} }6 6:3. } 1:5.2004 1:X = 951.6732. 1:183 5. What is the interest of $400, for 10 years, 3 months, and 6 days? 100 : 400 1:4 Divide by 1000 and 6. 1:61.6 1:x=$246.40. 6. What is the amount of £100 for 8 years ? 100 : 100 6:x=48, interest, by inspection. 1:8 100, principal. £148, amount. Case II.—The time, rate per cent., and amount, given, to find the principal. 1. What sum of money, put at interest at 6 per cent., will amount to $61.02 in 1 year and 4 months ? Here, as we have only one amount given, we must find another at the same rate and time, to complete the ratio. Let us find the amount of $100. 100 : 100 12:16 Divide by 100 and 12. 11:12 1:2 1:8) - 8, interest. 100, principal. $108, amount. Amt. Princ. 108 : 61.02 100: X. Removing the dot, viz. multiplying by 100, and dividing by 108, gives x=$56.50. 2. What principal, at 8 per cent., in 1 year and 6 months, will amount to $85.12 ? 100 : 100 1:12 Divide by 100 and 12. 1:6 100, principal. } 6:x. Amt. } 8:3. {1:6} } 112 : 85.12= 100: x=$76. Removing the dot, and dividing by 112, gives the answer, $76. 3. Suppose I owe a man $397.50, to be paid in a year, without interest, and I wish to pay him now. How much ought I to pay him, when the usual rate is 6 per cent. ? Evidently, such a sum, as, put to interest, would, in 1 year, amount to $397.50. Such a sum is called the present worth of $397.50. 100 : 100 6:2= -6, interest. 1:1 100, principal $106, amount. Removing dot, and dividing by 106, 106 : 397.50 = 100 : x = $375. Case III.-Time, rate, and interest, given, to find the principal. 1. What sum of money, put at interest 16 months, will gain $10.50, at 6 per cent. ? 6:10.50 100 : X. 16:12 Divide by 12 and 51: 1050 1: x=131.25, by inspec. remove dot. 28:1 2. A man paid $4.52 interest, at the end of 1 year and 4 months. What was the principal ? 6:4.52 100 : X. 12 Divide by 12 and 5 1:452 18:1 remove dot. 1:x=56.50, by inspection. 3. A man received for interest, at the end of a year, $20. What was the principal ? 6:20 100 : x = $333}, by inspection. 1:1 Case IV.-Principal, interest, and time, given, to find the rate per cent. 1. If I pay $3.78 interest, for the use of $36, for 18 months, what is the rate per cent. ? } 16 : } } } & 978:x=7. 7 Here we suppress the dot, and strike out 100; divide 36 and 12 by 12; and divide 378 by 3 X 18 54. 2. If I pay $2.34 for the use of $468, 1 month, what is the rate per cent. ? } 468 : 100 2.34:23 = 6. 1:12 6 Case V.-Principal, rate per cent., and interest, given, to find the time. 1. The interest on a note of $36, at 7 per cent., was $3.78. What was the time ? } 36 : 100 12:X = 18 months. 18 2. On a note of $600, paid interest $20, at 8 per cent. What was the time ? 600 : 109 12 : x=5. 8:20 & 5 The different cases of simple interest, then, are nothing more than compound proportion. If care be taken that the subject required is made the imperfect ratio, and, with respect to each of the other ratios, the question be always asked, What effect will it produce on the answer? will it make it more or less ? the student can never be at a loss in stating the question. If the answer be, More, of course the consequent must be the greater. If Less, the antecedent. A very few questions, worked out on the blackboard by an intelligent teacher, will give his pupils a practical knowledge of the whole system of arithmetic, which could not be easily attained by any other means ; and they will be able to perform such questions as the above, after a little practice, with still fewer figures. In this mode of teaching, the pupil is not embarrassed by a multiplicity of rules ; there is but one simple rule, the equality of the means and extremes. The other subjects generally connected with arithmetic, namely, compound interest, involution and evolution, arithmetical and geometrical progression, properly belong to algebra ; and are best understood in that connexion. Should the teacher, however, prefer the old course, these can be taught from any of the popular treatises on arithmetic. When a teacher introduces the system here presented, he should caution his class to pay no attention to the rules laid down in the books from which they will copy their practical questions, unless otherwise directed. Mingling the two systems would produce nothing but inextricable confusion. CHAPTER IX. INTELLECTUAL EDUCATION, CONTINUEI Geography. This science should be taught, as much as possible, upon maps; and the reason why all maps are imperfect should be pointed out. Every school should possess a small globe. Each pupil should have his skeleton maps, to be filled up from time to time ; and, whenever any place is mentioned, either in the course of reading or in composition or elocution exercises, the teacher should inquire where it is ; and whether it is on their maps. If its situation is not known, the name should be written on a corner of the blackboard, till the gazetteer is consulted. It would be well, if one set of skeleton maps were appropriated to this especial use, and hung up in a conspicuous part of the room The geographical treatise should be used as a reading book, and never conned, or committed to memory Parley's Geography should be the first book on this subject. History. Parley's First, Second, and Third, Books of History are good introductions to this science. In reading histotory, maps should always be consulted. They elucidate and give an air of reality to the subject. The teacher should satisfy himself, by appropriate questions, that the pupils have clear notions, both of the time and place of the events recorded. The American edition of Lavoisne's "Genealogical, Historical, Chronological, and Geographical Atlas,' and the “ American Atlas,' on the same plan, would form invaluable additions to the school library, in the hands of a skilful teacher. Human Physiology. An admirable little work for children, on this subject, by Mrs. Jane Taylor, has been published by the American Common School Society of New York, which might be used as a reading book, after ' Juvenile Lessons,' with great advantage. After a portion of it has been read, both question and answer, by the class, without study, let them close their books, the teacher read the questions, and the pupils give answers, in their own words. Botany. Some popular treatise on botany should be read aloud by the teacher, illustrated, as much as possible, by living plants. Specimens of all the plants growing in the neighborhood should be collected, whilst in flower, pressed, and dried, for the Herbarium. A Folium should also be formed, consisting of well-preserved specimens of leaves, of every variety of size and shape.. A few macerated leaves would be interesting in the folium. A considerable number of specimens of each kind, both of plants and leaves, should be preserved, so as to exchange with distant schools, lyceums, or individuals making collections. No amusements more completely absorb the attention or efforts of youth, than the collecting, arranging, labelling, and exchanging, natural specimens. And, when children and youth are thus engaged, they have neither time |