Education of youth is not a bow for every man to shoot in that counts himself a teacher; but will require sinews almost equal to those which Homer gave Ulysses.-Milton. The best rules to form a young man, are, to talk little, to hear much, to reflect alone upon what has passed in company, to distrust one's own opinions, and value others that deserve it. -Sir W. Temple. Parents, and mothers most especially, must learn that their parental duties have not ceased when the personal comforts of their children are provided for; that it is on their example, their attention, their firmness, that much of the moral worth of their offspring depends.- John Locke. Dr. Johnson being once asked what he thought the best system of education, he replied, "School in school hours, and home instruction in the intervals." On another occasion, a "Mrs. Gastrell set a little girl to repeat to him Cato's soliloquy, which she went through very correctly. The Doctor, after a pause, asked the child what was to bring Cato to an end.' She said it was a knife. 'No, my dear, it was not so.' 'My aunt Polly said it was a knife.” Why, aunt Polly's knife may do, but it was a dagger, my dear.' He then asked her the meaning of, 'bane and antidote,' which she was unable to give. Mrs. Gastrell said, 'You cannot expect so young a child to know the meaning of such words.' He then said, 'My dear, how many pence are there in sixpence ?' 'I cannot tell, sir,' was the half-terrified reply. "On this, addressing himself to Mrs. Gastrell, he said, 'Now, my dear lady, can anything be more ridiculous than to teach a child Cato's soliloquy, who does not know how many pence there are in sixpence?' What Goldsmith said almost a century ago, in regard to the mode of treating the subject of education, is to the point now, and a majority of the writers on the subject would do well to ponder it. "As few subjects are more interesting to society, so few have been more frequently written upon, than the education of youth. Yet is it not a little surprising, that it should have been treated by all in a declamatory manner? They have insisted largely on the advantages that result from it, both to the individual and to society, and have expatiated in the praise of what none have ever been so hardy as to call in question. Instead of giving us fine, but empty harangues upon this subject; instead of indulging each his particular and whimsical systems, it had been much better if the writers on this subject had treated it in a more scientific manner, repressed all the sallies of imagination, and given us the result of their observations with didactic simplicity. Upon this subject, the smallest errors are of the most dangerous consequence; and the author should venture the imputation of stupidity upon a topic, when his slightest deviations may tend to injure the rising generation." Give the sons of Massachusetts, small and comparatively unfertile as she is, the means of a good education, and they will stand against the world. Give me the means of educating my children, and I will not exchange its thirstiest sands, nor its barest peak, for the most fertile spot on earth, deprived of those blessings. I would rather occupy the bleakest nook of the mountain that towers above us, (Saddle Mountain, between Williamstown and Adams,) with the wild wolf and the rattlesnake for my nearest neighbors, with a village school, well kept at the bottom of the hill, than dwell in a paradise of fertility, if I must bring up my children in lazy, pampered, self-sufficient ignorance. A man may protect himself against the rattle and the venom; but if he unnecessarily leaves the mind of his offspring a prey to ignorance, and the vices that too often follow in its train, he may find too late for remedy, "How sharper than a serpent's tooth it is To have a thankless child." A thankless child! No, I will not wrong him. He may be anything else that is bad, but he cannot be a thankless child. What has he to be thankful for? No! the man who unnecessarily deprives his son of education, and thus knowingly trains him up in the way he should not go, may have a perverse, an intractable, a prodigal child, one who will bring down his gray hairs with sorrow to the grave, but a thankless child he cannot have.-Everett. It is the most touching of sights, the burial of a little creature, which shuts its eyes as soon as the glories of earth open to its view, without having known the parents whose tearful eyes are gazing on it; which has been beloved without loving in return; whose tongue is silenced before it has spoken; whose features stiffen before they have smiled. These falling buds will yet find a stock on which they shall be grafted; these flowers which close in the light of the morning, will yet find some more genial heaven to unfold them.-From the German of Paul. ALGEBRAIC PARADOX. "1. Let a=x, then, 2. multiplying by x, ax=x2, 3. adding-a, ax—a2—x2—a2, 4. resolving into factors, a(x-a)=(x+a) (x—a), 6. substituting a for x, a=a+a=2a, and 7. dividing by a, 1=2." In the October number, J. S. E. very properly decides that the fallacy is in passing from the fourth to the fifth equation. He might also with equal propriety, have objected to the preparatory step of resolving into factors, as equation three is, by equation one, 0=0, and zero has no factors. I have been requested by a teacher, to add a word on the actual meaning of equation six, and the determinate values of 8. Although 0 renders every quantity into which it enters as factor or divisor, an absurdity, so that the two steps in passing from equation three to equation five are both absurd, yet the physical or geometrical question may admit a rational solution when the algebraic solution fails. To obtain this true geomet rical or physical meaning of an absurd algebraic expression, we must substitute for 0 a very small quantity, and when the result is obtained, again substitute 0 for the infinitesimal. Thus equation seven is an absurdity, but its two members are in the ratio which the two members of equation three will have when x is very little larger than a. Suppose that I should draw such a line on the surface of the earth, that a man travelling in it should always find his latitude equal to the cube of his longitude, (both being expressed in miles,) at what angle would this line cross the equator? Solution. The line would evidently cross the equator at the point where the first meridian crosses; and when the latitude was small, the line might be considered as the hypothenuse of a triangle, of which the latitude and longitude were legs. Hence its direction depends on the ratio of these legs, that is, on the fraction which at the equator would be 8. But by the question lon.2-0. That is, the longitude would, when very small, be very much greater than the latitude, and when both were zero, the line would be absolutely parallel with the equator; a result perfectly rational and true, though derived from the algebraic absurdity 2. lat. lon. lon. lon. 3 Again, at what angle would it cross the parallel of 8' north? Here the legs of our infinitesimal triangle would be lat.-8' and lon.-2, and their ratio, would become at the required parallel. But in this case we should have lat.-8= lat.-8 lon.3-8', which divided by lon.-2' gives lon.2+2 lon. +4, which, when lon. is 2', 12. That is, the parallel of 8' crosses this line at the same angle which a hypothenuse makes with a leg of 1, the other leg being 12. Here is then again a definite actual result, in a physical question, which in the algebraic form is absurd. These questions are simple, but the principle is applicable to very intricate questions, and leading to very singular results. H. T. Waltham, Dec. 1850. The above remarks upon the effect of 0 in connection with numerals, suggest the expediency of a remark upon the simplest method of proving the value of fractional expressions when O is the denominator, e. g. 7. We have been told even, that the value of such a fraction is 0; because, say they, whenever O is a factor, 0 is the answer. The reverse of this is, however, the true answer. The expression is an unexecuted division. Division is but abbreviated subtraction, and in dividing, we simply inquire how many times we can subtract the divisor from the dividend. The question is, then, How many times can we subtract 0 from 7 without exhausting 7? The answer is an infinite number, and the value of is infinity. Many seemingly difficult mathematical points may be easily explained by per forming the multiplying and dividing processes in addition and subtraction.-Ed. x2+xy=8. PROBLEMS. x2+y=6. Required value of x and y. It is said that the above problem cannot be solved by the use of quadratic equations alone.-Ed. Suppose A to start from Boston on Monday noon, and travel west with the same rapidity as the sun. Suppose him to ask every man on his way, "What day is it?" and to receive from each an answer. Where will he meet the first man who will tell him that it is Tuesday? Again, suppose two persons to start from Boston exactly at noon on Monday, and travel with electric speed on the same parallel of latitude, one east, the other west, and meet in, say one minute. Each reckoning time according to the general rule of adding one hour for every remove of fifteen degrees east, and subtracting one hour for every remove of fifteen degrees west, will it be, at the place of meeting, one minute after twelve of Monday or Tuesday morning? And if we decide it to be either, say Monday, what day is it at the antipodes of any other place, say London, when it is Monday noon at London?-E'd. NORFOLK COUNTY TEACHERS' ASSOCIATION. REPORT OF THE PROCEEDINGS AT THE SEMIANNUAL MEETING HELD AT DEDHAM, DEC. 23d and 24th, 1850. THE Norfolk County Teachers' Association held its sixth semiannual meeting, at Temperance Hall, Dedham, on Monday and Tuesday, December 23d and 24th, 1850. Monday morning, at 10 1-2 o'clock, the Association was called to order by the President, George Newcomb, Esq., of Quincy, and the throne of grace was addressed by Rev. Dr. Lamson, of Dedham. The secretary read the report of the last meeting; after which the president and secretary being called on for written communications from teachers, on educational topics, reported that none had been received. The lecture of Mr. Hagar, which was in order for 11 o'clock, on motion, was deferred to the same hour of Tuesday. On motion, it was voted to invite all present, not members, to take part in the deliberations of the Association; it was also voted to restrict gentlemen in their remarks to ten minutes. The subject of spelling was then taken up and discussed by Messrs. Colburn, Reed, Dodge, Capen, Woodbury and Butler. All were of the opinion that the method of obliging scholars to write their words from dictation was the best that could be adopted. The importance of classifying derivative words under their respective Latin or English roots, and making this an aid to the scholar, was referred to, and Mr. Colburn explained the method taught in the Bridgewater Normal School: he also alluded to the necessity incumbent on teachers of aiming at correctness in their own orthography, and mentioned instances in which, in applying for situations, they had failed of success, merely on account of inaccuracy in this respect. The directors were appointed a Committee to furnish subjects for discussion. At one o'clock, the Association adjourned, and met again at two, P. M. The Committee on questions reported in favor of discussing either the subject of Arithmetic or Geography: the former subject was taken up and discussed by Messrs. Dodge, Alden, Colburn, Reed, and Capen. At three o'clock, the hour appointed for the lecture of Mr. Smith, it was voted to defer the lecture until half past three, and the discussion on Arithmetic was resumed, and continued by Messrs. Reed, Hagar, Colburn, and Capen. The discussion rested chiefly on the importance of thoroughness in teaching the elements of arithmetic. The use of keys, and of printed answers in any form by the pupil, as an |