HINTS ON SCRIPTURE LESSONS-No. 5. THE GOOD SAMARITAN. SELFISHNESS is a frightfully prevalent sin. Perhaps it is the very most frequent sin. There is scarcely an hour in the day that the selfish man does not bestow some attention on himself, to the sacrifice of some duty he neglects for it. With him, that which will minister to his comfort, or his pride, or his power, or his income, or his gratification, is always uppermost, and consideration for others always undermost in his mind. This is the exact spirit of self-love so frequently reprobated by our Lord, the opposite spirit being, in fact, the very essence of Christianity. The parable of the Good Samaritan is the best Scriptural picture of this principle carried out into practice, and the zealous teacher will take pains to improve it accordingly. It is a favourite one with children. Let us follow it in the narrative first, so as to continue our plan of suggestive comments for instruction. The parable, St. Luke x. 29, is introduced by the question of “ a certain lawyer-Who is my neighbour ? ” wishing, we are told,“ to justify himself.” Now this arose from the grand precept of the law just before uttered by the lawyer at the request of our blessed Lord“ Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy strength, and with all thy mind ; AND THY NEIGHBOUR AS THYSELF. This do (said our Lord) and thou shalt live.” The lawyer was trying, it seems, by his questions, to narrow the scope of this duty, and so to justify himself; and also, perhaps, to show off his powers of disputation with Jesus before the bystanders, and to get our Lord to propound other conditions of eternal life than those of the law : which would have answered the lawyer's purpose, and prejudiced Christ and Christianity with the Jewish populace. Our Lord took him up. (The Greek term inolaßwy does not mean merely answering, but rather retorting, or replying in argument.] And now begins the parable which is to teach us, as well as the lawyer, who is our neighbour, and what our conduct is to be towards him. V. 30.—“A certain man went down from Jerusalem.” This clearly means "A man of Jerusalem went down to Jericho.” There is a similar construction in Matt. xv. 1. The great feature of this parable lies in the countries, and their enmities, to which the men belonged who figure in the story. This Jew is robbed, beaten, stripped, and left nearly dead on the wayside. It was a road infested by banditti [Nyotal signifies murderous robbers). V. 31.-The priest, also a Jew, going by. Now he, of all others, was bound to be kind to this man : first, he was a fellow-townsman of his ; secondly, he was a priest : and if we turn to Hebrews v. 1, 2, we find it to be the especial duty of priests to have “compassion” on others. This priest, however, had none. He passed by, and left the poor man in his misery to die by the roadside. Then comes the Levite. Another of the same body of men devoted to the priesthood, and especially bound to help the Jew (Malachi ü. 4); yet he passed by on the other side. Dwell on the cruelty and selfishness of this conduct ; and give other illustrations of it. VV. 33, 34, 35.- These verses detail the arrival of the Samaritan, who renders to the poor maimed and deserted Jew the kind offices which his own fellow-countrymen failed to give him. The contrast is the stronger, owing to the fact, that the selfish men were priests, and therefore the more bound to do works of charity, while the benevolent man was a Samaritan, whose nation was not only at enmity with the Jews, but whose people (see 2 Kings xvii. for their origin) had no dealings with each other; as the woman at the well near Sychar said to our Lord—“The Jews have no dealings with the Samaritans ; " John iv. 9. The fact also should be remembered, that the man was on his journey, and in a distant country from his home. The money given to the host, two-pence, seems small; but the pence were Roman pence, in value about seven-pence-halfpenny of our money, and doubtless the charges of inns were in those days much less than at present. But the money was only in advance, as an instalment. The great lesson taught by this parable is, the Christian duty of doing as we would be done by. It teaches more; it shows that enmities and hatred and uncharitableness are obnoxious to God ; that we are not to cherish or act upon feuds, and allow our dislikes to interfere with our charities, as is the habit of hosts of people who call and think themselves Christians. The Jews circumscribed their social duties—“Thine own friend, and thy Father's friend forsake not,” &c.—Proverbs xxvii. 10. Christ enlarged them; he cleansed the Samaritan leper, and won his heart-Luke xvii. 16. Here is a grand lesson taught, though we never recollect to have seen or heard it noticed. Is not this fact intended to teach the virtue of kindness in allaying feuds, softening enmities, and making friends of foes ? Some people wish to carry the analogy in this parable further, and to push it to a representation of Christ, and his second coming (to repay the host). This, however, is doubtful ; and it will, perhaps, be better in the absence of direct authority, to avoid any narrowing of so useful a lesson of the law of love, but to give it its full breadth and bearing on the great practical duty of man. The various ways in which we neglect services to those who have no particular friendship for us, may be censured when reading this glorious parable. It is not every man who will leave a stranger to die by the roadside ; but their name is legion whose selfishness extends to a daily and hourly indifference to the wants, feelings, and interests of those to whom they are bound by no especial tie. Oh, that charities were cosmopolitan! What a millennium of peace would ensue! What a metamorphosis of the present arena of quarrels, mutual injuries, and warring interests, for an interchange of benefits, and a state of temporal welfare and social happiness, of which the world has never seen an example! And yet it is to be accomplished, whenever men who read the parable of the Good Samaritan, shall “ go and do likewise." S. THE RULE OF THREE. THE Rule of Three was generally taught as a case of proportion ; 1 and although in later books this plan is frequently discontinued, the writers seem to think that it is only by a sacrifice of theoretical consistence, to the shrine of simplicity. Now, although the Rule of Three direct can be made a case of proportion, this is not the case for the Rule of Three inverse. The Rule, in fact, belongs to a class of problems which are only soluble by proportion in one particular case. It seems better, therefore, to solve them by one general consideration in all cases. This will be done at the close of this article in a mathematical form. The question is first treated as it might be advantageously presented in the most elementary works on Arithmetic. Single Rule of Three Direct. We continually meet with two quantities which bear such a relation to one another, that we cannot multiply or divide one of them by any number without multiplying or dividing the other by the same number, · Thus, double the quantity is sold at double the price ; double the work done is paid for by twice the wages ; double the distance travelled is charged double fare ; double the capital employed should produce double the profit ; double the principal lent is paid for by double the interest ; double the labour expended produces double the work done ; double the number of eaters consume double the quantity of food ; and $o on. It must, however, be observed, that in most of these cases it is only within certain limits that the assertion is true. For example, in the case of buying and selling, the relation ceases at the point where retail transactions pass into wholesale, and conversely. Again, two men's work is often more than double one man's. Double labour bestowed on cultivation does not produce so much as double the crop. Double the heat applied to a body does not always expand it to double the size. And, in general, doubling the cause by no means always doubles the effect. Even a child will feel this, and he should be made then to understand that the assumption is frequently only true of averages. . In any case, therefore, in which we know two quantities which are so related to each other (universally, on an average, or between known limits), if we suppose either to change, we can readily find the corresponding change in the other, by multiplying and dividing that other in the same manner as we multiplied and divided the first to produce the given change in it. Thus, if 58. buy 7 yards of cloth, and we change 5s. into 8s., we, in fact, multiply 53. by 8, and divide the result (40s.) by 5. Hence we must also multiply the 7 yards by 8, and divide the result (56 yards by 5, thus obtaining 113, the answer to the question, how many yards would 8s. buy in that case ? The statement is as follows : If 5s. buy 7 yards, 958. or 88. buy 7 yards, or 11} yards. In this case, we clearly find the two lower quantities by multiplying the two upper by the lower given number (8), not the quantity, 8s., ånd dividing by the corresponding upper number (5). The order of the quantities (about which so much is usually said) is quite indifferent, provided we put together those which actually correspond, and keep like quantities under one another. Thus we may write If 7 yards cost 5s, 7 yards or 11+ yards cost 58. or 88. But as a matter of convenience, and that only, we may arrange them in one line instead of two, and place the quantity sought in the fourth place, thus : If 58. buy 7 yards, then 88. buy 7 yards, or 11} yards. . The rule then becomes “ To find the fourth quantity, multiply the second quantity by the third number, and divide the result by the first number, after the first and third quantities have been reduced to the same denomination.” This arrangement is most convenient when any reductions have to be made. Thus, s, d. yds. qr. S. d. Children may be led by the rule thus stated to overcome the two great difficulties they usually experience; viz. to tell, first, which is the multiplier and which the divisor; and secondly, what is the denomination of the result. At the same time, they may be able to judge whether any chance example is really one in the Rule of Three direct or not (often a great difficulty), and to feel the reasons for the operations they perform. The first examples set should involve very small figures, in order that the sole difficulties should lie in the statement, and the form of the questions should be as varied as possible. Single Rule of Three Inverse. We also often find two quantities so related to one another, that we cannot multiply the first by any number without dividing the other by the same number, and conversely.... Thus, doubling the length and halving the width, leave the area unaltered ; doubling the capital and halving the time should leave the profit unchanged ; doubling the number of men and halving the time of labour should leave their work unchanged ; doubling the eaters and halving the time of eating should make no change in the consumption ; doubling the speed and halving the time leave the space run over unchanged ; and so on. In this case, therefore, if we know the change in one we can readily find the change in the other, by multiplying and dividing this last by the same numbers by which we had to divide and multiply the first, in order to make the required change in it. Observe that division corresponds to multiplication, and conversely. Thus 17 feet in breadth correspond to 27 feet in length, 3 then 17.17 or 3 ft. in breadth correspond to 1.27 or 153 ft. in length. If we arrange the quantities in one line and put the quantity sought last, thus : If 17 feet in breadth correspond to 27 feet in length, then 3 feet in breadth correspond to ? feet in length. . We have the rule : “To find the fourth quantity, multiply the second quantity by the FIRST number and divide the result by the THIRD number, after reducing the first and third quantities to the same denomination.” Double Rule of Three. Sometimes a quantity depends on two others in such a manner that if the first is multiplied or divided by any number, either of the other two must be multiplied or divided by the same number, and consequently the first quantity remains unchanged if one of the others be multiplied and the other divided by the same number. Thus double the work will be done by double the men in the same time, or by the same number of men in double the time, but the same work will be done if the men be doubled and the time halved. Again, double the interest will be produced by double the principal in the same time, or by the same principal in double the time, while the interest remains unchanged if the principal is doubled and the time halved. Similar relations hold for the food eaten to the number of consumers and the time; for the space run over to the velocity and the time; the moving force to the weight and speed ; and so on. In this case we have in fact a direct and an inverse rule of three in the same example, and hence its name of double rule. The application of both rules therefore leads to the result. Thus— If 273 loaves are eaten by 26 men in 7 days „ 13 1. 8 To alter 26 men into 13 men we must multiply by 13 and divide by 26; hence 13 2 273 ......... 26 or 13 ......... 7 To change 7 days into 8 days we must multiply by 8 and divide by 7: hence 8 13 273 or 156 ......... 13 .......... 7 or 8. In this case each alteration has been made separately, first the loaves 8 |