r. May be moved and entered on the record when another has the floor, but the business then before the assembly may not be put aside. The motion must be made by one who voted with the prevailing side, and on the same day the original vote was taken. 1. Fixing the time to which an adjournment may be made; ranks first. 2. To adjourn without limitation; second. 3. Motion for the Orders of the Day; third. 4. Motion to lay on the table; fourth. 5. Motion for the previous question; fifth. 6. Motion to postpone definitely; sixth. 7. Motion to commit; seventh. 8. Motion to amend; eighth. 9. Motion to postpone indefinitely; ninth. 10. On motion to strike out words, "Shall the words stand part of the motion?" unless a majority sustains the words they are struck out. 11. On motion for previous question the form to be observed is. "Shall the main question be now put?" This, if carried, ends debate. 12. On an appeal from the chair's decision, "Shall the decision be sustained as the ruling of the house?" The chair is generally sustained. 13. On motion for Orders of the Day, "Will the house now proceed to the Orders of the Day?" This, if carried, supersedes intervening motions. 14. When an objection is raised to considering question, "Shall the question be considered?" objection may be made by any member before debate has commenced, but not subsequently. CUBICAL CONTENTS OF ROUND TIMBER. Ft. Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia long 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Ft. Dia Dia Dia Dia | Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia Dia long 22 23 24 25 8 21 31 34 87 37 41 43 48 52 36 38 41 44 40 43 46 49 55 60 64 47 50 53 57 60 64 67 59 63 67 71 75 61 65 69 73 77 82 25 27 29 32 34 37 9 24 26 28 31 33 10 26 11 29 12 32 31 13 34 37 41 44 48 51 56 60 14 37 15 40 43 16 42 46 50 55 59 63 68 73 78 17 45 49 18 48 52 51 55 59 64 69 73 78 84 89 95 100 106 112 118 83 89 95 101 107 113 119 126 89 95 101 107 114 121 127 135 94 100 106 114 120 128 134 142 99 106 112 120 127 135 142 151 58 63 68 73 78 61 66 72 77 82 19 50 55 GO 65 70 75 81 87 20 53 58 68 74 79 85 91 98 105 112 118 126 134 142 149 159 COMMERCIAL ARITHMETIC The object of the following pages is to set forth methods of making some of the calculations which occur in commercial arithmetic with greater rapidity and ease than attend the ordinary methods of making the same calculations. It is impossible to become proficient in arithmetical computations unless the fundamental principles of arithmetic have been fully mastered, and the more thorough this knowledge is, the more serviceable will the following methods prove to be. ADDITION Proficiency in addition can be acquired only by practice. There are no contractions by means of which addition may be performed with rapidity and ease. Practice, and practice only, will secure this first requisite of the accountant. However, a few practical suggestions will prove beneficial to those who have acquired but little proficiency in addition. 25 84 69 72 86 94 54 484 The Result Method of Addition Explanation.-Beginning with the lower figure in units column, name the result only of each successive addition; thus 4, 8, 14, 16, 25, 29, 34; then carrying the 3 to the next column add 3, 8, 17, 25, 32, 38, 46, 48. To Prove.-Add the columns downward. This method lies in the ability to see and combine the result of two or more figures without stopping to add each separately. The Group Method of Addition Explanation.-Beginning at the right add upward, 15, 25, 45; grouping 6, 4, 3 and 2 for 15; grouping 6 and 4 for 10 to add 15, making 25; and grouping 4, 7, 1 and 8 for 20 to add to 25, making 55, the result of first column. Carrying the 4 tens to the second column, adding as before, etc. To Prove. Add the columns downward, grouping as illustrated above. Note.- Practice in grouping will lead to great proficiency, and after one has become skilled in the same, it is advisable to skip about along the column in order to select those numbers which can be most conveniently grouped. Horizontal Addition Numbers when written in horizontal order, as in invoices and other business forms, may be added without being rewritten in vertical columns. In adding numbers written horizontally more care is requisite that the units shall be of like order, and great certainty of correctness can be had by adding first from left to right and then from right to left. The group method may be employed with equal advantage where numbers are written horizontally. Horizontal addition is not often practiced with numbers containing more than four or five figures. In adding dollars and cents it is best to omit the dollar sign. 4 2 7 6 57 4 1 Easy Methods for Adding Lengthy Single and Explanation.-Begin at 8 and add as near 20 as possible, 7 thus 8, 6, 317, reject the tens and place 7 to the right of 37 6 8 the last figure added, as in example; begin at 7 and add 7, 1, 4 and 5 = 17, reject the tens, place 7 to the right of 5, begin at 6 and add 6, 7, 2 and 4= 19. Now adding the figures in the new columns, 7, 7 and 9=23+3 tens 53 rejected=53. 17 8 Ans. Explanation. When the columns reach into the hun9105 dreds, as each hundred is reached note the amount opposite the last figure entering into its sum, as shown in example, and then begin to add again, finally adding these results. 89 8 7 9 6 8 9 8 The best method of proof is that usually employed by business men, viz., beginning at the top and adding down the column. If the result is like the first it may be safely assumed to be correct, for the same error, if there were one, would not be likely to occur in the reverse order. 186 112 Begin at the right and add each column separately; thus the sum of the first column equals 21, the second 28, the third 36, and so on, and then add the results as shown above. This method is used by civil service employes, bank clerks, and others who handle large sums of money. The advantage lies in the fact that one's attention may be called to other things and yet he is never at a loss to resume work where he left off. MULTIPLICATION The following are contractions in multiplication of simple numbers. 1. To multiply by 10, 100, etc., annex as many ciphers to the multiplicand as there are in the multiplier. 2. To multiply by 5, 50, 500, etc., annex as many ciphers to the multiplicand as there are figures in the multiplier and divide the result by 2. 3. To multiply by 25, 250, etc., multiply by 100, 1,000, etc., and divide the result by 4. 4. To multiply by any number ending in 9, multiply by the next higher number and then subtract the multiplicand. Example.-Multiply 83 by 39: 83 x 403,320—83=3,237. 5. To multiply any number of two figures by 11, write the sum of the two figures between them Example.-Multiply 45 by 11: 4+5=9, hence 495. Ans. 6. When the sum of two figures is 10 or over, add the 1 to the left-hand figure. Example. Multiply 74 by 11: 7+4=11, hence 814. 7. To square any number of 9's. Beginning at the left write 9 as many times less 1 as there are 9's in the given number, an 8, as many ciphers as 9's and 1. Example.-Square of 99 = 9,801, of 999 998,001. = Lightning Methods of Multiplication To multiply by 14, divide by 8, call it tens. To multiply by 13, divide by 6, call it tens. To multiply by 24, divide by 4, call it tens. To multiply by 33, divide by 3, call it tens. To multiply by 64, divide by 16, call it hundreds. To multiply by 83, divide by 12, call it hundreds. To multiply by 124, divide by 8, call it hundreds. To multiply by 163, divide by 6, call it hundreds. To multiply by 25, divide by 4, call it hundreds. To multiply by 314, divide by 32, call it thousands. To multiply by 334, divide by 3, call it hundreds. To multiply by 50, divide by 2, call it hundreds. To multiply by 663, divide by 15, call it thousands. To multiply by 834, divide by 12, call it thousands. To multiply by 125, divide by 8, call it thousands. To multiply by 1663, divide by 6, call it thousands. To multiply by 250, divide by 4, call it thousands. To multiply by 333, divide by 3, call it thousands. To multiply by 371, take § of the number, call it hundreds. To multiply by 87, take of the number, call it hundreds. To Multiply Numbers Ending with 5 To multiply two small numbers each of which ends in 5, such as 35 and 75, take the product of the 3 and 7, increase this by one-half the sum of these figures, and prefix the result to 25. Thus, 35 5 X 5 25 75 7 X 3=21, 21 +1(7+3) = 26 2,625 To Multiply Any Number by 21, 31, 41, etc. In multiplying any number by 21, or 31, or 401, or any num. ber of two figures where the last is 1, or of three figures, where the last two figures are 01, a good deal of time can be saved by abbreviating the ordinary process as here illustrated. For 231423 4628460 instance, suppose we have to multiply 231423 by 21. Instead of putting down 231423 with 21 under it, then drawing a line, multiplying by 1, then by 2 or 20, then adding, as is the ordinary custom; all that is necessary is simply to multiply by the 2, placing the product 4859883 |