should suggest 4 x 8 + 3, or 4 + 8 × 3, as required. If rows of figures be taken again, and if the exercise be repeated on each three figures consecutively, slowly at first, if necessary, but keeping strictly to the rule of allowing no additional words to be either articulated or thought of, it will not be found very difficult to make the results come as readily as those of the simple multiplication table. Thus, taking 62987401328, the object is to arrive rapidly at 21, 26, 79, &c., or 6 x 2 + 9, 2 × 9 + 8, 9 × 8 + 7, &c., and also at 24, 47, 65, &c., or 6 + 2 × 9, 2 -f- 9 × 8, 9 + 8 × 7, &c. 5. The next process is to catch the result of the preceding process, and to add it to another figure, naming the first result only, and none of its constituents. Thus, taking the last line of figures, the exercise consists in learning to form rapidly, "21 and 8, 29,' ," "26 and 7, 33," "79 and 4, 83," and so on; arising from (6 x 2 + 9)+8; (2 × 9+8)+7, &c., the reason of the distinction between the two addends being, that the first of them will be a carried figure, and therefore retained in the memory while the other is on the paper. In the same way it should be done when the carried figure is put first, which, in the preceding row, would require the rapid formation of 32, 81, 69, &c., or (6 + 2 × 9) + 8; (2 + 9X8) + 7, &c. 6. The next of these exercises resembles that in (2), only that the smaller number is formed as in (4). A product increased by a digit is to be taken from a number, of which the unit's place is before the operator, while the ten's is to be supplied as wanted, to make the defect not exceed 9. Thus, out of 7861 is to be instantly supplied, "62 and 9 make 71,' or 7x8+6 is to be made up to the next number that ends with 1. Thus, from the row of figures 79812563 is to be rapidly formed "71 and 0, 71;" "73 and 9, 82;" "10 and 5, 15;" and so on. 7. The last process is the inversion of (5), namely, finding the quotient and remainder of tens and units divided by a single digit. But this should be practised without repeating, as in "8 in 59, 7 times and 3 over; it should be at most "8 in 59, 7 and 3." A row of figures may be used for practice, as in the preceding cases. As soon as these seven rules become as familiar as counting, so soon, and no sooner, is the drudgery of computation annihilated. These are the steps by which the calculator walks; and, let his journey be in what direction it may, no single pace can be anything but one or another of the preceding.-Companion to the Almanac for 1844. SCRIPTURE LESSONS. THIRD SUNDAY AFTER TRINITY. MATT. vi. 19-34. SERMON ON THE MOUNT (CONTINUED).—CAUTIONS AGAINST WORLDLY CARE. 13. Moth and rust.-Even metals rust and wear away; and moths ate the costly garments which were kept in store by the rich, as part of their property, to a much larger extent than they needed for their use. (Compare Gen. xlv. 22. Judges xiv. 12, 13.) 22. If thine eye be single.-In a healthy state, though we have two eyes, we only see one and the same object with both; what confusion should we be in if we saw one object with one eye, and a different object with the other! The very member that is to guide us (“the light of the body,") would then only distract and perplex us! just so, the man who looks partly to earthly things, and partly to heavenly, is only distracted between the two, and able to do nothing to any good purpose. 23. Evil-Disordered; the contrary to "single." 24. Mammon.-A Syriac word for "riches." 25. Take no thought.-Do not be anxious about; the same word is used in Luke x. 41. xii. 11. Phil. iv. 6., in all which passages it denotes being full of care and anxiety. We are to take prudent thought in providing as far as we can foresee them for our future wants; but having done this, we are not to be anxious about the result, but cheerfully to leave it with God. More than meat.-Since God has given you life, how much more can he provide you with food! since he has formed your body, how much more can he clothe it! 26. Fowls of the air.-Perhaps pointing to some birds which were then flying about. Our Lord was always ready to draw a profitable lesson from every thing he saw around him. Better Of more importance-less likely to be forgotten by God. (See ch. x. 29.) 29. In all his glory.-(2 Chron. ix. 3-6, 13-28.) 30. Grass-or herbage-including the lilies and flowers. As fuel was scarce, dried grass and stubble were often used instead. 32. The Gentiles.-Who know not God have no better things to seek after than these. 34. Shall take thought.-Will give the opportunity for attending to what is necessary then. Sufficient.-We have enough of trouble and sorrow in this world every day without adding to it by undue anxiety about the morrow. SUMMARY. Our Lord next brings before his disciples the supreme importance of heavenly things, charging upon them to make these the first objects of their care and anxiety; confiding for the supply of their temporal wants to the love of him who daily provides for all his creatures, and whom they were permitted to look up to as their Father. LESSONS. I. How much better are heavenly treasures than any we can have upon earth! V. 19, 20. (Col. iii. 1, 2.) II. It will show us something of the state of our hearts, if we notice what we are thinking about most frequently. V. 21. (Ps. χείν. 19.) III. If we would be Christ's disciples we must be fully and decidedly his. V. 22-24. (Matt. xvi. 24-26.) IV. There are many reasons for not being anxious about the things of this world, for 1. God has given us our life; and it is less for him to preserve than to give it. V. 25. (Acts xvii. 25-28.) 2. He provides for the wants of creatures smaller and more insignificant than we are. V. 26, 28-30. (Luke xii. 6, 7.) 3. Our own anxiety can do us no good. V. 27. (1 Tim. vi. 7.) 4. Our heavenly Father knows all we want, and has promised to supply his children. V. 31-33. (Ps. xxiii. 1.) 5. Anxiety only brings upon us increased sin and needless sorrow. V. 34. (Luke x. 40-42.) FOURTH SUNDAY AFTER TRINITY. SERMON ON THE MOUNT (CONTINUED)..-DIRECTIONS AND PROMISES. MATT Vii. 1-14. 1. Judge not.-This does not mean that we are not to form an opinion about others, for directions are given in V. 15-20 to help us to do so; or that persons whose office it is are not to judge others but we are not to be ready to make ourselves judges of the conduct of other people, when we have no business to do so; and still less to judge harshly about them, when perhaps we understand little of their motives and circumstances. 2. Mete. An old word, which means to " measure." SCRIPTURE LESSONS. THIRD SUNDAY AFTER TRINITY. MATT. vi. 19-34. SERMON ON THE MOUNT (CONtinued). .-CAUTIONS AGAINST WORLDLY CARE. 13. Moth and rust.-Even metals rust and wear away; and moths ate the costly garments which were kept in store by the rich, as part of their property, to a much larger extent than they needed for their use. (Compare Gen. xlv. 22. Judges xiv. 12, 13.) 22. If thine eye be single.-In a healthy state, though we have two eyes, we only see one and the same object with both; what confusion should we be in if we saw one object with one eye, and a different object with the other! The very member that is to guide us ("the light of the body,") would then only distract and perplex us! just so, the man who looks partly to earthly things, and partly to heavenly, is only distracted between the two, and able to do nothing to any good purpose. 23. Evil-Disordered; the contrary to "single." 24. Mammon.-A Syriac word for "riches." 25. Take no thought.-Do not be anxious about; the same word is used in Luke x. 41. xii. 11. Phil. iv. 6., in all which passages it denotes being full of care and anxiety. We are to take prudent thought in providing as far as we can foresee them for our future wants; but having done this, we are not to be anxious about the result, but cheerfully to leave it with God. More than meat.-Since God has given you life, how much more can he provide you with food! since he has formed your body, how much more can he clothe it! 26. Fowls of the air.-Perhaps pointing to some birds which were then flying about. Our Lord was always ready to draw a profitable lesson from every thing he saw around him. Better Of more importance-less likely to be forgotten by God. (See ch. x. 29.) 29. In all his glory.-(2 Chron. ix. 3-6, 13-28.) As 30. Grass-or herbage-including the lilies and flowers. fuel was scarce, dried grass and stubble were often used instead. 32. The Gentiles.-Who know not God have no better things to seek after than these. 34. Shall take thought.-Will give the opportunity for attending to what is necessary then. Sufficient.-We have enough of trouble and sorrow in this world every day without adding to it by undue anxiety about the morrow. SUMMARY. Our Lord next brings before his disciples the supreme importance of heavenly things, charging upon them to make these the first objects of their care and anxiety; confiding for the supply of their temporal wants to the love of him who daily provides for all his creatures, and whom they were permitted to look up to as their Father. LESSONS. I. How much better are heavenly treasures than any we can have upon earth! V. 19, 20. (Col. iii. 1, 2.) II. It will show us something of the state of our hearts, if we notice what we are thinking about most frequently. V. 21. (Ps. χείν. 19.) III. If we would be Christ's disciples we must be fully and deecidedly his. V. 22-24. (Matt. xvi. 24-26.) IV. There are many reasons for not being anxious about the things of this world, for 1. God has given us our life; and it is less for him to preserve than to give it. V. 25. (Acts xvii. 25-28.) 2. He provides for the wants of creatures smaller and more insignificant than we are. V. 26, 28-30. (Luke xii. 6, 7.) 3. Our own anxiety can do us no good. V. 27. (1 Tim. vi. 7.) 4. Our heavenly Father knows all we want, and has promised to supply his children. V. 31-33. (Ps. xxiii. 1.) 5. Anxiety only brings upon us increased sin and needless sorrow. V. 34. (Luke x. 40-42.) FOURTH SUNDAY AFTER TRINITY. SERMON ON THE MOUNT (CONTINUED).—DIRECTIONS AND PROMISES. MATT Vii. 1-14. 1. Judge not.-This does not mean that we are not to form an opinion about others, for directions are given in V. 15-20 to help us to do so; or that persons whose office it is are not to judge others but we are not to be ready to make ourselves judges of the conduct of other people, when we have no business to do so; and still less to judge harshly about them, when perhaps we understand little of their motives and circumstances. 2. Mete-An old word, which means to 66 measure." |