A 121. A 56 25 9V B V160-18917 3 V2=18917. A straight fence through a triangular field cuts off just one acre. The sides of the field are 56 rd., 39 rd., and 25 rd.; if cross fence is the shortest possible, find its length and po39 sition. Solution: It is plain that in a triangle with a given vertical angle and given area, that the base is the shortest which is bisected by the altituuc-1. e., the triangle is isosceles. Also for a given area, that triangle has the shortest base whose vertical angle is the least. Therefore the fence is built across the smallest angle in such a way as to form an isosceles triangle. By trig. 11° 18' 36". Taking a as radius b tang, A.2000018+ b=.4+. .'. Area of the triangle equals altitude X.4 altialt. 2 5 and base 11.3136+. The two tude 28.284 = 160, whence altitude A = = 2 rods in chk. John Morrow, Charlestown, Ind. [Note. The first solution is the correct one. The second solution is one frequently offered. In this particular triangle the error is not very great.]-Ed. 122. 24÷(√/2+√3+v5)=? Can this problem be solved? If not, why not? = 1 day 86400 sec. = 86400 Solution: -4086360 sec. .. the ratio of the beats of the pendulum at sea level and on the mountain top is 86400:86360, or 2160: 2159. Let g the force of gravity at sea level and g1 the force at the top of the mountain. Also put d equal to the distance of the mountain top from the center of the earth. Then from the laws of gravity and the pendulum we have: g: g1 21602: 21592 and g: g1=d2: 79122, hence 21602: 21592: d2: 79122 or 2160 2159d: 7912, whence d= 7915. 664659+ mi. 7915.664659 7912 =3.664659+ mi. or 19349.39952+ ft., the height of the mountain. Geo. H. Telle, Salem. PERCENTAGE DRILL. Do your pupils have the notion that per cent. refers necessarily to money? If so, correct the impression by giving many problems in which no money transaction is involved. Let them translate per cent. into the simple phrase for each hundred. Eight per cent. is eight for each hundred; hence 8 per cent. of 525 sheep is five times eight plus a quarter of eight, etc. When the fact is thoroughly learned that percentage is only a convenient term used when we compute by hundredths, plenty of drill should follow, especially on the most commonly used aliquot parts of 100, until the class is able to translate instantly such fractional parts as the following into the corresponding terms of per cent. and vice Follow up this drill by insisting that whenever the per cent. is an exact part of 100 the operation should be done by division, otherwise by multiplying one per cent. of the number (found by shifting the decimal point) by the given per cent. It will be noticed that the first figure in the product is in each case one less than the multiplier. For instance, when the multiplier is six, the first figure in the product is 5. This fixes absolutely the figure in the tens place. It will also be seen that in each product the sum of the digits is always 9. This enables us to complete the answer. To illustrate, let us continue the work with 6 times 9. The tens figure must be 5, as shown above. The units figure must be 4, since the sum of the digits of the product must be 9. Therefore, the product must be 54. The same is true of all the other products here given. By this device, the whole nine table can usually be permanently impressed on the memory in a few minutes.-The Philadelphia Teacher. MENTAL PROBLEMS IN G. C. M. AND The following problems taken from McLellan and Ames' Mental Arithmetic are good and will suggest a number of fine exercises for the classes in these subjects: (1) What is the length of the longest board that can be used to build a fence around a garden 64 feet long and 40 feet wide? (2) What is the largest unit of money that can be used to pay each of two debts, one of $60 and the other of $100? (3) On attempting to divide 39 marbles. between several boys there were 4 left over. If there had been 58, there would have been 3 left over. How many boys were there? (4) Two bells toll at intervals of 5 seconds and 6 seconds, respectively, and begin to toll at the same instant. When will they next toll together? (5) What is the least number of acres that will admit of being divided into farms of 60 acres or 80 acres each? (6) What is the least number which, when divided by 6 or 7, leaves 3 as a remainder in each case? (7) Find the least number which, when divided by 4, 6 or 8, leaves 2 as a remainder in each case. (8) The fore and hind wheels of a carriage are 9 ft. and 12 ft. in circumference. Find the least number of revolutions that will bring them to the same relative positions as at starting. PUBLISHED MONTHLY. [Entered at the Indianapolis Postoffice as second-class matter.] D. M. GEETING, EDITOR. Missing Numbers. -Should your magazine fail to reach you by the 15th of the month, notify the publishers at once; they will then supply the missing number. Remittances.-Send Postal Money Order, Express Money Order, Draft, or money in Registered Letter. Give name of agent who took your subscription. Price. Subscription price is One Dollar a year. Single copies, 10 cents. Address all communications to THE EDUCATOR-JOURNAL COMPANY, Commercial Club Bldg., INDIANAPOLIS, INDIANA. Editorial. Suggestions for Thanksgiving Week. Arrange your work in such a way that all your lessons for this week will savor of Thanksgiving. For morning exercises use the story of the Pilgrims; tell the story of John Alden. Miles Standish, Priscilla, William Bradford and others. Make a study of "The Courtship of Miles Standish." This material will enter into your reading, language and history work nicely, if not used as opening exercises. In the geography classes, study Massachusetts, especially the eastern part, locating the journey and landing places of the Pilgrims. Make pictures of nuts, vegetables, furniture, etc., for busy work. For the spelling classes, let pupils write a list of things they might have for Thanksgiving dinner, and be able to spell all the words correctly. See who can write the greatest number of words a minute, in two minutes, or in five minutes. Use these words in stories and statements. In the arithmetic classes for the lower grades keen store, buy and sell things for Thanksgiving, making the problems to suit the needs of the class. For music use America, Whittier's Corn Song. For recitation Whittier's Huskers. We feel that these suggestions will materially help your school. Noise is not always disorder. Sometimes we mislead ourselves by thinking that a quiet school means that all are busy and properly employed, too. Look carefully after the way the work is being done. If any are doing it "just to get through," those are the ones that need direction. In preparing your lessons for the coming day's recitations, use at least one-half the time with book closed, reflecting upon the work to be done. Think of the individuals and try to find ways that will appeal and interest every one. Let preparation mean earnest reflection. The facial expression of your pupils will determine the interest manifested in the class. It is not physical attitude you want, but mental. If the pupil be interested his face will show it. Look for the expression that means something and you will see how well your explanation is comprehended. Next to the face, or as a part of it, notice the eye-these are the keys to the interest which you are trying to arouse. "All who have not finished their work will remain in their seats during recess." This remark was heard just as the gong rang for the signal for recess. Those who passed out had not been as faithful at their work as those who remained. Was effort put forth giving the proper recognition in that school? Do not the slow pupils need the invigorating effect of recesses more than the others? See to it that you encourage those faithful to duty. Watch the voice. A voice pitched too high creates confusion. A teacher's voice should be soft and musical. It is well worth the time and patience it takes to make it so. Shouting for order brings disorder. Perhaps the voice more than any other factor determines the order of the school. Become acquainted, educationally, with your pupils early in the term. What you need is a knowledge of their standing educationally and not socially. Try this to see the good in it. "Devices are the products of one's own thought." This is a good maxim for the teacher. Think over your plans and use the devices that suggest themselves to you by such study. Do not be afraid to use a device because it is your own-that may be the best proof that it is what will best suit the point under discussion. Use many devices, keeping those in memory that bring best results. More attention should be given to directing the work of the school than is usually given. If our pupils idle away their time it is because the lessons have not been well assigned. Children are not lazy naturally, but they do not do well. that which they can not clearly understand. Think over the assignment of lessons carefully and in all classes above the second grade give them in writing if possible. Lessons well assigned are generally well prepared. True Teaching. Any fool with knowledge can pour it into a clever boy; but it needs the skilled workman to be able to teach. Leave the strong for the present to take care of themselves. Let the sole figure in the field of sight be the stupid boy. Innumerable illusions vanish at once, and leave the course clear. The knowledge-fungus drop off at once; for stupid boys can never be learned as a body. The idolatry of force drops off at once; for stupid boys can never do the strongest brain work. The prize idolatry drops off at once; for the great majority can not be prize-winners. The true work is seen, and skill is enthroned as the true king, in the proper place, as making the many capable; and the noble life of weakness, that becomes strong by being good, is given a fair chance. So, at last, the teacher is left face to face with the world as it is, and not as philosophy and idolatry make it to be. The man who does not teach the stupid boy is no teacher, just as the man who can not find his way in lanes and by-paths is no guide. In fact, given fair play, "stupid boys" come to mean "bad teachers;" for intelligent teaching can make all get along with reasonable speed and certainty. Rule-printing and lecturing might be done by automatons to automatons of a higher order. Teaching is living intelligence, dealing with life. The rule-printer puts a boy into his printing press, sets the steam rollers going, and prints a rule on the mental page, if it is not already well filled up with cricket and other chromo-lithographs. The lecturer pours a stream of knowledge on something which is supposed to receive the stream. The teacher applies himself mind to mind. The two first have as their subject lessons and books. The last has as his subject the life he deals with. The ruleprinter says: "The verb must agree with its nominative case in number and person." And ever after repeats: "What's the rule?" varying the repetition by different dispensations of punishment, when the unintelligible has been undone by the intelligent. In a happier world than ours an automaton cane would do the work as well. a The lecturer says the rule as before, but then goes on: "You see that the third person plural ends in ‘ant,' and the like, which speaks of many, can not take singular noun which ends in 'us,' as 'dominus,' which speaks of one only." And then he leaves it, like a benevolent old verger, who seizes you and makes you stand in a certain place to look at the great cathedral, the glorious poem stone, and inspires you with fear lest he should seize your eye, too, and twist it round, as he drones out his tale, till at last you escape, rubbing your eyes, and blessing your stars that they are still in the right place, though he may have told you interesting things. in |