EXERCISES. 2. How many combinations of 5 letters in 10? 3. How many elections may be made from 24 letters of the alphabet? 4. How many combinations can be made with 5 letters out of the 26 of the alphabet? 5. How many changes can be rung with 4 bells out of 8? 6. How many varieties are there in the stops of an organ that has 8 sets of pipes? 7. In how many different orders may a party of 12 men be placed P 8. In how many different orders may a gardener plant 3 elms, 4 firs, and 5 oaks ? Those who wish to see the doctrine of combinations, permutations, and figurate numbers, &c. fully explained, may consult Simpson's Algebra, Emerson's Treatise on these subjects, or Dodson's Mathematical Repository. COMMERCIAL ARITHMETIC. BEFORE the student commences the study of Arithmetic, he should be well acquainted with most of the following Tables; but particularly before he enters on the study of Commercial Arithmetic. NOTE 1. Scots money is divided in the same manner as Sterling, and is one twelfth of its value. 2. A joannes 36s.; a moidore = 27s.; a jacobus = 25s.; a carolus 23s.; a guinea=21s.; a pistole 17s. 6d.; a mark=13s. 4d.; an angel = 10s.; a noble=6s. 8d.; a crown=5s,; a dollar=4s. 6d.; a tester=6d.; a groat-4d. Troy Weight. For Gold, Silver, Jewels, and Liquors. In Scotland, gold and pound; but the ounce is 30 grains, A lb. Troy Scots Troye. 240 silver are weighed by the Troy ounce and divided into 16 drops, and the drop into .822622 lb. Avoirdupois = .756302 lb. M This weight is the same as Troy, though differently divided. Avoirdupois Weight. Used, in England, for every sort of Merchandise, except the above. NOTE. A stone-14 lb., a sack of flour=280 lb., a barrel of flour =196 lb., a quartern loaf=694 oz., a barrel of candles=10 dozen, a gallon of oil=74 lb., a fother of lead=8 pigs of 214 stones each; at London, it is 194 cwt., and at the mines 224 cwt.; a load of hay at London 36 trusses of 56 lb. each of old hay, or 60 lb. each of new hay; a load of straw at London=36 trusses of 36 lb. each; a stone of glass=5 lb.; a seam of glass=120 lb. ; a firkin of soap=64 lb.; a firkin of butter=56 lb. ; a barrel of gunpowder=1 cwt.; a bushel of salt 56 lb.; a bushel of foreign salt 84 lb.; a bushel of rock salt 65 lb. A lb. Avoirdupois=1.215625 lb. Troy=91938 lb. Scots Troye. A palm=3 inches; a span=9 inches; a cubit 18 inches; a pace 5 feet. In Devon, and part of Somerset, a pole-5 yards; in Cornwall, a pole-6 yards; in Lancashire, a pole 7 yards; in Cheshire and Staffordshire, a pole-8 yards; in the Isle of Purbeck, and some other parts of Dorsetshire, a pole-15 feet, 1 inch. In Ireland, a pole 7 yards; and a mile-2240 yards. Cloth Measure. 1 nail; 4 nails 2 inches 1 quarter; 4 quarters quarters 1 English ell; 3 quarters 1 Flemish ell. The Irish acre is to the English as 49 to 30. An English acre =.7869407 Scots acre. The French arpent is 48400 French square feet-54974.4093 English square feet. The Roman acre was 28800 Roman square feet. |