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 A R I T If M them" into parcels,'then caft up each parcel feparately, and afterwards add the fums of the federal parcels into one total. 2. AVOIRDUPOIS WEIGHT. T A B L E.

Marked thus. r. C. lb. oz. dr. l — 201 “ 8o4 =— 2240 112 == 35840 1792 == 573440 28673 By Avoirdupois weight are weighed butter, cheefe, rofin, wax, pitch, tar, tallow, foap, fait, hemp, flax, beef, brafs, iron, iteel, tin, copper, lead, allum, and all grocery wares. Note, ipvC. of lead m^ke a fodder. In adding the following example, begin with the ounces, and fay, 15 and 10 make 25; which being above 16, dot, and carry away the excefs 9, faying, 9 cf excefs and 6 make 15, and 8 make 23 ; where again dot, and carry away the excefs 7, faying, 7 and 2 is 9, and 1 tenon the left is, 19; where dot, and proceed with the excefs 3, faying, 3 and 4 is 7, and .i ten orvthe left is 17; where dot, and carry the excefs 1, faying, 1 and 5 is 6, and 1 ten on the left is 16 ; where again dot, and there being no excefs, you have nothing to iet dewn. <I0) (20) (4) (28) (16) r. c. & ib. oz. 27. 74 24. 85 68 20 19. 52 50 18. 48 16 97 3 478 15 3 20 Proceed now to add the pounds ; faying 5 carried from the ounces, viz. one for evefy dot, and 3 make 8, and 6 make 14, and 1 ten on the left is 24, and 8 make 32 ; which being above 28, dot, and go on, faying, 4 of excefs and 1 ten on the left is 14, and 9 is 23, and 1 ten on the left 1333; where again dot, and go on, faying, ; of excefs and 20 is 25, and 4 is 29 ; where dot, and proceed, "faying, 1 of excels and 2 tens on thb left make 21, and 7 make 28 ; where dot, and the 2 tens, or 20, on the left, fet below. We Ihould now proceed to add the quarters ; faying, 4 carried from the pounds and 1 make 5, fcc.; but as you carry here 1 for every four, the quarters are added exactly as the farthings in addition of money. In the hundreds you carry at 20 ; which, therefore, are added .as (hillings. The tuns are integers; and added accordingly. Vox,. I. No. 16. 3

E T I C K. 169 III. Proof of Addition. Addition may be proved feveral ways, 1. Merchants and men of bufmsfs ufually add each column firft upwards, and then downwards, and, upon finding the fum to be the fame both waysr they conclude the work to be right: and this is all the proof that their time, or the hurry of bufinefs, will admit of. 2. It is a common practice in fchools, to prove the work by a fecond fumming without the top-line ; and if thus fum added to the top-line makes the firft total, the work is fuppofed to be right; as in the following example. L. s. d. Top-line 748 15 10I 674 13 ni 835 90 1817 "8Pi Total 2350 6 3-y Total without the top-line 1601 10 4^ Proof 2350 6 3t Note, This mark + fignifies added to. 3. Addition is alfo proved by calling out the 9’s; for if the excefs above the 9’s in the total be the fame as the excefs in the items, the 347 j work may be prefumed right. Thus, to 684 ~%J' prove the example in the margin, begin — with the items, and fay, 3-J-4=:7, and 1031 5 7+ 7= 14 = 1+4=5 ; with this 5 pafs to the next item, and fay, 5 + 6=11 = 1 + 1=2, and 2 + 8=10=1, and~i+4 = 5; which 5 being the excefs of the items, place at the top of the crofs, and proceed to caft the o’s out of the total, faying, 1+ 3=4, and 4 + 1= 5; which 5, being the excefs of the total, place at the foot of the crofs; and becaufe it is the fame with the figure at the top, you conclude the work to be right., If the items are of different denominations; as pounds, Ihillings, pence, ; you muft begin with the higheft denomination; and, after calling.out the 9’$, reduce the excefs to the next inferior denomination ; and then calling out the 9’s, reduce the excefs to the next inferior denomination ; proceed in like manner with this, and all the other lower denominations, placing the hit excefs at the top of the crofs; then, in the fame manner, caft the 9’s out of the total, placing the excefs aythe foot of the crofs ; and if the figure at rhe foot and top be the fame, the work may be prefumed right. If any operation, whether in addition, fubtradion, multiplication, or divifion, be right, this kind of proof will always Ihow it to be fo; but if an operation be wrong, by a figure or figures being mifplaced, or by mifcounting 9, or any juft number of 9’s, this kind of proof will not difoover the miftake. Chap, 5A