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.)

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    g — ^o^i^ ^jjk^- -SSS' ■sac --aw -***■ Ql !The Numbers on this Scale are arranged according to their Logarithmic Value; and occupy the same relation to each other in space that they do in value J of, ■inlngr on any given sum. le ; place ii opposite 1; L-le is the answer. bought at 38 tents per t, and opposite 1 is 1.18. Directum for using the Scale. To find Ih, 3 N B By placing the figures opposite each other. It will be Rule- Find the rale cm the moving ei found 10 contain two sets of numbers running from 1 to 1000, then opposite the sum InumI on ihe lived c ■ 3 revolutions ara-jnd the scale. The large size Attunes Required the per tent, profit tin nn.l.i- ~makin« the 1st, tnd coiiuining all the numbers under 10—tils gallon and sold at 33. Place 33 opposite '•2d size from 10 to 100—t'le 3d size to 100(1—running in full num-$1.18 for $1 is 18 per cent advance. 'bersto300, and frtcn 300 to 500 every oilier number with decimal lnlerest on any Sum of Money is computed at any Rale per cent., marks intervening and ftm 500 to lOMwilh numbers and dec,- ^ on Inar(:in_they ru mala as before. Observe all the divisions are m lOtblirod J SB arL f(1 ^ ,(h ^ ^^ lOOlhs. The large 1 e to be kert at the right hand unless o ^ mo| m. ^^ am, mll„rs |( 'necessity removed, as it keeps the figures in the best position Bit rei.ko|a.d .„„, (|;ns per JTilr Any sl„„ „,- mouey, at ,Juse- percent., lor any lengih of lime—Examples: 3 By placing the 1 opposv'e 2 It will give 1-2 of any number; 1 $114 (or 55 days— Place 01 opposite 11, and opposite 551s 88 cts JJopposite 3 gives 1-3 ; and i opposite 5, 3-5ths. ■ $3300 for one day—place 33 opposite 8,_ and.opposite 1 is 55 cents them 3j NOTE-On this Scale, all answers in multiplication and pro ^portion of numbers are found on the movable circle, and all an jjswara in division upon the fixed circle. To perform Multiplication. 3 Rule—Place the Multiplier found on the Movable Circle orpo Ssitethe large figure 1. then opposite the multiplicand found on lh< fixed part, is the answer on the Revolving Circle. 2 Example— What is the product of 4 multiplied by 2? Place! ground on the movable circle opposite figure 1 on the fixed circle -2lhen opposite 4 on the fixed is 8011 the revolving circle. 1 Note I. All numbers and parts of numbers on the fixed circle are now multiplied by 2, and the answers stand opposite on the movable circle. ; Note II. If in multiplying large numbers you cannot determine what is the last or unit figure in the answer, look opposite the lay- figure on the fixed circle which is the same as the unit or last ■ ure in your multiplicand, and the unit or last figure on the mot ,b<e circle standing against it, will be the answer. Example—What is the product of 234 multiplied by 8! Place 8 found on the movable circle opposite figure 1. Then opposite 234, on the fixed circle, is 187t something. Now K Junitor last figure, look opposite the large 4 on the fixed circle, (4 S 3bein the unit figure of the multiplicand ) and the unit or last fig- ure on the movable circle against it, is the answer, viz. 2: mak ing the answer 1872. Division. Find the Divisor on the Movable Circle; place it opposite 1 01 ithe fixed circle ; then opposite the dividend found circle is the answer on the fixed, ' Ithe Divisor. 'To Multiply by one number and Divide by another by one simpl, process. S 3 RuLE-PIace the multiplier found on the movable c irele opposite -' ^the divisor found on the fixed circle, then opposite the multiplicand glbund on the fixed circle, is the answer on the movable circle Exercises in Fractions—an easy way to get a h Sjf2 1 placed at 2 gives a half; at 3, a third ; at 4 a quarter ; and S Son. The numbers placed as they would be written, will give S ^desired result. If cloth cost $5.25 per yard, how much for 5-8lhs a yard? Place 5 opposite 8, and opposite 3.2o is 3.2i. To Reduce a Fraction to its Lowest and All its Terms. Rule—Place the numerator found on the movable circle opposite t &he denominator found on the fixed circle; then all the number, e islanding directly opposite each other, are other terms of saidfrac- , ana the lowest of said numbers are its lowest terms. Whole Number by a Fraction, or a Fraction by a Whole Number. Wk RULE-Place the numerator found on 'he movable circle opposil I gthe denominator found on the fixed circle; then opposite the whole r- number on the fixed circle is the answer. To Reduce Vulgar Fractions to Decimal Fractions. RuLE-Place the numerator foundon themovahle circle opposite the denominator found on the fixed circle ; then opposite he fixed circle, is the answer, or decimal fraction. To Reduce Decimal Fractions to Vulgar Fractions. i RuLE-Place the decimal found on the movable circle opposite!: II f thenany two figures standing directly opposite each other is the sue s 5.511. :in,I Make this 33.1 , and the it is 330,000, and Ihen the answer is $ tioils may be cast separately and added. To compute Interest for Years. Rules—Find the rate per cent, on the movable circle; pi opposite the large 1; then opposite the principal found circle is the interest. To find the Interest for Days and Months, at any rate per cent. Rule— Find the rate per cent, on Ihe movable circle ; place il oppo- site the 1 on the fixed circle; then opposite 365 found on the mova- ble circle is the gauge point fordays, and opposite 12 on the saint circle is the gauge point for months, at that rate per cent. If the answer required is Ban* fa/crest, or 30 days to the month then opposite 360 is the gauge point for days. To Compute Interest for Months. Rule—Place the principal (found on the movable circle) oppositi the gauge point for months at the given per cent.; then opposite the number of months found on the fixed circle is the answer. Discount. lthe fixed To get the Tonnage of a Ship. Rule—Multiply the lengih of ihe ship deducting 3-5 tne breadth of the beam, by Ihe breadth of the beam; set the product oppo- site 95, ihen opposite the depth in the hold is the answer. A ship is 120 feet long, 25 feet beam, one half of which, 12 1-2, Lethe depth In the hold. Set 25 opposite 1, and opposite 105 is 262 1-2—set this opposite 05, and opposite 12 1-2 is til 346t tons. Navigators, Masters, and Officers of Vessels. Will find the Scale of invaluable importance, in nearly all the different calculations required in a ship's reckoning. The follow- ing examples are sufficient lo illustrate the I'nct. If a ship run 9 1-2 miles per hour for 24 hours—place 9.5 op- posite 1, and opposite 24 is 2-28 miles. If she make 1-4 leeway in one mile, then in 2-28 miles how much? Set 1.25 opposite and opposite 228 is -28 1-2 miles. If the current set a ship out of her course 5-8ths of a mile per hour, how many miles in 15 l-2hours? Set 5 opposite 8, and op posite 15 1-2 is 9.70 Teachers of Navigation have recommended Ihe Seal the most undoubted assurance that the most difficult pans ul' I In- work will he readily done on the Scale. See rule for getting the apportionment of Whalemen's voyages. Required the amount due a Seaman of a Whale Ship, Drawing one 165th of a cargo of 72,000 gala. Place 165 opposite i. and opposite 72 is 437 gallons. Multiply this by 36 cents per gal- lon, the price paid for the oil, and the result is $157. If the voy- age has been of 17 months, how much would that be per month? Place 157 opposite 17, and opposite 1 is the answer, $9.25. Speed of Drums. Rule—Multiply the diameter of ihe drum by its number of<^ revolutions, and divide the product by diameter ol the driver. ThefciM quotient Will be the revolutions driven. The drum 8 niches, ina-X|/ g 1110 revolutions per minute—the driver is 5 inches—how innnyff-'jfj olunons will it make? Set 8 opposite 5, opposite 1 is 160, thc-J A the amount opposite 1, and opposite the sum to be com- puted, on the outside, is the answer. Required the discount on $150 at 5per cent. Place 95 opposite 1, and opposile 150 is 142.5 What is 9 1-2 per cent, advance on $200 1 Place 109.5 opposite d opposile 200 is 219. This rule will be found to apply equal ly well to all kinds of articles, as well as money. Equation of Payments by Casting Interest on each Sum, Example—$155 dan. 1 y.To Multiply Tin Ware. To get the cubic inches and Gallo ine35mtan diamater. Multiply this by W8S& U nenes and the re ult ,s 400 inches Cubic. Divide this by Rule for Price of Metals, u a pennyweight of gold is worth $1.05, how much for 14 pen ISnyweighl! Place 105 opposite 1, and opposite 14 is 14.7, Ihe ans Weight of Water. Tf a cubic foot of water .veigh 62 1-2 P^^J^.^Z 'much will a barrel or 31 1-2 gallons weigt. 1-2, and opposi To ascertain the Rate per cent. RULE-Plaeethe less sum found on the moving circle opposite ?the larger; then opposite 1 on the June 15—165 days—$4.26 Interest. I $iti8 Feb. 28 to June 15—105 days—$2.99 $145 May 1 to June 15— 45 days— $1.09— $50 June 15. Total $518. Interest $8.34 .| Set $518 opposite 6 per cent, and opposite 8 34 on the outside the number of days equal lo the interest, 96 1-2 days. If the credit is 4 months, 23 1-2 days will make it equal. Equation of Payments. Rule—Multiply the first sum by the second and divide by the amount of both. $300 on the lsl of April ad $400 ledge of the Scale. May—when shall a note embracing both sums be dated Place 4 opposite 7, and opposile 3 is 17.2. April 17, Ans. Should $300 also he added on the 1st of July, making Ihe s total $1010 ! Tlace 3 opposite 10. and opposite 7 is 21 day If $400 more be added July 23d, li Place 10 opposite 14, and opposite 10 These days added together give the time. Insurance. Required the premium on $7,000 at 3-8 percent, site 8. and opposite 7 oil the outside is 26 1-4. 1-4 per cent is assessed upon Ihe premium ni Co. Role—place 3 1-4 opposite 1, and opposite any amounl on the outside is the assessment. Rule for reducing the different Currencies to Dollars,Cents, and Mills. Place any sum of foreign currency opposite any equal sum ol Federal money. If $4.44 be £1 .how much for £10 IOs.1 l'lac. 4 44 opposite 1, and opposite 10.5 is 46.70.- If 5 francs be 94 ct: now much is 68 francs' '■ the answer. OR—Place the 1 on the movable circle opposite the number of shillings and decimal pans of a shilling composing a dollar of Ihe urrenry to be reduced ; then opposite the given number of shillings, n the fixed circle, is the answer. Measure of Boxes. Place the product of thewidlh by the thickness opposite 1728, and opposite the breadth in inches is the answer Example, 16 bv 19 and 22-place 16 at 1, opnosit If a 12 inch drum makes 100 revolutions, how large is the drumj o make 200? Set 12opposile 200, then opposite 1 is f>, the answer.L.|^ f an 8 inch pulley makes 250 revolutions—how large shall it beg g o make 100 1 Set 8 opposite 1, then opposite 250 is the ans. 20in.e p Required ilie speed ol a 5 inch pulley, if the 10 inch throw 65£ urns per minute. Place 5 opposite 65, and opposite 10 is 130. Speed of Pulleys. If one inch pulley throw 84 turns, h.iw many 2 inch T Place 2g opposite 84, and opposite 1 is 43. If one inch throw 84, how many 8 inch ? Set 8 opposite 84 and opposite 1 is 105. To get the number of Cogs for any size Wheel. A wheel 18 feel diameier will require how many cogs at 6 1-5 to the foot! Place C in circle opposite 1,and opposile 18 is56 1-2 Place 6 1-2 opposite 1 and opposile 56 1-2 is 367. In a wheel 19 inches diameter, how many teeth of 5 8 inch pltct from centre of one to centre of the nexitoolhi Place C in circlt opposile 1, and opposile 19 is 59 3-4. Then set 5 opposite 8, ani opptislie59 3 4 is 95 3-4. Geering of Wheels. Multiply the number of teeth in the driver by its number of rev olutions, and divide Ihe product by the number of leelh in theg driven—the quotieot is the number of revolutions of the driven.g: Example—the driver has 80 teeth, making 30 revolutions ' -v drive i has 40 teeth : how many revolutions will it make' Place so opposite 40, and opposite 30 is 60, the answer. Geering of Wheels. A Wheel with 740 teeth runs upon one with 64.C Rule—Place 84 opposite 1 and opposite 740 is the answer, 8 A wheel with 18 teeth runs upon this, and this goes into 84=4 This may be carried lo any extent. Speed of Locomotive Engines. How many revolutions would the driving wheel of an englnt make in running from Greenport to Brooklyn, the height of wheelj ... 27 opposite 9, and opposite being 6 1-2 feet, and the distance being 96 miles • In gable end, set 20 opposite cle opposite 1, and opposite 6 1-2 is 20.4^plj Price of Freight. Required the price of 16801ns. freight at $1.75 per ton 1.75 opposite 20, and then opposile 1680 is 1.47 Superficies. Required the number of feet of boards to cover a house 27 feet high and 40 by 54 feet square. Place 27 opposite 1, and opposite 188 [the feet round the same] is 5060 ft. Ans. If the rafters art 24 ft. or 3-5ths the width of the house, Ihen place 54 opposite 1 and opposile 48 is 2592. If the gable ends are 40 by 14. then plact 20 [half of 40| opposile 1, and opposhe 14 is 280. To bring thi first and Inst inio square yards 188 is 562- square'yard 9, and opposite 14 is 31,. »_- - j .u j ,. ■ . , 'mile—place this 258 opposite 1, and opposite Required the square yards of carpeting to covers floor twelve ^ 7BRl rv ' rr feel squ il, and opposite 5280, the feet per mile, Place 12 opposite 0, and opposile 12 is the answer, 16 yards. « To measure the outside of a house in feet or yards. A house is 27 feet high, and 40 by 54 in breadth and length.— Place 27 opposile 1, Ihen opposite 188 is 5076. the 1st of To get square yards, set 27 opposite 9, then 188 is the yards. Gable Ends—Tlace 20 [half of width) opposite I, then opposite the height is the answer. If for yards, place 20 opposite 9, and opposite the height is the yards. To Measure Plank. A plank 13 1-2 wide. 3 1-2 thick, and 15 1-2 long: what is th< contents t Place 3 l-2opposile 1. then opposite 13 1-2 is 47.-2— set this 47.2 opposite 12, and opposite 15 1-2 is 8111. board measure. The Price, at $27 per 1000—Set 27 opposite l.then opposite 61 is 165, the price. To get the Price of Ijumber, 13.50 per 1000 for 800 feet—Place 13.50 opposite 1, opposite 800 Is the price, 10.80. Land Measure. Observe the lbs.^ i the'outside, and the price at $5.25 is> Place 3 oppo | :es of a Mutnal Coffee-pot 5 inches Di :ircle is the answer. Barter or Exchange. V 67 cents will buy a bushel of corn and 73 cents will buy ,n,Ll of rle how many bushels of e, , ftp 49 bushels of rye !- P°ac<-6°opposite 73, «* opposite 49 is 53.5 theanswer. i 5 opposite 94,'opposite 68 is 12.80. cubic feet.- How many 1, then at 43,560, and the How The sides and end long' 19 by 24 is long. IS by 75 is 1350 this by 144 and 12 1-2 feet place this opposite 1728, and the answer is 3 7-8 feet. Required the Cubic Inches in a Cylinder. 12 inches diameter and 12 inches long—place 144, the square of 12, opposite 1, (this is the surface of a foot including cor look opposite to Area of circle near 8, (the corners o!T,)-plai 113 opposite 1, and theanswer is opposite 12: 13.56. Rule of Three, or Proportion. If a barrel of flour cost $5 25. what cost 28 lbs.? Place 555 op- posite 196 (the pounds in a barrel,) and opposite 28 Is 75 cents. Required the Cubic feet in a Block of Granite. A block 3 feet wide, 2 12 feel thick, and 6 feet long. Set 3 oppo le 1 and opposite 2 1-2 is 7.50—thw by 6 leet length 12 feet of ftuincy granite weigh a ton—pi opposite 45 is the weight, 7500 dounds, Rule to Measure Gram by its Weight. Plnce the actual Weight found on the movable circle opposite the wei.'ht required bvstatuie. Then opposite the number.of running -'—'- '■) the number of lawful bushels 45 feet. 12 opposite 20 and 3 3-4 tons. 441 n a piece of lantl 350 bv 444 feet ? Place 356 the iiiimher of feet. 158.00—divide this by is 3.63.100 opposite the number of feet. y feel of Boards which ar The lop le, and 64 inches d boitom are i8 inches These added make 1806—divide ih.- Number of Threads in a yard of Cloth. cotton cloth have 50 threads to one inch, how many thread totheyard? Set 50 opposile I, then opposite 36 is l.Hllil. In 51 yards how many threads' 50 by |si«i is Ol.tinil. 50 yards lor 1-2 s is how many for one hour? Place 5 opposile 12, opposile 1 How many Brick are required to lay a Wall. 21 1-2 to the cubic loot—llie wall 36 feel high. 60 long, ant inches thick. Place 36 opposite 1. and opposile 60 is 2160- tipiy this by selling 125 III I, and opposite 216 is'27.011—multiply this by 21 1-2, the brick in a fool, and the answer is 58.000. To get the Cubic feet in a Cistern, and change the same to Gallons Required the number of cubic reef ill a cistern measuring 6 II or 72incites in diameter andtl II. or 72 inches deep. Place 72 at 1 opposite 72 is 51S. Set this at 1, and opposile area circle is 407- set this opposite 144, and opposile lite depih.6 feet ply this by 7.48, and the answer is 1270 gallons. S 72 by 72, and that product bv 72. and that by 34—01 for Wine Gallons, gives 1270. Rule for Dry Goods Merchants in taking Account of Stock. 17 yards of calico al 38 cents—place 17 at I. and at 38 is 6.46, pi.—4 1-2 broadcloth a; $4 20.4 oppoti 258, ihe answer for one! the answer—^ 24,768.' To get the number of tons of Coal in quantity lying i Multiply the feet into cubic measure, and divide by the cubicj feet in one tun. Required the tons of coal in a parcel 7 feet deep and 24 feet square. 24 by 24 is 576, this by 7 is 4032. If 36 feets| weigh 2000, 36 into 4032. Set 36 opposite 1, and opposite 4032 is! 112 Inns, theanswer. L Required ihe price per bushel of coal at $11 per cauldron of 36^ bushels. Place 11 opposite 36, opposite 1 is 30.5—and for 7 1 bushels is 2.29. Price and Weight of Coal. If coal be $5.25 per ton gross weight, how much for 20001bs.? Plnce 5.25 opposile '2240, then opposite 20 i of coal gross weight a opposite, inside. If the coal be reckoned at 2000 for 5.25, then set that sum 5.25jc opposite 2000, and you have the result in net pounds To Measure Wood. Place the height of the pile found on the movable circle opposite on the fixed circle ; then opposite the length found on the flxedtS rele is the number of feet and lOthsof a foot, which ir diTidedg by 8 will give the cords. Another Rule to measure any load or range of Wood. Rule—Place the product of the height by .be width opposite to 16, and opposite to the lengih is the answer in wood measure.—' Id-quired ihe contents of a load of wood 3 1-2 feer wide, 7 1-2 feelj high, and 7 1-2 feet long. Place 3.5 opposite to 1, and opposite t f 5 is 26 1-4; place this opposite to 16, and opposite 7.5 Is the- aswer, 12.3 r. The Price of the same is found by placing the price per cordg oprosite 8. Required Ihe price of 12.3 at $4.50 per cord. Place, 4.50 opposile 8, and opposite 12.3 is 6.91, the answer. To Measure and find the Weight of a Cast Iron Shaft. a iron shaft is 12inches diameier and 23 feet long: howm« c feet will it contain, and what is Ihe weight at 7465 ounces ibic foot on being reduced to pounds ? 7465 divided by 16 isn_ lbs to the square loot. The square or 12 cuts opposite 144.^ Place 144 opposile 1, and opposite area of circle is 113—place thisrf at 144 and opposile 23, the length, is the cubic feet, 18t; now place,. 166 opposile 1, and opposile 18, the cubic feet, is 84001bs=4 I 400 pounds, the answer. If 3.57 cubic inches make a pound, then^. 481 pounds make a cubic foot, the shaft would then weigh S73Slbs.1T 4 ions 725 The latter is the u-ual standard for cast iron. To find the capacity of a Cistern. Acistern is 10 feet diameter and 14 feet deep. Place 120 [the; inches] opposite l.and opposite 120 is 144—placo this opposite I Opposite 108 the inches in 14 feet i gauge point al 1, then at Wine Gallon gauge point is ...= ....»..-, , 170—mult 1 = 21.37 1-2. , found, 242. Place this;. . ihe answer, 8225. Divideg; i i by 31 1-2 and you have the barrels, 261 f. To get the Cubic Yards of earth in any Cellar. eiv 24 feet square ami 7 feet deep. 24 by 24 is 5760— this by ' 403.00—divide by-27 and the square is 149, the alls- :c ;