Improvement to Palmer's endless self-computing scale and key : adapting it to the different professions, with examples and illustrations for each profession, and also to colleges, academies and schools : with a time telegraph making, by uniting the two, a computing telegraph / by John E. Fuller.

  • Fuller, John E. (John Emery), 1799-1878
Date:
1851
Catalogue details

Licence: Public Domain Mark

Credit: Improvement to Palmer's endless self-computing scale and key : adapting it to the different professions, with examples and illustrations for each profession, and also to colleges, academies and schools : with a time telegraph making, by uniting the two, a computing telegraph / by John E. Fuller. Source: Wellcome Collection.

Provider: This material has been provided by the National Library of Medicine (U.S.), through the Medical Heritage Library. The original may be consulted at the National Library of Medicine (U.S.)

    10/16
    43 45 47 What are the solid contents of a ball 5 inches in diameter ? Place 5 opposite 1: then opposite d. is 15-7 inches, the circumference. Also, opposite 15-7 inches is 78-4 inches, the area. £ of 5 is 835. Place this opposite 1 : then opposite 784 inches (the area) is 654 inches, the solid contents. There is a ball 20 inches in circumference : what are its solid contents? Place 20 opposite letter d. Opposite 20 is 127, the area. £ of the diameter is 1-06. Place this opposite 1: then opposite 127 is 1350 inches, the solid contents. To find the Area of an Ellipse. r I ^ Rule.—Place the product of the trans- ^— verse diameter multiplied by the conjugate diameter opposite 1: then opposite letter a is the answer. Example.—What is the area of an ellipse whose transverse diameter is 12 inches, and conjugate diameter 10 inches ? 10X12= 120. Place 120 opposite 1: then oppo- site letter a is 94-25, the area. 6-7x6-7=45, and 45x6.7=301-5. Place 301-5 opposite 1: then opposite 14 is 42-29 pounds, the answer. A ball 5-54 inches diameter ? Answer, 24 pounds nearly. A ball 32 inches circumference ? Place 32 opposite d: then opposite 1 is the diameter. Now cube the diameter, and place that cube opposite 1: then opposite 14 is 148 pounds, the answer. To find the Weight of a Leaden Ball from its Diameter or Circumference. Rule.—Place the cube of the diameter opposite 1: then opposite 21-5 is the weight. A ball is 6-6 inches in diameter: what is its weight ? Answer, 61-6 pounds. A ball 5-3 inches in diameter? Answer, 32 pounds nearly. To find the Diameter of an Iron Ball from its Weight. Rule.—Place the weight opposite 1: then oppo- site 7-11 is a product, the cube root of which is its diameter Specific Gravity and Weight of Bodies. Pure Platina oz. 23000] Clay . . . cz. 2160 Fine Gold 19400] Brick . . . 2000 Standard Gold 17720 Common Earth 1984 Quicksilver . 13600 Nitre . . . 1900 Lead . . . 11325 Ivory . . . 1825 Fine Silver . 1109l!Brimstone . 1810 Common Silver 10535 Solid Cunpowd€ r 1745 Copper . . 9000 Sand . . . 1520 Copper Pence 8915 Coal . . . 1250 Gun Metal . 8784 Mahogany 1063 Cast Brass 8000 Boxwood . 1030 Steel . . . 7850JSea Water . 1030 Tron . . . 7645iCommon Water 1000 Cast Iron . . 7425JOak . . . 925 Tin ... 7320 Gunpowd 'r shook close937 Crystal Glass 3150 in a loose heap 836 Granite 3000 Ash ... 800 White Lead . 3160 Maple . . . 755 Marble . . 2700 Beech . . . 700 Hard Stone . 2700 Elm . . . 600 Green Glass . 2600[Fir .... 550 Flint . • • 2570 Cork . . . 240 Common Stone 2520 Air at a mean state H Note.—The several sorts of wood are supposed to be dry. Also, as a cubic foot of water weighs just 1000 ounces, the numbers in this table express, not only the specific gravities of the several bodies, but also the weight of a cubic foot of each, in avoirdupois ounces; and there- fore the weight of any other quantity, or the quantity of any other weight, may be found, as in the next two propoai- tions. 44 Gauging Casks. To find the Mean Diameter of a Cask. Rule.—Add §• of the difference between the head and bung diameter to the head diameter. This re- duces the cask to a cylinder. Then multiply the square of the mean diameter by the length. Place the product opposite 1: then opposite bg is the num- ber of beer gallons, and under wa is thp number of wine gallons. Example.—There is a cask whose head ammeter is 25 inches, bung diameter 31 inches, and whose length is 36 inches : how many beer gallons and how many wine gallons does it contain ? 6 is the difference between 25 and 31. $ of 6 is 4. This, added to 25, makes 29 inches, the mean diameter. The square of 29 is 841. Place this opposite 1: then opposite 36 is 302-)-. Place this last opposite 1: then opposite bg is 85 gallons, and opposite wg is 103 gallons, the answer. To find the Weight of an Iron Ball, from its Diameter. Rule.—Place the cube of the diameter opposite 1 : then opposite 14 is the weight. Example.—What is the weight of an iron ball 6-7 inches in diameter ? 46 What is the diameter of a 24 pound ball ? Answer, 5-54 inches. To find the Diameter of a Leaden Ball from its Weight. Rule.—Place 14 opposite 3: then opposite the weight is a product, the cube root of which is the answer. A ball 8 pounds in weight is 3-34 inches in diameter. 48 To find the Magnitude of any Body from its Weight. Rule.—Place the weight of the material in ounces under its specific gravity: then opposite 1728 is its magnitude in cubic inches; and opposite 1 is the answer in cubic feet. Example.— How many cubic inches of gunpowder are there in one pound weight, shaken close ? Place 16 (the number of ounces in a pound) oppo- site 937 : then opposite 1728 is its content or magni- tude, 29£ inches. How many cubic inches are there in 3 pounds of cast brass ? Place 48 (the number of ounces in 3 pounds) oppo- site 8000 : then opposite 1728 is the answer, 103-5. To find the Weight of a Body from its Magnitude. Rule.—Place the contents of the body opposite 1728 : then opposite its specific gravity is its weight in ounces. How many ounces avoirdupois in 864 cubic inches of sand ? Place 864 opposite 1728: then opposite 1520 (the specific gravity of sand) is 760 ounces, the answer.