El alma Una Francesa. La muEl juez. El médico. La criada. ger. El hermano. Un criado. El alma. Un ama. del hombre. La hermana del Americano. La hija de la Francesa. La criada de la muger. Lo cierto. Lo bello. Un criado del juez. Una hija del médico. Lo futuro. Al marido de la Francesa. A la muger del juez. Al alma del ama. El hambre del criado. El hijo del hermano del médico. El criado de la muger. Al hermano del juez. A la hermana del Americano. Al hijo de la Francesa. A una hija del Americano. Lo pasado. A lo bello. The plural of such words in the above vocabulary as end with a vowel, is formed by adding s to the singular; as, hombre, man; hombres, men. Los hombres. Los maridos. Las criadas. Las hermanas de la Francesa. Los hijos del médico. A las hijas de la muger. A los hermanos del juez. Las almas de las Francesas. Las hijas del Americano. Las criadas de los médicos. Los hermanos del marido de la Francesa. Las hijas de los Americanos. Los hermanos de las criadas. ENGLISH-SPANISH. The man. The woman. The soul. The men. The physician. The daughters. A woman. A judge. A famine. A mistress. The brother of the physician. The son of the French-woman. The hushand of the woman. The maleservant of the American. The sister of the judge. The brothers. The sisters. The sons of the American. To the brothers of the physician. To the souls of the female servants. The daughters of the French-woman. The sisters of the judge. The male servants of the sons of the physician. The sons of the sisters of the American. The husbands of the daughters of the judge. The brothers of the female ser vants. OF THE NOUN, Nouns are divided into proper and common, as in English; and to them belong gender, number, person, and case. GENDER. In Spanish Grammar, every noun is considered as either masuline or feminine, whether it really has any gender or not; thus, pan, bread; sombrero, hat; plato, plate; papel, paper; azúcar, sugar-are masculine; while casaca, coat; manteca, butter; água, water; mesa, table-are feminine. The following are the rules for distinguishing the gender:Nouns which are the names of males, as well as those which denote the ranks, offices, professions, or employments of males, are masculine; as, hombre, man; perro, dog; rey, king; cura, rector; pintor, painter; zapatero, shoemaker. Nouns which are the names of females, as well as those which denote the ranks, offices, professions, or employments of females, are feminine; as, muger, woman; vaca, cow; reina, queen; costurera, seamstress; zapatera, shoe-maker's-wife. And of those which are not comprehended in the above rules : Nouns which end in a, d, ion, is, and ez, are feminine; as, marca, mark; locura, folly; soledad, solitude; religion, religion; hipótesis, hypothesis; timidez, timidity. Nouns which do not end in a, d, ion, is, and ez, are masculine; as, zapato, shoe; honor, honour; té, tea; jabon, soap. Nouns used only in the plural are of the gender to which they would belong, from their termination, if they had a singular form. Thus, calzones, breeches, is masculine, and grevas, greaves, is feminine, because calzon and greva would be of these respective genders, from their termination. Llares, fasces, and fauces, are exceptions to this rule, they being feminine. Remark. There are some few masculine nouns having femine endings; and some few feminine nouns which end otherwise than in a, d, ion, is, and ez. The gender of the noun can always be distinguished by the article used before it, except in the case of feminine nouns singular, begining with a or ha, accented on the first syllable. These, however, are very few in number. In Spanish, nouns have but two cases, the nominative and objective, the former being the agent or subject of the verb; the latter the object of an action expressed by the verb, or of a. relation expressed by a preposition. There is no possessive case in Spanish; property or possession is expressed by means of the preposition de; as," El hijo de Juan, the son of John, i, e. John's son. La casa de la muger, the house of the woman, i, e. the wo¬ man's house. La conciencia del hombre, the conscience of the man, i. e. the man's conscience. El libro es de María, the book is of Mary, i. e. the book is Mary's. La pluma es del escribiente, the pen is of the clerk, i. e. the pen is the clerk's. One noun cannot serve as an adjective for another noun, as in English; thus, such phrases as,-the York road; a paper hat; an ivory spoon; are in Spanish to be rendered el camino de York; un sombrero de papel; una cuchara de marfil; i. e. the the road of (to or from) York; a hat of paper; a spoon of should be fully expressed thus: "fué á casa de su hermano,” he ivory. In Spanish, the sentence "he went to his brother's," went to (the) house of his brother. Remark. That the learner may be able to translate and to form complete sentences, a few verbs will now be placed in the vocabulary. But as he is not yet acquainted with the form of conjugating verbs in Spanish, it is necessary to mention that of the few verbs for the present given in the vocabulary, those ending with n are in the third person plural, and of course are to be used when plural nouns are nominative to them: those in the vocabulary not ending with n are in the third person singular. In English we say, "the man wrote," and "the men wrote," (the verb being spelt alike in both the third persons singular and plural); but in Spanish we should say, el hombre escribió, "the man wrote," and, los hombres escribieron, "the men wrote." In Spanish the general rule of consructing sentences is to produce clearness and harmony. Hence it is by no means important to place the nominative before the verb, as is usually the case in English. Thus in Spanish we can say, Pedro dió el libro á María, Peter gave the book to Mary; or, Pedro dió á María el libro, Peter gave to Mary the book; or, Pedro á María dió el libro, Peter to Mary gave the book; or, Pedro á María el libro dió, Peter to Mary the book gave; or, d María dió Pedro el libro, to Mary gave Peter the book; or, dió Pedro d Maria el libro, gave Peter to Mary the book; and each of these positions of the words is allowed by the rules of the Spanish construction, that form which is most clear, forcible, and harmonious being always preferred. The learner will be able to distinguish the gender of nouns, either from their sex or from their termination. Any noun forming an exception to the general rules of gender, will have its gender specified in the vocabulary, and should be remembered by the learner. The Spanish for ship carpenter, is carpintero de navío, car penter of ship. So, ship surgeon, coach horses, would besurgeon of ship, horses of coach. It cannot be said in Spanish, I am hungry, I am thirsty, I am afraid, but, I have hunger, I have thirst, I have fear. El impresor tiene hambre, should be translated in English, the printer is hungry, and not, the printer has hunger. So, John is thirsty, should be translated in Spanish, Juan tiene sed, John has thirst. The painters have money. The printers have books. The women have husbands. The carpenters gave a book to the son of the judge. The sons of the American gave money to the male servants of the physician. The daughters of the French-woman wrote letters to the sons of the judges. The physician wrote letters to the mother of the painter. The male servants of the physician wrote letters to the female servants of the French-woman. The printers went to (the) house of the judge. The horses are hungry. The men are thirsty. The oxen are thirsty. LESSONS IN ARITHMETIC.-No. XXXI. SUBTRACTION OF DECIMAL FRACTIONS. Example.-From 425-684 subtract 216.96. Explanation. Operation. 425-684 216 96 208.724 Ans. Having written the less number under the greater, so that units may stand under units, tenths under tenths, etc., we proceed exactly as in subtraction of whole numbers. Thus, 0 thousandths from 4 thousandths leaves 4 thousandths. Write the 4 in the thousandths' place. Since the figure 9 in the lower line is larger than the one above it, we borrow 10. Now 9 from 16 leaves 7; set the 7 under the column and carry 1 to the next figure. Proceed in the same manner with the other figures in the lower number. Finally, place the decimal point in the remainder directly under that in the given number. To subtract one Decimal Fraction or Mixed Number from another. RULE. Write the less number under the greater, placing units under units, tenths under tenths, hundredths under hundredths, etc. Subtract as in whole numbers, and point off the answer as in addition of decimals. PROOF.-Subtraction of Decimals is proved in the same manner as Simple Subtraction. When there are blank places on the right hand of the upper number, they may be supplied by ciphers without altering the value of the decimal. EXERCISES. 1. From 456-0546 take 364-3123. 8. From 10 take 000001. 19. From 24681 take 87623. 22. Take 00000099 from 99. 23. From 1 thousandth take 1 millionth. 24. From 7 hundred take 7 hundredths. 30. From 2874 millionths take 211 billionths. 31. From 6231 hundred thousandths take 154 millionths. 32. From 7213 ten thousandths take 431 hundred thousandths. 33. From 8436 hundred millionths take 426 ten billionths. MULTIPLICATION OF DECIMALS. Example.-If a man can reap 96 of an acre in a day, how much can he reap in 5 of a day? Analysis. Since he can reap 96 hundredths of an acre in a whole day, in 5 tenths of a day he can reap 5 tenths of that Casa, when it means a house, as a place of residence, or home, does not quantity. But multiplying by a fraction, we have seen, is take the article before it, as in English. taking a part of the multiplicand as many times as there are 7. Multiply 381 ten thousandths by 10000; and 6504 ten millionths by 100000. 8. Multiply 834 thousandths by 1000000; and 1 millionth by 10000000. II. When the number of decimal places in the multiplier and multiplicand is large, the number of decimals in the product must also be large. But decimals below the fifth or sixth order, express such small parts of a unit, that when obtained they are commonly rejected. It is therefore desirable to avoid the unnecessary labour of obtaining those which are not to be used. Bxample 1.-It is required to multiply 1.3569 by -36742, and retain five places of decimals. Explanation. It is evident from the nature of decimal notation, that if the partial product of each figure in the multiplier is advanced one place to the right instead of the left, the operation will correspond RULE.-Multiply as in whole numbers, and point off as many figures from the right of the product for decimals, as there are decimal places both in the multiplier and multiplicand. If the product does not contain so many figures as there are decimals in both factors, supply the deficiency by prefixing ciphers. PROOF.-Multiplication of Decimals is proved in the same man-with the descending scale, and at the ner as Simple Multiplication. 125 The reason for pointing off as many decimal places in the product as there are decimals in both factors, may be illustrated thus:-Suppose it is required to multiply 25 by 5. Supplying the denominators we have 25%, and 51% Now, Yox. But 125; that is, the product of 25 X5, contains just as many decimals as the factors themselves. In like manner it may be shown that the product of any two or more decimal numbers, must contain as many decimal figures as there are places of decimals in the given factors. EXERCISES. 1. In 1 rod there are 16·5 feet: how many feet are there in 41.3 rods? 2. In 1 degree of the earth's circumference there are 69.05 British miles: how many miles are there in 360 degrees? 3. In 1 barrel there are 31.5 gallons: how many gallons in 65.25 barrels ? 4. In 1 inch there are 2.25 nails: how many nails are there in 60.5 inches? 5. In 1 square rod there are 30-25 square yards: how many square yards are there in 26.05 rods? 6. In 1 square rod there are 272.25 square feet: how many square feet are there in 160 rods? 7. How many square rods are there in a field 60·5 rods long and 40.75 rods wide? Multiply the following decimals into each other, and point the products according to rule : 8. 1.0013 X 25. 21. 40-4368 X 1.2904. 9. 44.046 X 43. 22. 100-0008 X 000306. 10. 3.6051 X 4.1. 23. 75-35060 X 62.3906. 11. 0-1003 X 6.12. 24. 31-50301 X 17.0352. 12. 8.0004 X .004. 25. 0 000713 X 2.30561. 13. 35-601 x 1.032. 26. 42-10062 X 3.821013. 14. 213-02 X 4.318. 27. 1.0142034 X 0620034. 15. 0.0006 X 00012, 28. 25067823 0000001. 16. 0-3005 X 0035. 29. 64-301257 X 1·000402. 17. 10.2016 X 38 26. 30. 394-20023 X 00000003. 18. 164 023 X 1.678. 31. 2564-21035 X 4·300506. 19. 9-40061 X 15.812. 32. 840003 1709 X 112.10371. 20. 7.31042 X 10.021 33. 0-834567834 X 00000008. CONTRACTIONS IN MULTIPLICATION OF DECIMALS. I. When the multiplier is 10, 100, 1000, etc., the multiplication may be performed by simply removing the decimal point as many places towards the right as there are ciphers in the multiplier. EXERCISES. 1. Multiply 85-4321 by 100; and 42930-213401 by 10. 2. Multiply 1067 2350123 by 100; and 608-34017 by 1000. 3. Multiply 30-467214067 by 10000; and 446 3214022 by 100000. Operation 81414 949 83 541276 27138 49855 2198 Ans. without them, same time will give the true product. Contraction. 1.3569 ⚫36742 •40707 8141 54 3 49855 Ans. Beginning at the right hand, we first multiply the multiplicand by the tenths' figure of the multiplier, and place the first figure of the partial product under the figure multiplied. In obtaining the second partial product (i. e. multiplying by 6), it is plain we may omit the right hand figure of the multiplicand, for, if multiplied, its product will fall to the right of the upright line, as seen above, and therefore will not be used. But if we multiply 9 into 6, the product is 54; and there is 5 to carry to the next product 36, which makes 41. Again, in the third partial product (i. e. in multiplying by 7), we may omit the two right hand figures of the multiplicand; for, their product will fall to the right of the upright line. But by recurring to the rejected figures, it will be seen that the product of 7 into 6 is 42, and 6 to carry make 48; we, therefore, add 5 to the product of 7 into 5, because 48 is nearer 50 than 40; consequently, it is nearer the truth to carry 5 than to carry 4. In the fourth partial product we may omit the three right-hand figures, and in the fifth or last, the four right-hand figures. Example 2.-Multiply 2356 by 3765, and retain 4 decimals in the product. Multiplying as before, the first figure of the partial product must be set in the fifth order, or one place to the right of the figure multiplied; for there are four decimals in the multiplicand, and the one by which we multiply makes 5. But since we wish to retain only 4 decimals in the product, we may omit this figure, carrying 2 to the next product. Proceed in the same manner with the other figures in the multiplier. Finally, the sum of the partial products which are retained is the answer required. 1 0887 Ans, decimal figures in the product. RULE.-Count off in the multiplicand as many decimal places less one, as are required in the product. Then beginning at the right hand figure counted off, multiply the multiplicand by the tenths or first decimal figure of the multiplier, and set the first figure of the partial product one place to the right of the figure multiplied, increasing it by the nearest number of tens that would arise from the rejected figure if multiplied. Next multiply by the second decima. figure, omitting the next right-hand figure of the multiplicand and carrying as before. Proceed in the same manner with all the figures of the multiplier whose product will come under the decimal places counted off, omitting an additional figure on the right of the multithou-plicand, as you multiply by each successive figure, and set the first figure of each partial product under that of the prece'ing. Finally, 6. Multiply 48 hundred thousandths by 100000; and 248 from the sum of the partial products, cut off the required number thousandths by 10000. 4. Multiply 21-3456782106 by 100000; and 5 tenths by 1000. 5. Multiply 75 hundredths by 100000; and 65 ten sandths by 1000. of decimals, and the result will be the answer In order to determine where to place the decimal point in the product, we have only to observe that the product of the righthand figure of the multiplicand into the tenths of the multiplier is of the order denoted by the sum of the orders of the two figure smultiplied; and when the multiplier is tenths it is of the order next lower than the figure multiplied. For this reason the first partial product is set one place to the right of the figure multiplied. But since we count off one decimal less than is required in the product, the right-hand figure in the sum of the partial products must consequently be the righthand decimal place in the answer. If the multiplier contains units, tenths, hundredths, etc., in multiplying by the units, we must begin one figure to the right of those counted off, and set the first figure of the partial productjunder the figure multiplied. In multiplying by the tens, we must begin two figures to the right of those counted off, and set the first figure of the partial product under that of the units; in multiplying by the hundreds, we must begin three figures to the right, and set the first figure of the partial product under that of the preceding, etc. This will bring the same orders under each other. Example 1.-Multiply 72543414 by decimal places in the product. Explanation. Having counted off 4 decimals in the multiplicand, increase the product of 2 into 4 by 1, because the prduct of the 3 rejected, into 2 is nearer 10 than 0. Set the 9 one place to the right of the figure multiplied, and proceed as directed. The four in the last partial product, is the number which would be carried to this order, if the 7 were multiplied by 6. 24826421, retaining 5 Operation. •7254'3414 •2482 6421 1450 9 290 2 58 0 14 4 1800 9 Ans. The quotient must, therefore, have as many decimal figures, as the decimal places in the dividend exceed those in the divisor; that is, the decimal places in the divisor and quotient together, must be equal in number to those in the dividend. Example.-What is the quotient of 0072 divided by 2 4? Explanation. Operation. 2.4) 0072(003 Ans. 72 Since the dividend has three deci mals more than the divisor, the quotient must have three decimals. But as it has but one figure, we prefix two ciphers to it to make up the deficiency. It will be noticed that 3, the first figure of the quotient, denotes thousandths; also the product of 2, the units figure of the divisor, into the first quotient figure, is written under the thousandths in the dividend. The first figure of the quotient, therefore, is of the same order, as that figure of the dividend under which is placed the product of the units of the divisor into the first quotient figure. To divide one decimal fraction by another. RULE.-Divide as in whole numbers, and point off as many figures for decimals in the quotient, as the decimal places in the dividend exceed those in the divisor. If the quotient does not contain enough of figures, supply the deficiency by prefixing ciphers. PROOF.-Division of Decimals is proved in the same manner as Simple Division. When there are more decimals in the divisor than in the dividend, annex as many ciphers to the dividend as are necessary to make its decimal places equal to those in the divisor. After all the figures of the dividend are divided, if there is a remainder, ciphers may be annexed to it and the division continued at pleasure. For ordinary purposes, it will be sufficiently exact to carry the quotient to three or four places of decimals; but when great accuracy is required, it must be carried farther. When there is a remainder, the sign + is Example 2.-Multiply 67-1498601 by 92 4023553, retaining usually annexed to the quotient, to show that it is not comfour decimals in the product. Explanation. the Operation. 67-149'8601 92.402 3553 6043.487 4 134.299 7 26.859.9 134 3 20 1 plete. EXERCISES. 1. How many boxes will it require to pack 71.5 lbs. of butter, if you put 5·5 lbs. in a box? 2. How many suits of clothes will 29.6 yds. of cloth make, allowing 3-7 yds. to a suit? 3. If a man can walk 30-25 miles per day, how long will it take him to walk 150.75 miles ? In this operation we multiply first by the tens figure of the multiplier, beginning two places to the right of those counted off in the multiplicand: that is, we begin at 6 in the multiplicand, two places to the right of first figure on the right to be retained, and multiply by 9 the first figure on the left of the multiplier. It is immaterial as to the result whether we multiply by the tenths first, or by the units, tens, or hundreds, provided we set the first figure of lbs. to a bale? the partial product in its proper place. EXERCISES. 34 3 6204-805 1 Ans. 1. Multiply 863541 by 10983 retaining 5 decimal places. 2. Multiply 1.123674 by 1.123674 retaining 6 decimal places. 3. Multiply 26736 by 28758 retaining 4 decimal places. 4. Multiply 1347866 by 288793 retaining 7 decimal places. 5. Multiply 681472 by 01286 retaining 5 decimal places. 6. Multiply 053407 by 047126 retaining 6 decimal places. 7. Multiply 3857461 by 0046401 retaining 6 decimal places. DIVISION OF DECIMAL FRACTIONS. Example.-How many bushels of oats, at 2 of a crown per bushel, can you buy for 84 of a crown? Analysis. Since 2 tenths of a crown will buy 1 bushel, 84 hundredths of a crown will buy as many bushels, as 2 tenths is contained times in 84 hundredths. Now, 84; and 2=10, or 100. And 14%, or 41%. But, 4 4.2, which is the answer required. 4. How many loads will 134642 156 lbs. of hay make, allowing 1622.2 lbs. for a load? 5. If a team can plough 2-3 acres in a day, how long will it take to plough 63.75 acres? 6. How many bales of cotton in 56343·75 lbs., allowing 375 Find the quotients indicated by the following expressions:— 7. 46.84 7.9. 8. 1.65825. 9. 6723485. 10. 4.003346.31. 11. 73-8243-061. 12. 0.00033011. 13. 236 041-175. 14. 60-0001-1.01. 15. 300 402-12.1. 16. 4.32067-001. 17. 0.00006 003. 18. 167342-002. 19. 684234 62682. 20. 0.000045-9. 21. 7.23106812. 22. 26-3845125. 23. 400001. 24. 60000001. 25. 0.80000002. 26. 6541 234567-21. 27.7461-30765-112. CONTRACTIONS IN DIVISION OF DECIMALS. I. When the divisor is 10, 100, 1000, etc., the division may be performed by simply removing the decimal point in the dividend as many places towards the left, as there are ciphers in the divisor, and it will be the quotient required. EXERCISES. 1. Divide 4672-3 by 100. 2. Divide 0.8 by 10000. 4. Divide 10342.306 by 100. 5. Divide 42643 621 by 100000. 6. Divide 6723000 45 by 10000000. When the divisor contains a large number of decimal figures, the process of dividing may be very much abridged. ON PHYSICS, OR NATURAL PHILOSOPHY. No. LVIII, (Continued from page 476.) ELECTRICITY. ACTION OF ELECTRISED BODIES ON BODIES IN THEIR NATURAL STATE.-ELECTRICAL MACHINES. Electrisation by Influence.-An electrified body acts upon a body in a neutral state in the same manner as a magnet acts upon soft iron; that is to say, it decomposes the neutral fluid, attracts the electricity of a contrary kind to that which it possesses, and repels that of the same kind. To express this effect, which is a consequence of the mutual action of the two electricities, we say that the body, which was at first in a neutral state, is now electrised by induction or influence. Electrification or electrisation by influence, is proved by means of a yellow copper cylinder, isolated on a glass support, and having at its ends two small electric pendulums formed of pith balls suspended by conducting threads made of hemp. Place this cylinder about an inch or less from one of the conductors m of an electrical machine, and this latter, as will be soon seen, will become charged with positive electric fluid, and will attract the negative and repel the positive fluid, so that the fluids being then distributed as the signs + and For of electricity, or on bringing this latter to a neutral state by touching it with the finger. 2, When a conducting body is electrised by influence, if it is touched at any one of its points, whether with a metallic stick or the finger, it is always the fluid of the same name as that of the electric source which disappears in the earth, the fluid of a contrary name being retained by the attraction of the fluid of the source. example, in the above cylinder, it is the negative fluid that remains, whether it is touched at the positive or the negative end or in the middle. It is in consequence of electrisation by influence that an electrical machine cannot be charged if there is a metallic point in communication with the ground near it; in fact, the positive fluid of the machine acting by influence upon the point, a continual current of negative fluid flows from it and neutralises the electricity of the machine. Communication of Electricity at a Distance.-In the experiment represented in fig. 383, the contrary electricities of the conductor m and the cylinder tend to unite, and they are only kept at the surfaces of the two bodies by the resistance of the air. But if the distance is diminished or the tension increased, the attractive force of the two electricities overcomes the obstacle that separates them, and they then re-unite through the air, giving rise to a spark more or less bright accompanied by a cracking sound. The negative electricty of the cylinder being then neutralised by the positive electricity of the machine, there remains in the cylinder only the positive electricity which is preserved, though the influence has just ceased. The same phenomenon takes place when the finger is presented to Fig. 383. poses the natural electricity of the hand by influence, attracts with a spark a contrary fluid, and repels into the ground the fluid of the same name. As to the distance at which explosion takes place, it varies according to the tension of the electric fluid, the form of the bodies, their conducting power, and the greater or less resistance of the surrounding media. All that we have said hitherto applies to the electrisation of good conductors. Bad conductors are not easily electrised by influence, but when once electrised they retain their electric state a considerable time after the cause which has produced it. marked in our engraving, each pendulum will be repelled. | a body highly charged with electricity. The body decom To ascertain the species of electricity with which the ends of the cylinder are charged, rub a stick of sealing-wax, and on presenting it to the pendulum nearest the electrical machine, repulsion is observed, which shows that the pendulum is charged with the same electricity as resin, that is to say, with negative fluid. On presenting a glass tube that has been rubbed to the second pendulum, there is also repulsion, consequently the pendulum is electrised positively. Therefore, a body electrised by influence possesses at the same time, in two opposite quarters, the two sorts of electricity in a free state. Between the parts electrised in a contrary way, there is necessarily a middle region in a neutral state, which may be proved by arranging several small pendulums along the cylinder. Their divergence decreases rapidly as we recede from the ends, and disappears towards the middle. A body electrised by influence acts in its turn upon neighbouring bodies so as as to separate their two fluids, as is seen in the isolated ball represented next to the cylinder. It is proved by placing a second cylinder with pendulums in a line with the first. All bodies electrised by influence exhibit the two following principles: 1. Directly the influence ceases, the two fluids are re-combined and the body retains no trace of electricity. This principle is proved with the cylinder in fig. 383, for the balls of the two pendulums fall back on being removed from the source VOL. V. Motion of Electrised Bodies.-The theory of electrisation by influence, explains the motions of attraction and repulsion Fig. 384. о which take place in electrised bodies. A fixed body M, fig. 384, electrised positively being given, and a moveable body 136 |