MR. EDITOR I am confident that every teacher of even ordinary ability, will be pleased with the Practical Department of your Journal. Experience has proved to many of us, that knowledge, rightly used, only is power; and that in the school-room, above all other places, knowledge must be practically applied to be valuable. Exercises that awaken mutual energy, break the monotony, and create excitement are often profitably introduced. The ingenious teacher, can collate from every department of study, exercises that will accomplish this end; that will abundantly pay for all the trouble they cost in preparing. 1. We will give some examples in Arithmetic, which not only amuse, but discipline the mind, by inducing rapid thought, and are of the highest practical utility, in the practical operations of life. The teacher can first commence by giving examples in adding and subtracting, thus: 8+4—2+5—1+6−2+6+1+2—10—5— = how much? Every scholar will have his hand up when he asks, These exercises should at first be carried on slowly. Soon greater rapidity can be used; and then multiplication and division, involution and extraction of square and cube roots, may be com ད་ 7X3+4v,-1X8-2X3+10 √,-1,·12÷4X8+1X2-1√,X5+1√,-2×8= Then fractions may be introduced by multiplication and division, as 12 XV, X7+4√, ÷ +1√,÷%+4√ = After facility of calculation is acquired in this kind of examples, various valuable contractions may be learned, and exercises made under them. To multiply by 5, you can annex a 0 and divide by two. = When the sum of the units equal 10 and the 10s are alike: e. g., 34X 36 1224. 3X4 12, and the product of the units, 24, annexed. So 4248-4520. Annex the product of 2×8, the units=2016. [Some examples here given are omitted, as the same or similar ones appear in the report of the Institute at Columbus, on another page.-Ed.] Taking aliquot parts, for multiplication, is noticed in some of our textbooks, and may be carried cut quite extensively and profitably, not only in multiplication and 'division, but in calculating interest and percentage. Teachers need only to study and tax ordinary ingenuity a little, and they cannot fail to find means to break the monotony of school exercises, and please themselves and their pupils. Hereafter we will continue this subject, in Arithmetic and other departments of study, and hope it may prove acceptable. Truly, J. H. SOLUTION-BY JAMES F. ROBERSON. Using fractional exponents, reducing these exponents to a common denominator, and factoring, 8 7 7 x6 (x+y)=129, 8 7 7 y6 (x6 +y6 )=33024, 8 ; or, ყნ Extracting the 8th root, 6 1 62 256 y6. which gives y=64x; substituting in either of the primitive equations, we find x=1, aud y=64. PROBLEM No. 211. The hold of a vessel partly filled with water (which is uniformly increased by a leak) is furnished with two pumps worked by A and B, of whom A takes three strokes to two of B; but four of B's throw out as much water as five of A's. Now B works for a time in which A, alone, could have emptied the hold; A then pumps out the remainder, and the hold is cleared, in 13 hours and 20 minutes. Had they worked together, the hold could have been emptied in three hours and forty-five minutes, and A would have pumped out 100 gallons more than he did. Required the quantity of water in the hold at first, and the hourly influx of leak. SOLUTION-BY JAMES F. ROBERSON. Let &= the quantity of water in the hold, The relative effects of the pumps are as 3×4: 2 × 5—6 : 5. Since the hold can be cleared in 334 hours, +334x=the whole quantity of water discharged, and +33⁄4x_4 z+15x = the quantity The conditions of the problem readily give the following equations: MR. EDITOR.-In view of my position on the above Committee, it seems my duty to announce to the teachers of the State, the action of the State Teachers' Association relative to Institutes. The Association recognizing the value of Institutes, and desiring to give sanction and efficiency to the same, enacted at its last annual session, the following: "Resolved, That this Association appoint a State Institute Committee, to consist of one member from each congressional district, who shall be charged for the coming year with the organizing and holding of Institutes (so far as practicable,) in all the counties in their respective congressional districts." The limiting clause, "so far as practicable," though not in the published resolution, was, I believe, in the original; at all events, the committee will most likely need its saving influence. Teachers will please note. that the Association by this act, declares its unequivocal approval of Institutes. In order to aid teachers in conferring with the members of the com mittee, I here insert their names and postal address, so far as known.— 1st Dist. D. E. Hunter, Princeton, Gibson County. Jas. G. May, Salem, Washington Co. 3rd, E. P. Cole, Bloomington, Monroe Co. 64 4th, S. R. Adams, Moore's Hill, Dearborn Co. 5th, A. C. Shortridge, Centerville, Wayne Co. 6th, G. W. Hoss, Indianapolis. 7th, " 8th. " 9th, 10th " 11th, "J. Baldwin, Kokomo, Howard Co. The resolution seems to indicate the separate action of the members of the committee. This may or may not have been the intention of the Association, but in the absence of an authorized interpretation, we shall interpret it as above indicated, viz., separate action. Teachers, you will permit a suggestion at this point; namely—while the presumption obtains that the committee-man of your district will see or correspond with some teacher or teachers of each county in said district, yet our suggestion is that you do not always wait for this, but on the contrary make it YOUR business to see or write him concerning this matter. Or if he be not the man your teachers desire to organize and hold your Institute, see or write to the man desired; the resolution of the Association by no means interfering with the largest liberty in this matter. Further, we ask the permit of a word of advocacy in behalf of this suggestion: 1st. These committee men are all teachers, hence like yourselves, busy, consequently have not the time for this work which its magnitude and importance demand.-2nd, In some cases the committeeman may feel a delicacy in moving first, fearing that he may incur the charge of officiously thrusting his services upon his fellow-teachers.-3rd, And generally the cause is worthy your early and earnest efforts. This we pre sume will be granted; if not, however, we prove it by enlightened example:-Connecticut, though annually sending over two hundred students to her Normal School, holds an annual Institute in each of her counties. Massachusetts, though sending over four hundred students to her Normal Schools, held Institutes last year in nine of fourteen counties. Maine held, in '58, an Institute in every one of her counties, and our younger sister, Illinois, held eighty-four Institutes during last year. Without mnltiplying examples, we think this evidences our position; namely, that the cause of Institutes is worthy the teacher's early and earnest efforts. As further evidence, we venture the opinion, that Insti tutes are the appropriate, if not indispensable forerunners of Normal Schools.-yes they are the prophetic voice of one crying in the wilderness, saying prepare ye the way for Popular Education, make her paths straight for she is coming in triumph, in triumph even to Indiana! Hence believe and work; work and believe, and according to your faith, be it unto you. In closing, we will state to members of committee and others holding Institutes, that our live and worthy Snperintendent of Public Instruction, will take it as a favor to be informed of times of session of Institutes, that he may, so far as practicable, visit the counties at said times. Gentlemen of the Committee, allow me to iudulge the hope, that Indiana through our, and other agencies, will hold three, yes three times as many Institutes this year, as in any preceding year. April 5, '61. G. W. Hoss, Ch'n. State Ins't. Com. Since writing the above, Mr. Vawter informs me, that it is not practicable for him to serve. He recommends for his district the appointment of Rev. L. Tarr, of Stockwell; S. S. Kilborn, of Lafayette; and Rev. Staley, of the Battle Ground. Three is a departure from the Association basis, yet presuming and hoping no objection will arise from this course, we herby confirm the recommend. G. W. H. We find the usual Associate-Editorial space pretty well filled this month by the very excellent address of Mr. Cole, which will be found to richly repay a perusal. We therefore write two or three short articles, and turn to investigate the contents of the " Drawer," in the absence of the Resident. Here are letters, reports, exchanges, &c., in abundance, inviting a look over. We shall take them as they come,' and hope our friends will be pleased; for certain we are that the intelligence thus communicated will be more interesting and read sooner than anything we can write in these excited, "perilous times." First is SCHOOL REVENUE. DEPARTMENT OF PUBLIC INSTRUCTION) I find that very many persons throughout the State imagine that our new School Law is of no effect, in that it makes no provision for a revenue. Permit me to say that this is provided for in another bill; which other bill also provides for the raising annually of $50,000 additional to the old tax, for the purpose of paying back the children the State's indebtedness to the school revenue. This $50,000 will be apportioned by the Superintendent semi-annually, until the entire amount of over $300,000 with interest, is refunded. MILES J. FLETCHER. |