and a number multiplied by of itself equals of its square. 33,635 is of 47,089; and the square root of 47,089 is 217, the number required. G. W. FRANKS. Apple Creek, O. More than thirty solutions of this little problem have been sent in, some of them by old teachers; but we do not think any are better than the above.-ED. Q. 9, p. 134.-The sum of $1.00 paid each year, at 6 per cent, would amount in 4 years to 1.00 + 1.06 + 1.1236 + 1.191016 $4.374616. The compound amount of $4500 for 4 years at 6 per cent. = $5681.1465. $5681.1465 $4.374616 = $1298.66, Ans. D. N. C. = The same answer, or very nearly:-W. P. Perry, O. F. Williams, H., M. C. H., E. M., Fenton Gall, W. C. B., T. F. M., J. S. B., C. E. F., and W. C. M. Four or five other answers differ from the above and from each other.-Ed. Q. 10, p. 134.—The dimensions of the box have a common factor, a certain number of feet. This common factor is taken 5 times for the length, 3 times for the width, and 2 times for the depth of the box; then 65,910 30 times the cube of the common factor, and 65,910 302197 the cube of the common factor, and the cube root of the common factor. .. 65 ft. is the length, 39 ft. the width, and 26 ft. the depth of the box. 2197 13 H. To the same effect, C. E. F., W. T. Perry, W. C. M., T. F. M., J. S. B., J. L. Lasley, E. M., W. H. L., O. F. Williams, M. C. H., E. D. K., E. F. K., P. P. P., F. G., Geo. Rossiter, Jacob Zerbe, B. Rankin, W. C. Boyd, H. L. Mc., W. T., M. A. Reed, L. M. R., and G. W. Leahy, F. W. B's solution is incorrect. Q. 11, p. 134. Divide the L. C. M. by the G. C. D., separate the quotient into two factors prime to each other, and multiply the G. C. D. by each of these factors. The two products will be the two numbers required. If more than two numbers are sought, divide as before, and form as many factors of the quotient, having no common divisor greater than unity, as there are numbers required. Multiply the G. C. D. by each of these factors, and the products will be the required numbers. W. T. The correct solution of problems like this depends upon the following principles: 1st. The G. C. D. of two or more numbers is equal to the product of all the prime factors common to the two numbers. 2nd. The L. C. M. of two or more numbers contains all the prime factors of each of the given numbers and no other factors. 3rd. The least common multiple of several numbers is equal to the product of their G. C. D. by those factors of each number not found in the others. Now since 35 = 5×7 ... by principle 1st 5 and 7 are factors of each of the required numbers. The prime factors of 840 are 7, 5, 3, 2, 2, 2.. by principle 2nd these are all the different prime factors of the two required numbers. Now, by principle 3rd, if we divide the L. C. M. by the G. C. D., the quotient will contain all the prime factors of each number not found in the other.. 840 ÷ 35 = 24 = 2X 2X2X3, required factors. ..one number is 7X5X3 = 105, and the other number is 7X5X2 X2 X2 = 280. C. E. FLANAGAN. Answered also by E. F. Korns, E. D. Klose, O. F. Jacob Zerbe, J. L. Lasley, H. L. Mc., J. S. B., C. E. F. G., and anoymously. Q. 12, p. 134.-Perimeter of square acre = rds. Williams, J. S. Brown, 41 160 = = 50.5964 + Circumference of circular acre = √160 X 3.1416 = 44.8306 + -7854 W. H. L. Perimeter of a square containing one acre 44.8 + rd. 50.6 44.8 = 5.8 rd. W. T. Answered by C. E. Flanagan, R. E. McKesson, V. E Rudy, R. T. Dennis, Geo. Rossiter, O. F. Williams, W. T. Perry, F. W. B., M. C. H., L. M. R., C. E. D., and anonymously. Jacob Zerbe says an exact answer is impossible. Q. 13, p. 134.-"Is" does not "agree with its subject in number." Is it not time to drop that grammatical fiction, "Finite verbs agree with their subjects in person and number?" H. "Du Is agrees with the logical and not the grammatical subject. ration" or its equivalent is the logical subject. The duration of two hours is, etc. F. G. In this sentence, "is" does not agree with "hours," but with time understood. GEO. ROSSITER. When the subject is a mere word or sign, an infinitive, a phrase, or a clause, the verb should be in the third person, singular. C. E. D. "Is" should be changed to "are" to agree with its subject. West Lodi, O. E. D. KLOSE. I would refer F. B. to Harvey, p. 83, (94,) Remark 2, (2), as au. thority for this use of is. L. M. R. If F. B. will read carefully our best English writers he will find many examples of an apparent plural the subject of a verb in the singular. It is the familiar construction, according to sense, rather than strict grammar. I give a few examples: Two-thirds is mine by right. -Sheridan. The three Pigeons expects me down every moment.—Goldsmith. For thy three thousand ducats here is six.-Shakspere. While there's leaves in the forest, etc.—Scott. What means these questions ?— Young. A tedious twelve years. -Fletcher. This fourteen years.— Shakspere. C. W. S. Q. 14, p. 134.-"For" is an introductory [Harvey, Rem. 4, p. 122,] preposition, having "One to betray his country" for its object; or it is an introductory expletive [Holbrook, par. 624 and 752.] "For one to betray his country" is the subject. Some, however, parse "it" as subject, and regard "For one to betray his country" as in apposition with "it." [See Williams' Parsers' Manual.] J. L. LASLEY. Plymouth, O. "For one to betray his country," is a clause used as a noun, subject of "is." "For" is an introductory prep. used to introduce abridged infinitive clause. Q. 15, p. 134.-The sentence is correct. "I" is predicate nominative. F. W. BURGOON. "It" is subject of "was." O. F. WILLIAMS. Not correct. To be me is better. JACOB ZERBE. The sentence is correct, but "The people thought it to be me is more elegant. It is a pronoun, personal, simple; its antecedent is I, which it introduces, but with which it does not agree, [See Holbrook's Grammar, Art. 276,] 3d, sing., neut., nom., sub. of It was I. I is a pronoun, per., sim., its ant. is the name of the speaker, sing., to agree with its antecedent, nom., pred. QUERIES. gen., first, J. L. LASLEY. The number of queries received since last issue is so large that we are unable to use more than one fourth of them. We select those that seem likely to interest the greatest number of our readers. Contributions for this department should reach us as early as the 15th of the month.-ED. I. Have not high school commencements outgrown or outlived their usefulness? What changes in the manner of conducting them are needed? H. 2. What order should be observed in teaching etymology and syntax? Which should precede? or should both be taught together? V. E. R. Should higher arithmetic be taught in country schools? Give reasons for or against. J. O. S. 4. Could the time devoted to the study of English grammar in common schools be used to better advantage in some other way? A. R. T. 5. What man was most responsible for the secession movement in the South? S. M. L. 6. What position of the earth's axis would make the temperate zones each 30 degrees wide? R. J. J. 7. Why does the sun sometimes shine in at our north windows when it only reaches a northern latitude of 23% degrees? 8. What is the difference of altitude between the Atlantic and Pacific Oceans at the Isthmus of Panama? How can the difference be accounted for ? C. E. F. 9. IO. Of what use are silent letters ? B. R. B. R. II. What is the correct pronunciation of Arkansas? M. C. A. What is the greatest number which will divide 27, 48, 90, and 174, and leave the same remainder in each case? 12. J. N. 13. A man has a square meadow, and, after mowing ninety feet from each side (of the field), is half done. What is the size of the field? 14. tive? Arith. solution. H. L. Mc. What is the difference between a pure and an impure apposi A. S. L. Give the con E. M. 15. Question: What shall I do? Ans.; Wait. struction of "what" and "wait." 16. Hypocrisy is a sort of homage that vice pays to virtue. "sort" and "that." 17. M. E. P. Parse italicized words, or explain idioms: Go not my horse the better I must become the borrower of the night. J. O. V. EDITORIAL DEPARTMENT. THE NEW ORLEANS MEETING. The last week in February was education week in New Orleans, and it is not necessary to add that the crowd was some less than at the Mardi Gras the previous week! The International Congress of Educators and the Superintendents' Department of the National Educational Association held meetings daily in the city, and attendance on them was supplemented by visits to the great Exposition, with its extensive and interesting educational exhibits. A public reception was given to the two bodies on Monday afternoon. The International Congress held two sessions daily (afternoon and evening), from Tuesday to Friday inclusive, and the Superintendents' Department met in the forenoon of Tuesday, Wednesday and Thursday. The "Committee of Fifty," appointed by the National Educational Association at Madison, had a brief meeting on Thursday, some fifteen of the appointed members being present. Committees were appointed to make reports on the different departments of the Exposition. The public reception on Monday afternoon in Werlein Hall, was attended by many citizens of New Orleans and by the teachers of the city, the public schools being closed to give the teachers an opportunity to be present. Addresses of welcome were made by Hon. Louis Bush, President of the Louisiana Educational Association, who presided, Judge Charles G. Fenner, of the Supreme Court of the State, and Col. W. P. Johnston, President of Tulane University. Responses were made by Gen. John Eaton, U. S. Commissioner of Education, Dr. John Hancock, of Ohio, Dr. F. Louis Soldan, President of the National Educational Association, and Rev. A. D. Mayo, of Boston. The addresses were appropriate and felicitous, with the exception of Colonel Johnson's references to sectional questions, including such assertions as "we (the people of the South) are not sorry for what we have done," and "one of the rules governing us is that the intelligence of the community, as at present embodied in the white race, must in some form or other govern the Southern States." The utterance of these sentiments somewhat marred a happy occasion in which all sectional differences should have been entirely ignored. As a rule, as many as three papers were read at each session of the Congress, and when the body adjourned on Friday evening nearly a dozen of the papers received had not been read. The papers read included "Public Education in Jamaica," by G. W. Hicks, Inspector of Schools; "Respect for Authority Developed in the School Room," by Brother Justian, of the Christian Brothers, New York; "History of Education in Canada," by J. G. Hodgins, ViceMinister of Education; "Philosophy of Kindergarten Instruction," by W. H. Hailman, Supt. Schools, La Porte, Ind.; "The Kindergarten," by Mrs. John Ogden, Teacher of the Kindergarten Schools at the Exposition; "The Kindergarten in Canada," by Prof. J. L. Hughes, of Toronto; "The Kindergarten |