER.–To Female Teachers of our Common Schools, we will send the Journal one year (Vol. III) for fifty cents, or the Journal and a copy of the Gleanings for seventy-five cents. We are induced to make this liberal offer, partly from the desire to bring the Journal into the hands of our practical teachers, and partly because our female teachers are so poorly paid for their services.• WANTED.-A few energetic and responsible agents to canvass for the Vermont School Journal. Massachusetts has provided liberally for the education of her teachers. She has four State Normal Schools ; at Salem, Framingham, Bridgewater and Westfield. The two 1 first educate female teachers only; the others admit teachers of both sexes. The tuition is free to all who in. . tend to teach in the public schools of the State ; pecuniary aid is also given to Massachusetts pupils when needed. Text-books are furnished mostly from the libraries of the schools. New York has one Normal School, located at Albany. She has also a reserved fund in the hands of the Regents of the University, which is appropriated to pay the tuition of common school teachers, (forty in each county,) during four months of each year, under instruction in two Academies appointed for this purpose. Vermont has no Normal School and pays but a mere pittance for the education of her teachers ! Indiana has 514,468 pupils between the age of 5 and 21 years, but only 215,078 have attended school during the past year. The school fund of the State amounts to over $6,000,000. The School Muster is abroad.— There are more than 1000 Teachers in the single city of New York. Boston has 533 Teachers and 32,641 pupils. Married.--At West Bridgewater, Mass., Feb. 12, Prof. A. Crosby, Principal of State Normal School at Salem, Mass., to Miss Martha, daughter of Joseph Kingman, Esq., of W. B. Mr. Benjamin Holt, for many years a teacher in the Hawkins street School in Boston, died at Lancaster, Mass., on March 9, at the age of 87 years and 7 months. He married a daughter of Rev. Thomas Baldwin, D. D., for many years pastor of the Second Baptist Church in Bogton, and was the father-in-law of William D. Ticknor, Esq., senior member of the publishing house of Ticknor & Fields. Rev. James Upham, D. D., has been unanimously elected President of the Institution at Fairfax, Vt., vice Dr. Eli B. Smith, lately deceased. Prof. Samuel Elliot is to be inaugurated as President of Trinity College, Hartford, Ct., on the 8th day of April. |