<!DOCTYPE ETS PUBLIC "-//UMDLPS//DTD EEBOPROOF 2.0//EN">
<ETS>
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<DATE>2012-04-25</DATE>
<RESPSTMT>
<NAME>Alexis Jakobson</NAME>
<RESP>MURP</RESP>
</RESPSTMT>
<ITEM>*Proofed title page(s).
*Reviewed structure.
*Checked division-marking material at heads and feet of divisions (HEADS, CLOSER, OPENER, ARGUMENT, EPIGRAPH, SIGNED, BYLINE, etc.).
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*Converted <GAP DESC="illegible" RESP="KEYERS" EXTENT="2 letters">s to GAP DESC="illegible" RESP="[vendor name]".
*Revalidated.</ITEM>
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</TEMPHEAD>
<EEBO>
<IDG S="marc" R="UM" ID="A96062">
<STC T="W">W1031A</STC>
<STC T="C">R230807</STC>
<BIBNO T="umi">99896052</BIBNO>
<VID>153738</VID>
</IDG>
<GROUP>
<TEXT LANG="eng">
<FRONT>
<DIV1 TYPE="introduction">
<PB REF="1" MS="y">
<PB REF="1">
<PB REF="2">
<PB REF="2">
<PB REF="3">
<P><HI>THE following Report was made to the Royal Society at</HI> Gre&s;ham <HI>Colledg the Third of</HI> April, <HI>1700. by the Ingenious Dr.</HI> Hook.</P>
<P>That he had con&s;ider'd the U&s;e of the <HI>Portable Scale,</HI> Invented by Mr. <HI>Tho. Wa&s;tell,</HI> and finds it to be Ingenious, and of good U&s;e for the more expeditious Performance of the Operations mentioned, to be thereby per|formable in the Title of his Book.</P>
</DIV1>
<DIV1 TYPE="title page">
<PB REF="3">
<P>THE APPLICATION OF A New Portable SCALE, (Being the Fir&s;t of this Nature) In Re&s;olving Que&s;tions in the fol|lowing Particulars, <HI>viz.</HI></P>
<LIST>
<ITEM>INTEREST, For any Sum, Time or Rate.</ITEM>
<ITEM>DISCOUNT, Of Bills, Tallies, Stock, <HI>&amp;c.</HI></ITEM>
<ITEM>FACTORIDGE At all Rates.</ITEM>
<ITEM>BROKERIDGE At all Rates.</ITEM>
<ITEM>COMMISSION At all Rates.</ITEM>
<ITEM>EXCHANGE, <HI>&amp;c.</HI> At all Rates.</ITEM>
<ITEM>VALUE Of any Quantity of Goods, Mer|chandize, or any Fractional part of an Intiger. Of any Num|ber of Pi&s;tols, Dollers, or other Foreign Coin. Of Wages due to any Workmen or Seamen, for any Time or Rate: As al&s;o Short Allowance.</ITEM>
<ITEM>NUMBER, Of Days in any di&s;tance of Time.</ITEM>
<ITEM>PROPORTION, Of any Sum <HI>per Annum,</HI> to One or any Number of Dayes. And &s;everal other profitable USES.</ITEM>
</LIST>
<P>The Second Edition, with Additions.</P>
<P>Invented by <HI>THO. WASTELL.</HI></P>
<P><HI>London,</HI> Printed for the Author, and Sold by <HI>Richard Mount,</HI> at the <HI>Po&s;tern</HI> on <HI>Tower-Hill.</HI> 1700.</P>
</DIV1>
<DIV1 TYPE="dedication">
<PB REF="4">
<PB REF="4">
<HEAD>To the Honoured <HI>Charles Sergi&s;on,</HI> <ABBR>E&s;q</ABBR> CLERK of the Acts OF HIS Maje&s;ty's Royal Navy.</HEAD>
<P>THis Scale (which is the Product of &s;ome vacant Minutes) is in Grateful Acknow|ledgment of many Fa|vours mo&s;t humbly de|dicated and pre&s;ented by</P>
<CLOSER><SIGNED>His mo&s;t Dutiful and Obedient Servant <HI>Tho. Wa&s;tell.</HI></SIGNED></CLOSER>
</DIV1>
</FRONT>
<BODY>
<DIV1 TYPE="text">
<PB REF="5">
<HEAD>How to Tabulate any Number on this SCALE.</HEAD>
<P>EAch of the &s;ix Reds hath the nine Digits, and a proper Sum to each Digitt on the right hand of it; which Rods are numbred on the outermo&s;t end with 1. 10. 100. 1000. 10000, <HI>&amp;c.</HI> and are to be drawn out 'till the proper Figure (and the Sum appertaining) come into the vacancy on the right hand end of the Scale, clear of any other Sum: All Units are to be found on the Unit-Rod, Tens on 10 Rods, Hundreds on 100 Rod, and Thou&s;ands on the 1000 Rod, <HI>&amp;c.</HI> To Tabulate 743, pull out the 100 Rod to 7, 10 Rod to 4, and Unit Rod to 3; and place the Numbers exactly one under another, and add the Sums to an&s;wer the Que&s;|tion, and the like for any other Sum.</P>
<P>In &s;hifting the Sides, turn the <HI>Rods</HI> one by one into their own Places.</P>
<DIV2 TYPE="part">
<PB N="7" REF="5">
<HEAD><HI>Intere&s;t</HI> at any <HI>Rate,</HI> for any <HI>Time</HI> or <HI>Sum. <HI>Found on the Fir&s;t Side.</HI></HI></HEAD>
<P><HI>R&V;LE.</HI> MUltiply the Sum by the Number of Days, and the Product by the Rate of Intere&s;t, Tabulate this la&s;t Product as before, and add the &s;everal Sums found, for the Intere&s;t required.</P>
<P>Intere&s;t of Shillings is found by the &s;ame Rule, dividing the la&s;t Product by 20.</P>
<P>Three Quarters, Half, a Quarter, and Half Quarter <HI>per Cent.</HI> Is that proportion of the Pro|duct of the Sum, Multiplied by the Number of Days, and to be added to the Product when multiplied by the even Rate.</P>
<P><HI>Note,</HI> Farthings are expre&s;s'd by Dotts, and fifth part of Farthings by (&tprime;) and where four fifths happen, one ought to be added.</P>
<P>The la&s;t Figure on the right hand need not to be Tabulated, in any Operation on the Fir&s;t Side; therefore the Unite-Rod is omitted.</P>
<DIV3 TYPE="examples">
<HEAD>Examples at large.</HEAD>
<P>What 354 <HI>l.</HI> at 5 <HI>per Cent.</HI> for 321 <HI>days,</HI>
<GAP DESC="math"></P>
<PB N="8" REF="6">
<P>What 67 &ratio; 16 &ratio; 0 for 73 <HI>days</HI> at 9 <HI>per Cent.</HI>
<GAP DESC="math"></P>
<P>Or by one Operation, if Shillings and Pence be turn'd into Decimals.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Di&s;count</HI> of <HI>Bills, Tallies,</HI> or <HI>Stocks.</HI></HEAD>
<HEAD TYPE="sub">On the Fir&s;t Side.</HEAD>
<P><HI>R&V;LE.</HI> Multiply the Sum by 365, and the Product by the Rate of Di&s;count, which la&s;t Product Tabulate, and Subtract the Intere&s;t found, out of the Principal.</P>
<P><HI>Note.</HI> Fractions either in Sum or Rate are re|&s;olved as in Intere&s;t.</P>
<DIV3 TYPE="examples">
<HEAD>Examples at large.</HEAD>
<P>What 230 <HI>l.</HI> at 7 <HI>per Cent.</HI> Di&s;count.
<GAP DESC="math"></P>
<PB N="9" REF="6">
<P>What 150 <HI>l.</HI> at 4&frac12; <HI>per Cent.</HI> Di&s;count
<GAP DESC="math"></P>
<P>What 2123 <HI>l.</HI> at 2&frac34; <HI>per Cent.</HI> Di&s;count.
<GAP DESC="math"></P>
<PB N="10" REF="7">
<P>What 315 <HI>l.</HI> at 17 <HI>per Cent.</HI> Advance.
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Brokeridge, Factoridge, Commi&s;|&s;ion, Exchange, <HI>&amp;c.</HI></HEAD>
<HEAD TYPE="sub">On the Fir&s;t Side.</HEAD>
<P>Are all performed by the &s;ame <HI>R&V;LE.</HI></P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>What 7562 <HI>l.</HI> at 1&frac12; and &frac12; Quarter <HI>ptr Cent.</HI>
<GAP DESC="math"></P>
<PB N="11" REF="7">
<P>What 412 <HI>l.</HI> at 5 <HI>per Cent.</HI>
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Gold</HI> or <HI>Foreign Coin</HI> to ca&s;t up.</HEAD>
<HEAD TYPE="sub">On the Second Side.</HEAD>
<P>Pi&s;tols at 17 <HI>s.</HI> 6 <HI>d.</HI> Multiply their Number by 7, and then by 30, and Tabulate as above.</P>
<P>Dollers, Pieces of Eight, <HI>&amp;c.</HI> Multiply their Number by the value of Pence in each, and Tabulate.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>What 513 Pi&s;tols at 00 &ratio; 17 &ratio; 6 each.
<GAP DESC="math"></P>
<P>What 1714 Dollers at 54 <HI>d.</HI> each.
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<PB N="12" REF="8">
<HEAD><HI>Value</HI> of <HI>Goods</HI> or <HI>Merchandize.</HI></HEAD>
<HEAD TYPE="sub">On the Second Side.</HEAD>
<P>Multiply the Number of Yards, Ells, Pounds, Ounces, <HI>&amp;c.</HI> by the Value of one, in Pence, and Tabulate the Product.</P>
<P>Half pence or Farthings, Take Half, Quar|ter, or three Quarters of the Numbet or Quan|tity, and add to the Product.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>What 227 Ounces at 5 <HI>d. per</HI> Ounce?
<GAP DESC="math"></P>
<P>What 1345 Yards at 20 <HI>l. per</HI> Yard.
<GAP DESC="math"></P>
<P>What 5602 Feet at 2 <HI>d.</HI> &frac12; <HI>per</HI> Foot.
<GAP DESC="math"></P>
<P>What 730 at 4 <HI>d.</HI> &frac14; each.
<GAP DESC="math"></P>
<PB N="13" REF="8">
<P>Or, if the Price of the Commodity, <HI>&amp;c.</HI> con|&s;i&s;t but of one Figure, Tabulate the Number or Quantity given, and multiply it by the &s;aid Figure on the Scale, by beginning at Units, removing the Rod to the proper Figure when multiplied, and carry the Tens to the next Rod, and &s;o on; adding up the Sums apper|taining to the Product for an&s;wering the Que&s;|tion.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Wages</HI> to <HI>Workmen</HI> at <HI>Day-work.</HI></HEAD>
<HEAD TYPE="sub">On the Second Side.</HEAD>
<P>Multiply the Number of Days, by the Num|ber of Pence for one Day, and Tabulate; Fractions, found as the la&s;t.</P>
<P>What 83 Days at 21 <HI>d. per Diem?</HI>
<GAP DESC="math"></P>
<P>What 365 Days at 2 <HI>s.</HI> 2 <HI>d. per Diem?</HI>
<GAP DESC="math"></P>
</DIV2>
<DIV2 TYPE="part">
<PB N="14" REF="9">
<HEAD><HI>Wages</HI> to <HI>Workmen</HI> by the <HI>Year.</HI></HEAD>
<HEAD TYPE="sub">On the Fir&s;t Side.</HEAD>
<P>Multiply the Sum <HI>per Annum</HI> by the Number of Days required, add two Cyphers to the right hand of the Product and Tabulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>At 24 <HI>per Annum,</HI> what 77 Days?
<GAP DESC="math"></P>
</DIV3>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>At 36 10 <HI>per Annum,</HI> what 112 Days?
<GAP DESC="math"></P>
<P><HI>Note,</HI> No Cyphers are to be added where Decimals are u&s;ed.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Seamen</HI>'s <HI>Wages</HI> by the <HI>Year.</HI></HEAD>
<HEAD TYPE="sub">On the the Fir&s;t Side.</HEAD>
<P>Multiply the Decimal of the Sum <HI>per Annum</HI> by the Number of Days, Tabulate the Pro|duct, omitting the la&s;t Figure to the right Hand.</P>
<DIV3 TYPE="examples">
<PB N="15" REF="9">
<HEAD>Examples.</HEAD>
<P>What 28 Days at <HI>l.</HI> 24 &ratio; 8 &ratio; 10 <HI>per Annum.</HI>
<GAP DESC="math"></P>
<P>What 90 Days at <HI>Ditto.</HI>
<GAP DESC="math"></P>
<P>What One Day at <HI>Ditto.</HI>
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Wages</HI> to <HI>Seamen <HI>per Men&s;em.</HI></HI></HEAD>
<HEAD TYPE="sub">On the Second Side.</HEAD>
<P>As 280 is to the Rate <HI>per</HI> Month, in Pence, &s;o is the Number of Days to a Number re|quired; to which add a (0) to the right Hand and Tabulate.</P>
<P>The Pence may be taken Full or Nett.</P>
<P><HI>Note,</HI> Cut off the odd pence of the Sum found.</P>
<DIV3 TYPE="examples">
<PB N="16" REF="10">
<HEAD>Examples.</HEAD>
<P>What 365 Days at 24 <HI>s. per Men&s;em.</HI>
<GAP DESC="math"></P>
<P>What 1210 Days at 4 &ratio; 6 &ratio; 2 <HI>per Men&s;em.</HI>
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Short Allowance.</HEAD>
<HEAD TYPE="sub">On the Second Side.</HEAD>
<P>Multiply the Number of Days by the Num|ber of Pence for one Day, and Tabulate: For Fractions, add the proportion of the Number of Days.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>What 307 Days at &frac23; of all Provi&s;ions.
<GAP DESC="math"></P>
<P>What 145 Days at &frac12; Allow. of all Provi&s;ions.
<GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<PB N="17" REF="10">
<HEAD><HI>A Yearly Sum, Pen&s;ion, Sala|ry, <HI>&amp;c.</HI></HI> being given, to find the <HI>Proportion</HI> to any <HI>Number</HI> of <HI>Days.</HI></HEAD>
<HEAD TYPE="sub">On the fir&s;t Side.</HEAD>
<P>Multiply the Sum by the Number of Days, add (00) to the right hand of the Product and Tabulate.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>At 450 <HI>l. per Annum,</HI> what 49 Days?
<GAP DESC="math"></P>
<P>At 60 <HI>l. per Annum,</HI> what 99 Days?
<GAP DESC="math"></P>
<P>If there be Shillings in the Yearly Sum, take the Decimal and work as before, without ad|ding the (00)</P>
</DIV3>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>At <HI>l.</HI> 11 &ratio; 17 &ratio; 0 <HI>per Ann.</HI> what 32 Days?
<GAP DESC="math"></P>
<PB N="18" REF="11">
<P>For one Day, add (00) to the Sum <HI>per Ann.</HI> if an even Sum, and Tabulate; but if a De|cimal Tabulate the Decimal.</P>
</DIV3>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>At 70 <HI>l. per Ann.</HI> what a Day? 7000 Tab. gives 0 &ratio; 3 &ratio; 10.</P>
<P>At 48 &ratio; 10 &ratio; <HI>per Ann.</HI> what one Day? 4850 Tab. <HI>l.</HI> 0 &ratio; 2 &ratio; 3&frac14;.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>The <HI>Price</HI> of a <HI>Load</HI> of <HI>Timber,</HI> be|ing given, to find the <HI>Value</HI> of any <HI>Number</HI> of <HI>Feet</HI> under a <HI>Load.</HI></HEAD>
<HEAD TYPE="sub">On the Fir&s;t Side.</HEAD>
<P>Multiply the Price <HI>per</HI> Load (in Decimals) by (73) and that by the Number of Feet, cut off two Figures to the right hand of the Pro|duct, and Tabulate the Remainder.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>At 3 &ratio; 7 &ratio; 6 <HI>per</HI> Load, what 17 Feet?
<GAP DESC="math"></P>
<PB N="19" REF="11">
<P>At <HI>l.</HI> 5 &ratio; 10 &ratio; 9 <HI>per</HI> Load, what 11 Feet, and what one Foot?
<GAP DESC="math"></P>
<P>Or if by the Tun or 40 Feet, Multiply by 912, 5.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Common Multiplicands,</HI> to find the Value of any Number of <HI>Feet,</HI> of <HI>Plank</HI> of any Thickne&s;s under a <HI>Load,</HI> at any <HI>Price <HI>per</HI> Load:</HI> By the foregoing <HI>Rule.</HI></HEAD>
<P><TABLE>
<ROW>
<CELL ROLE="label"><HI>Inches thick.</HI></CELL>
<CELL ROLE="label"><HI>Multipl.</HI></CELL>
<CELL ROLE="label"><HI>Inches. thick.</HI></CELL>
<CELL ROLE="label"><HI>Multipl.</HI></CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>608,33</CELL>
<CELL>5</CELL>
<CELL>304,1</CELL>
</ROW>
<ROW>
<CELL>9&frac12;</CELL>
<CELL>577,97</CELL>
<CELL>4&frac12;</CELL>
<CELL>279,43</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>550,52</CELL>
<CELL>4</CELL>
<CELL>243,33</CELL>
</ROW>
<ROW>
<CELL>8&frac12;</CELL>
<CELL>521,43</CELL>
<CELL>3&frac12;</CELL>
<CELL>212,92</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>486,66</CELL>
<CELL>3</CELL>
<CELL>182,5</CELL>
</ROW>
<ROW>
<CELL>7&frac12;</CELL>
<CELL>456,25</CELL>
<CELL>2&frac12;</CELL>
<CELL>152,1</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>425,85</CELL>
<CELL>2</CELL>
<CELL>121,65</CELL>
</ROW>
<ROW>
<CELL>6&frac12;</CELL>
<CELL>392,62</CELL>
<CELL>1&frac12;</CELL>
<CELL>91,25</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>365,</CELL>
<CELL>1</CELL>
<CELL>60,83</CELL>
</ROW>
<ROW>
<CELL>5&frac12;</CELL>
<CELL>332,61</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
<PB N="20" REF="12">
<P>And by the &s;ame Rule may the value of any part or proportion of the Particulars following be re&s;olved at any Rate.</P>
<LIST>
<ITEM>Great Hundred or (112) if multiplied by 326,</ITEM>
<ITEM>Neat Hundred, or (100) W^t^. or N^o^. by 365,</ITEM>
<ITEM>6 Score to the C. or (120) W^t^. or N^o^. by 304,2</ITEM>
<ITEM>If to the Hundred (108) W^t^. or N^o^. by 337,96</ITEM>
<ITEM>For a Hog&s;head of (63) Gall.&mdash;by 579,38</ITEM>
<ITEM>For a Tun of &mdash;(252) Gall.&mdash;by 144,84</ITEM>
</LIST>
<P>Or any other Denomination what&s;oever; fir&s;t finding out its common Multiplier by this Rule, Divide 36500, by the Number or parts in the Denomination, and if any Fraction re|main, add Cyphers to the Dividend, and pro|ceed as far as it will allow, &s;eperating the Quotes got by the Addition of Cyphers, for Decimal parts, and the Quotient will be the common Multiplier to that Denomination.</P>
<P><HI>Note,</HI> That in all Operations where Deci|mals are multiplied; as many places to the right hand of the Product be cut off, as there are Decimals in the <HI>Multiplicand,</HI> and <HI>Multi|plier,</HI> and the re&s;t only Tabulated on the Scale.</P>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Time</HI> to Ca&s;t into <HI>Days.</HI></HEAD>
<HEAD TYPE="sub">On the back &s;ide of the Rule.</HEAD>
<P>The Number on the right hand of the Dia|gonal Line, are the Number of Days from the fir&s;t of <HI>January</HI> to the fir&s;t of the Month over it; the Number on the left hand are from the
<PB N="21" REF="12"> la&s;t of <HI>December</HI> to the la&s;t of the Month; the Days in the Month to be added or &s;ubtracted.</P>
<P>From the Number of Days to the la&s;t Day given; &s;ubtract the Number of Days to the fir&s;t Day, from the fir&s;t of <HI>January.</HI></P>
<P>This Table is ca&s;t for Four Years.</P>
<P>From 1 <HI>January</HI>
<GAP DESC="math"></P>
<P>To 17 <HI>October</HI>
<GAP DESC="math"></P>
<P>From 12 <HI>April</HI>
<GAP DESC="math"></P>
<P>To 31 <HI>December</HI>
<GAP DESC="math"></P>
<P>From 1 <HI>January</HI> 9 8/9
<GAP DESC="math"></P>
<P>To 23 <HI>November</HI> 1700
<GAP DESC="math"></P>
<P>From 1 <HI>January</HI> 9&frac34;
<GAP DESC="math"></P>
<P>To 10 <HI>May</HI> 97
<GAP DESC="math"></P>
<P>From 11 <HI>June</HI> 98
<GAP DESC="math"></P>
<P>To 9 <HI>May</HI> 99
<GAP DESC="math"></P>
<PB N="22" REF="13">
<P>From 3 <HI>April</HI> 96
<GAP DESC="math"></P>
<P>To 21 <HI>December</HI> 99
<GAP DESC="math"></P>
<P>From 1 <HI>October</HI> 97
<GAP DESC="math"></P>
<P>To 19 <HI>January</HI> 9 8/9
<GAP DESC="math"></P>
</DIV2>
<DIV2 TYPE="part">
<HEAD>For Reducing Shillings, Pence <HI>and</HI> Farthings <HI>into</HI> Decimals, <HI>the</HI> Intiger <HI>being</HI> One Pound.</HEAD>
<P><TABLE>
<ROW>
<CELL ROLE="label"><HI>Sh.</HI></CELL>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>Sh.</HI></CELL>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>Sh.</HI></CELL>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>19</CELL>
<CELL>9500</CELL>
<CELL>10</CELL>
<CELL>5000</CELL>
<CELL>1</CELL>
<CELL>0500</CELL>
<CELL>4</CELL>
<CELL>0168</CELL>
</ROW>
<ROW>
<CELL>18</CELL>
<CELL>9000</CELL>
<CELL>9</CELL>
<CELL>4500</CELL>
<CELL><HI>d.</HI></CELL>
<CELL>&nbsp;</CELL>
<CELL>3</CELL>
<CELL>0125</CELL>
</ROW>
<ROW>
<CELL>17</CELL>
<CELL>8500</CELL>
<CELL>8</CELL>
<CELL>4000</CELL>
<CELL>11</CELL>
<CELL>0458</CELL>
<CELL>2</CELL>
<CELL>0083</CELL>
</ROW>
<ROW>
<CELL>16</CELL>
<CELL>8000</CELL>
<CELL>7</CELL>
<CELL>3500</CELL>
<CELL>10</CELL>
<CELL>0417</CELL>
<CELL>1</CELL>
<CELL>0042</CELL>
</ROW>
<ROW>
<CELL>15</CELL>
<CELL>7500</CELL>
<CELL>6</CELL>
<CELL>3000</CELL>
<CELL>9</CELL>
<CELL>0375</CELL>
<CELL><HI>far.</HI></CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>14</CELL>
<CELL>7000</CELL>
<CELL>5</CELL>
<CELL>2500</CELL>
<CELL>8</CELL>
<CELL>0333</CELL>
<CELL>3</CELL>
<CELL>0031</CELL>
</ROW>
<ROW>
<CELL>13</CELL>
<CELL>6500</CELL>
<CELL>4</CELL>
<CELL>2000</CELL>
<CELL>7</CELL>
<CELL>0292</CELL>
<CELL>2</CELL>
<CELL>0021</CELL>
</ROW>
<ROW>
<CELL>12</CELL>
<CELL>6000</CELL>
<CELL>3</CELL>
<CELL>1500</CELL>
<CELL>6</CELL>
<CELL>0250</CELL>
<CELL>1</CELL>
<CELL>0010</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>5500</CELL>
<CELL>2</CELL>
<CELL>1000</CELL>
<CELL>5</CELL>
<CELL>0208</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
<P>Or, if the Shillings be even, take half for the fir&s;t Figure of the Decimal; if odd, add 5 for the &s;econd Figure; reduce the Pence into Far|things,
<PB N="23" REF="13"> to which add the Farthings (if any to be reduc'd) and add the Tens to the &s;econd Figure whether 0 or 5, and put the Remainder in the third Place: But if the Number of Farthings be above 24, one more ought always to be added.</P>
<P>Any Decimal given are reduced into Shil|lings, Pence and Farthings, by the Rever&s;e of this Rule.</P>
</DIV2>
<TRAILER>FINIS.</TRAILER>
</DIV1>
<DIV1 TYPE="text">
<PB REF="14">
<PB REF="14">
<HEAD>Some further U&s;es this SCALE is applicable to, Occur'd &s;ince the Fir&s;t Edition, <HI>VIZ.</HI>
<LIST>
<ITEM>Compound <HI>Intere&s;t,</HI> or <HI>Rebate.</HI></ITEM>
<ITEM>Annuities, <HI>Forbearance, Di&s;count</HI> or <HI>Purcha&s;e.</HI></ITEM>
<ITEM>Divi&s;ion, to <HI>Three Decimal Parts.</HI></ITEM>
<ITEM>Rule of Three, <HI>Direct</HI> or <HI>Inver&s;e.</HI></ITEM>
<ITEM>Reduction, <HI>A&s;cending</HI> or <HI>De&s;cending.</HI></ITEM>
<ITEM>Fellow&s;hip, <HI>Lo&s;s</HI> or <HI>Gain.</HI></ITEM>
<ITEM>Exchange, <HI>Inwards</HI> or <HI>Outwards.</HI></ITEM>
<ITEM>Tare <HI>and</HI> Trett.</ITEM>
<ITEM>Equation of Payments, <HI>and</HI></ITEM>
<ITEM>Further Directions for Ca&s;ting Seamens Wages, at any Rate <HI>per Men&s;em,</HI> &amp;c.</ITEM>
</LIST></HEAD>
<BYLINE>By <HI>THO. WASTELL.</HI></BYLINE>
<DIV2 TYPE="part">
<PB N="26" REF="15">
<HEAD><HI>Compound Intere&s;t at</HI> 6 per Cent.</HEAD>
<P><TABLE>
<ROW>
<CELL ROLE="label"><HI>Years.</HI></CELL>
<CELL ROLE="label"><HI>Increa&s;e of Money.</HI></CELL>
<CELL ROLE="label"><HI>Rebate of Money.</HI></CELL>
<CELL ROLE="label"><HI>Forbearance of Annuities.</HI></CELL>
<CELL ROLE="label"><HI>Di&s;count of Annuities.</HI></CELL>
<CELL ROLE="label"><HI>Purcha&s;e of Annuities.</HI></CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>2190,00</CELL>
<CELL>34433,85</CELL>
<CELL>0000,00</CELL>
<CELL>34433,85</CELL>
<CELL>38690,00</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>4511,40</CELL>
<CELL>32484,85</CELL>
<CELL>2190,00</CELL>
<CELL>66917,70</CELL>
<CELL>19908,19</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>6971,86</CELL>
<CELL>30646,09</CELL>
<CELL>6701,40</CELL>
<CELL>97564,93</CELL>
<CELL>13415,01</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>9579,15</CELL>
<CELL>28911,39</CELL>
<CELL>13673,26</CELL>
<CELL>126476,33</CELL>
<CELL>10533,53</CELL>
</ROW>
<ROW>
<CELL>5</CELL>
<CELL>12345,03</CELL>
<CELL>27184,81</CELL>
<CELL>23253,78</CELL>
<CELL>153751,24</CELL>
<CELL>8664,73</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>15275,61</CELL>
<CELL>25731,04</CELL>
<CELL>35588,81</CELL>
<CELL>179482,32</CELL>
<CELL>7422,64</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>18382,49</CELL>
<CELL>24274,48</CELL>
<CELL>50874,79</CELL>
<CELL>20375<GAP DESC="illegible" RESP="MURP" EXTENT="1 letter">,90</CELL>
<CELL>6538,25</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>20675,16</CELL>
<CELL>22760,53</CELL>
<CELL>69257,29</CELL>
<CELL>226657,40</CELL>
<CELL>5877,59</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>25165,65</CELL>
<CELL>21604,27</CELL>
<CELL>90932,81</CELL>
<CELL>248261,72</CELL>
<CELL>5366,23</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>28865,56</CELL>
<CELL>20381,27</CELL>
<CELL>116098,83</CELL>
<CELL>268646,13</CELL>
<CELL>4958,89</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>32787,58</CELL>
<CELL>19227,72</CELL>
<CELL>144964,86</CELL>
<CELL>287870,86</CELL>
<CELL>4627,83</CELL>
</ROW>
<ROW>
<CELL>12</CELL>
<CELL>36944,93</CELL>
<CELL>18139,36</CELL>
<CELL>177752,81</CELL>
<CELL>306010,26</CELL>
<CELL>4353,35</CELL>
</ROW>
<ROW>
<CELL>13</CELL>
<CELL>41351,58</CELL>
<CELL>17112,62</CELL>
<CELL>214697,74</CELL>
<CELL>323122,89</CELL>
<CELL>4123,04</CELL>
</ROW>
<ROW>
<CELL>14</CELL>
<CELL>45022,85</CELL>
<CELL>16143,95</CELL>
<CELL>256049,69</CELL>
<CELL>339266,87</CELL>
<CELL>3926,67</CELL>
</ROW>
<ROW>
<CELL>15</CELL>
<CELL>50974,07</CELL>
<CELL>15130,17</CELL>
<CELL>302072,54</CELL>
<CELL>354497,05</CELL>
<CELL>3758,04</CELL>
</ROW>
<ROW>
<CELL>26</CELL>
<CELL>56222,77</CELL>
<CELL>14368,07</CELL>
<CELL>353046,98</CELL>
<CELL>368865,45</CELL>
<CELL>3611,67</CELL>
</ROW>
<ROW>
<CELL>17</CELL>
<CELL>61786,10</CELL>
<CELL>13554,78</CELL>
<CELL>409269,75</CELL>
<CELL>382420,20</CELL>
<CELL>3483,56</CELL>
</ROW>
<ROW>
<CELL>18</CELL>
<CELL>67683,04</CELL>
<CELL>12787,41</CELL>
<CELL>471056,22</CELL>
<CELL>395207,47</CELL>
<CELL>3370,77</CELL>
</ROW>
<ROW>
<CELL>19</CELL>
<CELL>73934,03</CELL>
<CELL>12163,68</CELL>
<CELL>578739,63</CELL>
<CELL>407271,19</CELL>
<CELL>3271,13</CELL>
</ROW>
<ROW>
<CELL>20</CELL>
<CELL>80560,24</CELL>
<CELL>11380,84</CELL>
<CELL>612674,03</CELL>
<CELL>418652,08</CELL>
<CELL>3182,07</CELL>
</ROW>
<ROW>
<CELL>21</CELL>
<CELL>87570,94</CELL>
<CELL>10736,62</CELL>
<CELL>693224,28</CELL>
<CELL>429393,30</CELL>
<CELL>3102,50</CELL>
</ROW>
</TABLE></P>
<P>THroughout the Fir&s;t Part the Operations are all performed at large, and is, I hope, &s;ufficient to explain the Nature of the Scale, and its application to the &s;everal U&s;es therein mentioned, as well as to render this Part more brief, by allowing the u&s;e of the&s;e
<PB N="27" REF="15"> few Characters undermentioned, in the &s;everal Examples performed therein; which I doubt not but will be as acceptable to the Ingenious, and an&s;wer my De&s;ign, in rendering the whole Por|table (as well as the Scale) on any occa&s;ion.</P>
<LIST>
<ITEM>For multiplied by &times;</ITEM>
<ITEM>Sum or Product z</ITEM>
<ITEM>Equal to &equals;</ITEM>
<ITEM>Added to &plus;</ITEM>
<ITEM>Fir&s;t &s;ide of the Scale A</ITEM>
<ITEM>Second &s;ide of the Scale B</ITEM>
</LIST>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Compound Intere&s;t or increa&s;e of a Sum of Money, forborn at <HI>6 per Cent.</HI> Side <HI>A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Tabular Number again&s;t the Year forborn, by the Sum; cut off the De|cimals, and Tabulate the Integers, adding the Principal to the Sum found.</P>
<DIV3 TYPE="examples">
<HEAD>Examples.</HEAD>
<P>What doth 34.<HI>l.</HI> 8.<HI>s.</HI> 0.<HI>d.</HI> amount to, being for|born 9 Years, at 6 <HI>per Cent. per Ann.</HI> Compound Intere&s;t.</P>
<P><TABLE>
<ROW>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>l.</HI></CELL>
<CELL ROLE="label"><HI>s.</HI></CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
</ROW>
<ROW>
<CELL>9&equals;25165,65x34,4z865698[360&equals;</CELL>
<CELL>23.</CELL>
<CELL>14.</CELL>
<CELL>4&frac14;</CELL>
</ROW>
<ROW>
<CELL>Principal &plus;</CELL>
<CELL>34.</CELL>
<CELL>8.</CELL>
<CELL>0.</CELL>
</ROW>
<ROW>
<CELL>An&s;wer <HI>l.</HI></CELL>
<CELL>58.</CELL>
<CELL>2.</CELL>
<CELL>4&frac14;.</CELL>
</ROW>
</TABLE></P>
<PB N="28" REF="16">
<P>What is the amount of 100 <HI>l.</HI> forborn, 21 Years at 6 <HI>Ditto?</HI></P>
<P><TABLE>
<ROW>
<CELL>21&equals;87570,94x100z8757094[00&equals;</CELL>
<CELL>239.</CELL>
<CELL>18.</CELL>
<CELL>4&frac34;.</CELL>
</ROW>
<ROW>
<CELL>Principal &plus;</CELL>
<CELL>100.</CELL>
<CELL>0.</CELL>
<CELL>0.</CELL>
</ROW>
<ROW>
<CELL>An&s;wer <HI>l.</HI></CELL>
<CELL>339.</CELL>
<CELL>18.</CELL>
<CELL>4&frac34;.</CELL>
</ROW>
</TABLE></P>
<P>10 <HI>l.</HI> forborn 7 Years at <HI>Ditto</HI> Rate.</P>
<P><TABLE>
<ROW>
<CELL>7&equals;18382,49x10z183824[9&equals;</CELL>
<CELL>5.</CELL>
<CELL>0.</CELL>
<CELL>8&frac12;.</CELL>
</ROW>
<ROW>
<CELL>Principal &plus;</CELL>
<CELL>10.</CELL>
<CELL>0.</CELL>
<CELL>0.</CELL>
</ROW>
<ROW>
<CELL>An&s;wer <HI>l.</HI></CELL>
<CELL>15.</CELL>
<CELL>0.</CELL>
<CELL>8&frac12;.</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Compound Rebate or Di&s;count at</HI> 6 per Cent. Side A.</HEAD>
<P>Multiply the Tabular Number again&s;t the Year by the Sum, cut off the Decimals and Ta|bulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What is the pre&s;ent worth of 50 <HI>l.</HI> due 11 Years hence at 6 <HI>per Cent.</HI> Compound Intere&s;t?</P>
<P><TABLE>
<ROW>
<CELL ROLE="label">&nbsp;</CELL>
<CELL ROLE="label"><HI>l.</HI></CELL>
<CELL ROLE="label"><HI>s.</HI></CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
</ROW>
<ROW>
<CELL>11&equals;19227,72x50z961386[00&equals;</CELL>
<CELL>26.</CELL>
<CELL>6.</CELL>
<CELL>9&frac14;.</CELL>
</ROW>
</TABLE></P>
<P>126.<HI>l.</HI> 10.<HI>s.</HI> 00<HI>d.</HI> due 6 Years hence, What is its pre|&s;ent worth at <HI>Ditto</HI> Rate?</P>
<P><TABLE>
<ROW>
<CELL ROLE="label">&nbsp;</CELL>
<CELL ROLE="label"><HI>l.</HI></CELL>
<CELL ROLE="label"><HI>s.</HI></CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
</ROW>
<ROW>
<CELL>6&equals;25731,04.x126,5.z3254976[560&equals;</CELL>
<CELL>89.</CELL>
<CELL>3.</CELL>
<CELL>6&frac12;</CELL>
</ROW>
</TABLE></P>
<PB N="29" REF="16">
<P>What is the pre&s;ent worth of 37 <HI>l.</HI> 16 <HI>s.</HI> 00 <HI>d.</HI> due 13 Years hence at <HI>Ditto</HI> Rate?</P>
<P><TABLE>
<ROW>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>l.</HI></CELL>
<CELL ROLE="label"><HI>s.</HI></CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
</ROW>
<ROW>
<CELL>13&equals;17112,62x37,8.z646857[036&equals;</CELL>
<CELL>17.</CELL>
<CELL>14.</CELL>
<CELL>5&frac14;</CELL>
</ROW>
</TABLE></P>
<P>One Pound due 7 Years hence, What is it now worth at <HI>Ditto</HI> Rate?</P>
<P><TABLE>
<ROW>
<CELL>&nbsp;</CELL>
<CELL ROLE="label"><HI>l.</HI></CELL>
<CELL ROLE="label"><HI>s.</HI></CELL>
<CELL ROLE="label"><HI>d.</HI></CELL>
</ROW>
<ROW>
<CELL>7&equals;24274,48x1.z24274[48&equals;</CELL>
<CELL>00.</CELL>
<CELL>13.</CELL>
<CELL>3&frac12;</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Forbearance of Annuities at <HI>6 per C.</HI> Compound Intere&s;t. <HI>Side A.</HI></HEAD>
<P><HI>Rule</HI> 1. Multiply the Number again&s;t the Years forborn, by the Yearly Annuity; cut off the Decimals and Tabulate.</P>
<P N="2">2dly, Multiply the Annuity by the Number of Years, and add the Product to the Sum before found.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>A Yearly Rent, Annuity, Pen&s;ion, <HI>&amp;c.</HI> of 20 <HI>l.</HI> being forborn 5 Years, What does it amount to at 6 <HI>per Cent</HI> Compound Intere&s;t?</P>
<P><TABLE>
<ROW>
<CELL>5&equals;23253,78x20z465075[60&equals;<HI>l.</HI></CELL>
<CELL>12.</CELL>
<CELL>14.</CELL>
<CELL>10</CELL>
</ROW>
<ROW>
<CELL>5&times;20&equals;100</CELL>
<CELL>100.</CELL>
<CELL>00.</CELL>
<CELL>00</CELL>
</ROW>
<ROW>
<CELL><HI>An&s;wer</HI></CELL>
<CELL>112.</CELL>
<CELL>14.</CELL>
<CELL>10</CELL>
</ROW>
</TABLE></P>
<PB N="30" REF="17">
<P>A Yearly Rent of 13 <HI>l.</HI> 10 <HI>s.</HI> having lain 7 Years in the Tenants hands, What mu&s;t now be receiv'd at <HI>Ditto</HI> Rate?</P>
<P><TABLE>
<ROW>
<CELL>7&equals;50874,79x13,5.z686809[665&equals;</CELL>
<CELL>18.</CELL>
<CELL>16.</CELL>
<CELL>04</CELL>
</ROW>
<ROW>
<CELL>13,5x7&equals;94,5&equals;</CELL>
<CELL>94.</CELL>
<CELL>10.</CELL>
<CELL>00</CELL>
</ROW>
<ROW>
<CELL><HI>An&s;wer</HI></CELL>
<CELL>113.</CELL>
<CELL>06.</CELL>
<CELL>04</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Di&s;count of Annuities at <HI>6 per Cent.</HI> Compound Intere&s;t. <HI>Side A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Number in the Table a|gain&s;t the Year, by the Annuity, cut off the De|cimal parts and Tabulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What is the pre&s;ent worth of an Annuity, Pen|&s;ion, <HI>&amp;c.</HI> of 60 <HI>l.</HI> to continue 4 Years?</P>
<P>4&equals;126476,33x60z7588579[80&equals;<HI>l.</HI> 207. 18. 1&frac12;</P>
<P>What an Annuity of <HI>l.</HI> 32 10 00 for 7 Years <HI>Dit.</HI></P>
<P>7&equals;203756,90x32,5.z6622099[250&equals;<HI>l.</HI> 181. 8. 6&frac12;</P>
<P>What is the pre&s;ent worth of <HI>l.</HI> 17. 07. 06. An|nuity to continue 12 Years at <HI>Ditto?</HI></P>
<P>12&equals;306010,26x17,375.z5316928[26750&equals;<HI>l.</HI> 144. 15. 4 &frac34;</P>
<P>What one Pound to continue 21 Years at <HI>Dit.</HI></P>
<P>21&equals;429393,30x1z429393[30&equals;<HI>l.</HI> 11. 15. 3&frac14;</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<PB N="31" REF="17">
<HEAD>Purcha&s;e of Annuities at <HI>6 per Cent.</HI> Compound Interest. Side <HI>A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Number in the Table a|gain&s;t the Year, by the Sum you have to purcha&s;e with, cut off the Decimals and Tabu|bulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What will be the Annuity 300 <HI>l.</HI> will purcha&s;e, to continue 7 Years?</P>
<P>7&equals;6538,25.x300z1961475[00&equals;<HI>l.</HI> 53. 14. 09.</P>
<P>What will 1000 <HI>l.</HI> purcha&s;e, to continue five Years?</P>
<P>5&equals;8664,73x1000z8664730[00&equals;<HI>l.</HI> 237. 7.9&frac12;</P>
<P>What will one Pound purcha&s;e, to continue 21 Years at <HI>Ditto?</HI></P>
<P>21&equals;3102,50x1.z3102[50&equals;<HI>l.</HI> 00 01 8 1/<GAP DESC="illegible" RESP="KEYERS" EXTENT="1 letter"></P>
<PB N="32" REF="18">
<P><TABLE>
<HEAD>A Table of Proportion to the Side A.</HEAD>
<ROW>
<CELL>&nbsp;</CELL>
<CELL ROLE="label">1</CELL>
<CELL ROLE="label">10</CELL>
<CELL ROLE="label">20</CELL>
<CELL ROLE="label">30</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL>0</CELL>
<CELL>00000</CELL>
<CELL>3650,0</CELL>
<CELL>1825,0</CELL>
<CELL>1216,6</CELL>
<CELL>912,50</CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>36500</CELL>
<CELL>3318,2</CELL>
<CELL>1738,1</CELL>
<CELL>1177,4</CELL>
<CELL>890,24</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>18250</CELL>
<CELL>3041,5</CELL>
<CELL>1659,0</CELL>
<CELL>1140,5</CELL>
<CELL>869,05</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>12166</CELL>
<CELL>2807,6</CELL>
<CELL>1586,9</CELL>
<CELL>1106,0</CELL>
<CELL>848,28</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>9125,0</CELL>
<CELL>2607,1</CELL>
<CELL>1520,8</CELL>
<CELL>1073,5</CELL>
<CELL>829,54</CELL>
</ROW>
<ROW>
<CELL>5</CELL>
<CELL>7300,0</CELL>
<CELL>2433,3</CELL>
<CELL>1460,0</CELL>
<CELL>1042,7</CELL>
<CELL>811,12</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>6083,3</CELL>
<CELL>2281,2</CELL>
<CELL>1403,8</CELL>
<CELL>1013,9</CELL>
<CELL>793,48</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>5214,2</CELL>
<CELL>2147,0</CELL>
<CELL>1351,8</CELL>
<CELL>986,48</CELL>
<CELL>776,59</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>4562,5</CELL>
<CELL>2027,7</CELL>
<CELL>1303,2</CELL>
<CELL>960,52</CELL>
<CELL>760,41</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>4055,5</CELL>
<CELL>1921,0</CELL>
<CELL>1258,6</CELL>
<CELL>935,90</CELL>
<CELL>743,18</CELL>
</ROW>
<ROW>
<CELL>&nbsp;</CELL>
<CELL ROLE="label">50</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label">70</CELL>
<CELL ROLE="label">80</CELL>
<CELL ROLE="label">90</CELL>
</ROW>
<ROW>
<CELL>0</CELL>
<CELL>730,00</CELL>
<CELL>608,33</CELL>
<CELL>521,43</CELL>
<CELL>456,25</CELL>
<CELL>405,55</CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>715,68</CELL>
<CELL>598,36</CELL>
<CELL>514,08</CELL>
<CELL>450,81</CELL>
<CELL>401,09</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>701,91</CELL>
<CELL>588,71</CELL>
<CELL>506,94</CELL>
<CELL>445,12</CELL>
<CELL>396,74</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>688,68</CELL>
<CELL>579,36</CELL>
<CELL>500,00</CELL>
<CELL>439,65</CELL>
<CELL>393,37</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>675,92</CELL>
<CELL>570,31</CELL>
<CELL>493,24</CELL>
<CELL>434,52</CELL>
<CELL>388,29</CELL>
</ROW>
<ROW>
<CELL>5</CELL>
<CELL>663,62</CELL>
<CELL>561,53</CELL>
<CELL>486,66</CELL>
<CELL>429,41</CELL>
<CELL>384,21</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>651,78</CELL>
<CELL>552,90</CELL>
<CELL>480,26</CELL>
<CELL>424,41</CELL>
<CELL>380,20</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>640,35</CELL>
<CELL>544,77</CELL>
<CELL>474,02</CELL>
<CELL>419,54</CELL>
<CELL>376,28</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>629,31</CELL>
<CELL>536,76</CELL>
<CELL>467,74</CELL>
<CELL>414,74</CELL>
<CELL>372,44</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>618,64</CELL>
<CELL>528,99</CELL>
<CELL>462,02</CELL>
<CELL>410,11</CELL>
<CELL>368,68</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Divi&s;ion on the <HI>Side A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Number found in the pre|cedent Table again&s;t the Divi&s;ior by the Dividend,
<PB N="33" REF="18"> cut off the Decimals and Tabulate. The Pounds found will be Integers, and the Shillings and Pence Decimals.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What will be the Quote of 821 divided by 31?</P>
<P>31&equals;1177,4x821z.966645[4&equals;26,483</P>
<P><HI>Ditto</HI> 2000 divided by 98.</P>
<P>98&equals;372,44x2000.z744880[00&equals;20,408</P>
<P>There is 323 <HI>l.</HI> 10 <HI>s.</HI> 00 <HI>d.</HI> to be equally di|vided among 73 Men, What is each Man's &s;hare?</P>
<P>73&equals;500,00x323,5z161750[000&equals; 04<HI>l.</HI> 08<HI>s.</HI> 7&frac12;<HI>d.</HI></P>
<P>There is 10 <HI>l.</HI> to be divided among&s;t 78 Men, What is each Man's &s;hare?</P>
<P>78&equals;467,74x10z4677[4&equals; 00<HI>l.</HI> 02<HI>s.</HI> 6&frac34;<HI>d.</HI></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Rule of Three Direct. <HI>Side A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Tabular Number to the fir&s;t Term, by the 2d Term, and the Product by, the 3d Term, cut off the Decimals and Tabu|late.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>If 12 Yards, Ells, <HI>&amp;c.</HI> co&s;t 15 <HI>l.</HI> what will 17 co&s;t?</P>
<P>12&equals;3041,5x15x17z775582[5&equals;<HI>l.</HI> 21 05 00</P>
<PB N="34" REF="19">
<P>If 26 Acres of Land give 64 <HI>l.</HI> what will 36 of the &s;ame give?</P>
<P>26&equals;1403,8x64x36z3234355[2&equals;<HI>l.</HI> 88 12 3&frac34;</P>
<P>If the Diameter of a Circle be 7, and its Cir|cumference 22, What is the Circumference of another Circle, who&s;e Diameter is 13?</P>
<P>7&equals;5214,2x22z13&equals;1491261[2&equals;40,856</P>
<P>If 54 Yards, Ells, Pounds, <HI>&amp;c.</HI> co&s;t 11<HI>l.</HI> 14<HI>s.</HI> 9<HI>d.</HI> What will one co&s;t?</P>
<P>54&equals;675,92x11,737x1.z7933[27304&equals;<HI>l.</HI> 0 4 4&frac14;</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Rule of Three Inver&s;e. <HI>Side A.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Tabular Number to the la&s;t Term by the 2d Term, and the Product by the 1&s;t Term, cut of the Decimals and Tabu|late.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>If 45 Men build a Wall in 30 Days, in how many Days will 270 build it?</P>
<P>270&equals;135,18x30x45z182493[00&equals;5 Days.</P>
<P>If 12 Men perform a Work in 5 Days, in what time will 7 Men perform it?</P>
<P>7&equals;5214,2x5x12z.312852[0&equals; 8<HI>d.</HI> 13&frac12;<HI>h.</HI></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<PB N="35" REF="19">
<HEAD><HI>Reduction a&s;cending.</HI> Side B.</HEAD>
<P><HI>Rule.</HI> Tabulate any Number of Pence on the Scale, gives how many Pounds, Shillings and Pence.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>In 375022 Pence, how many Pounds, Shil|lings and Pence.</P>
<P>375022 Tabulated&equals;<HI>l.</HI> 1562. 11. 10.</P>
<P>So 39325 <HI>d.</HI> Tab.&equals;<HI>l.</HI> 163. 17. 1.</P>
<P>In 79462 Farthings, how many <HI>l. s. d.</HI></P>
<P>19485 Tab.&equals;<HI>l.</HI> 811. 18. 9&frac12;.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Reduction De&s;cending.</HEAD>
<P><HI>Rule.</HI> Tabulate the Sum, and the Index &s;hews the Pence.</P>
<P>In 250 <HI>l.</HI> how many Pence, 250 <HI>l.</HI>&equals;60000 <HI>d.</HI></P>
<P>In <HI>l.</HI> 79. 5. 7. how many Pence, Tab. the next le&s;s, till the Sum is compleated.</P>
<P><LIST>
<ITEM>41. 13. 4.</ITEM>
<ITEM>37. 10. 0.</ITEM>
<ITEM>1. 8.</ITEM>
<ITEM>7.</ITEM>
</LIST> &equals; Index 19027 <HI>d.</HI></P>
</DIV2>
<DIV2 TYPE="part">
<PB N="36" REF="20">
<HEAD><HI>Fellow&s;hip, Gain.</HI> Side A.</HEAD>
<P><HI>Rule.</HI> Multiply the Tabular Number to the whole Stock by the whole Gain, and the Pro|duct by each Man's Stock gives his Gain, <HI>viz.</HI></P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>A 100 <HI>l.</HI> B 40 <HI>l.</HI> C 10 <HI>l.</HI> the whole Stock 150 <HI>l.</HI> and the whole Gain &mdash; 43 What is each Man's Proportion of it?</P>
<P>150&equals;243,33x43x100z1046319[00&equals;<HI>l.</HI> 28. 13. 3&frac34; A</P>
<P>40z418527[60&equals;<HI>l.</HI> 11. 9. 4 B</P>
<P>10z104631[90&equals;<HI>l.</HI> 2. 17. 4 C</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Lo&s;s.</HEAD>
<P>By the &s;ame Rule placing, and working the <HI>Lo&s;s</HI> as in the <HI>Gain.</HI></P>
<P>All Que&s;tions of Fellow&s;hip with time, may be re&s;olved by the &s;ame Rule.</P>
<P>Fir&s;t, Multiplying each Man's &s;hare by the N^o of Months it was in the Stock, and work as before.</P>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Exchange, Foreign into Sterling. <HI>Side B.</HI></HEAD>
<P><HI>Rule.</HI> Multiply the Number of Dollers, <HI>&amp;c.</HI> by the Number of Pence, in the Rate of each, and Tabulate.</P>
<DIV3 TYPE="example">
<PB N="37" REF="20">
<HEAD>Example.</HEAD>
<P>What is 1000 Doll. at 53 Pence <HI>per</HI> Doller?</P>
<P>1000x53z53000&equals;<HI>l.</HI> 220. 16. 8.</P>
<P>But by rea&s;on, that many times the following Fractions happen in the Rate, it will not be a|mi&s;s to give the Decimal proper to each; which after Multiplication are to be cut off, <HI>viz.</HI></P>
<P>For
<LIST>
<ITEM>&frac12;&equals;5.</ITEM>
<ITEM>&frac38;&equals;375</ITEM>
<ITEM>&frac14;&equals;25</ITEM>
<ITEM>&frac58;&equals;625</ITEM>
<ITEM>&frac34;&equals;75</ITEM>
<ITEM>&frac78;&equals;875</ITEM>
</LIST></P>
</DIV3>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What 2300 pieces 8/8 at 57 &frac58; <HI>per</HI> piece.</P>
<P>2300x57,625,z132537[500&equals;<HI>l.</HI> 552. 4. 9.</P>
<P>What 729 Doll. at 55 &frac78; <HI>per</HI> Doll.</P>
<P>729x55,875z40732[875&equals;<HI>l.</HI> 169. 14. 4&frac78;</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Engli&s;h into Foreign.</HEAD>
<P><HI>Rule.</HI> Reduce the Rate of one Pound Flemi&s;h into a Decimal; which multiply by (240) and that by the Number of Pounds Sterling to be remitted, cut off the Decimals and Tabulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>For how many Pounds Flemi&s;h, mu&s;t a Bill be drawn for, to remit to <HI>Rotterdam</HI> 100 <HI>l.</HI> Sterling at 34 <HI>s.</HI> 2 <HI>d.</HI> Flemi&s;h.</P>
<P>240x1,708x100z40992[000&equals;<HI>l.</HI> 170. 16. 0.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<PB N="39" REF="21">
<HEAD><HI>Tare.</HI> Side A.</HEAD>
<P><HI>Rule.</HI> Multiply the Tabular N^o to 112, which is (325,89) by the Rate of Tare, and that by the N^o of gro&s;s Pounds, cut off the Decimals and Tabulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What is the Tare of 1071 <HI>l.</HI> gro&s;s at 14 <HI>l.</HI> to every 112 <HI>l.</HI>?</P>
<P>325,89x14x1071z4886394[66&equals;133&frac34;</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD><HI>Tret.</HI> Side A.</HEAD>
<P><HI>Rule.</HI> Multiply 693,83 by any Number of &s;ubtle Pounds and Tabulate, cutting off the De|cimals.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>What is the Tret of 2420 <HI>l.</HI> gro&s;s?</P>
<P>693,83x2420z1679068[60&equals;46 <HI>l.</HI> Tret.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Equation of Payments. <HI>Side A.</HI></HEAD>
<P><HI>Rule.</HI> 1. Multiply each Sum by the time of its becoming due, and add the &s;everal Products for a Multiplier.</P>
<P N="2">2. Multiply the Tabular Number to the Sum of the whole Debt by the &s;aid Agregate, cut off the Decimals and Tabulate.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>One oweth me 5 <HI>l.</HI> to be paid 3 Months hence.</P>
<P><TABLE>
<ROW>
<CELL>3</CELL>
<CELL>6</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>9</CELL>
</ROW>
<ROW>
<CELL>36</CELL>
<CELL>12</CELL>
</ROW>
</TABLE></P>
<PB N="38" REF="21">
<P>At what time ought the whole to be paid at one Payment.</P>
<P><GAP DESC="math"></P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>The Monthly Wages allowed to Seamen in all Rates.</HEAD>
<P><TABLE>
<ROW>
<CELL ROLE="label" COLS="3"><HI>per Month.</HI></CELL>
<CELL ROLE="label" ROWS="2"><HI>Decim.</HI></CELL>
<CELL ROLE="label" COLS="3"><HI>per Month.</HI></CELL>
<CELL ROLE="label" ROWS="2"><HI>Decim.</HI></CELL>
</ROW>
<ROW>
<CELL ROLE="label">l.</CELL>
<CELL ROLE="label">s.</CELL>
<CELL ROLE="label">d.</CELL>
<CELL ROLE="label">l.</CELL>
<CELL ROLE="label">s.</CELL>
<CELL ROLE="label">d.</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>91,250</CELL>
<CELL>1</CELL>
<CELL>16</CELL>
<CELL>0</CELL>
<CELL>23,462</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>6</CELL>
<CELL>0</CELL>
<CELL>82,125</CELL>
<CELL>1</CELL>
<CELL>15</CELL>
<CELL>0</CELL>
<CELL>22,762</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>13</CELL>
<CELL>8</CELL>
<CELL>61,050</CELL>
<CELL>1</CELL>
<CELL>14</CELL>
<CELL>0</CELL>
<CELL>22,158</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>6</CELL>
<CELL>2</CELL>
<CELL>56,158</CELL>
<CELL>1</CELL>
<CELL>13</CELL>
<CELL>9</CELL>
<CELL>21,995</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>52,141</CELL>
<CELL>1</CELL>
<CELL>12</CELL>
<CELL>0</CELL>
<CELL>20,854</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>17</CELL>
<CELL>6</CELL>
<CELL>50,512</CELL>
<CELL>1</CELL>
<CELL>10</CELL>
<CELL>0</CELL>
<CELL>19,550</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>10</CELL>
<CELL>0</CELL>
<CELL>45,625</CELL>
<CELL>1</CELL>
<CELL>8</CELL>
<CELL>0</CELL>
<CELL>18,250</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>6</CELL>
<CELL>0</CELL>
<CELL>42,016</CELL>
<CELL>1</CELL>
<CELL>6</CELL>
<CELL>8</CELL>
<CELL>17,379</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>1</CELL>
<CELL>5</CELL>
<CELL>40,029</CELL>
<CELL>1</CELL>
<CELL>6</CELL>
<CELL>0</CELL>
<CELL>16,945</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>39,104</CELL>
<CELL>1</CELL>
<CELL>5</CELL>
<CELL>0</CELL>
<CELL>16,291</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>16</CELL>
<CELL>2</CELL>
<CELL>36,608</CELL>
<CELL>1</CELL>
<CELL>4</CELL>
<CELL>0</CELL>
<CELL>15,641</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>10</CELL>
<CELL>0</CELL>
<CELL>32,587</CELL>
<CELL>1</CELL>
<CELL>3</CELL>
<CELL>4</CELL>
<CELL>15,208</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>7</CELL>
<CELL>10</CELL>
<CELL>31,175</CELL>
<CELL>1</CELL>
<CELL>0</CELL>
<CELL>8</CELL>
<CELL>13,467</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>5</CELL>
<CELL>0</CELL>
<CELL>29,329</CELL>
<CELL>1</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>13,033</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>2</CELL>
<CELL>0</CELL>
<CELL>27,375</CELL>
<CELL>0</CELL>
<CELL>19</CELL>
<CELL>0</CELL>
<CELL>12,382</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>26,070</CELL>
<CELL>0</CELL>
<CELL>14</CELL>
<CELL>3</CELL>
<CELL>9,287</CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>17</CELL>
<CELL>6</CELL>
<CELL>24,441</CELL>
<CELL>0</CELL>
<CELL>9</CELL>
<CELL>6</CELL>
<CELL>6,291</CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>16</CELL>
<CELL>8</CELL>
<CELL>23,895</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
</DIV2>
<DIV2 TYPE="part">
<PB N="40" REF="22">
<HEAD><HI>Seamen's Wages.</HI> Side A.</HEAD>
<P><HI>Rule.</HI> Multiply the Tabular Number again&s;t any Rate <HI>per Men&s;em,</HI> by the Number of Days; cut off one Figure to the Right-hand and Tabu|late.</P>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>At <HI>l.</HI> 1. 17. 6 <HI>per</HI> Month, what 202 Days?</P>
<P>1.17.6&equals;24,441x202z493708[2&equals;<HI>l.</HI> 13. 10. 6&frac14;.</P>
<P>At <HI>l.</HI> 1.3.4. <HI>per</HI> Month, what 341 Days?</P>
<P>1.3.4&equals;15,208x341z518592[8&equals;<HI>l.</HI> 14. 4. 2.</P>
<P>If the Tabular Number to any Sum <HI>per Men|&s;em,</HI> be Tabulated on the Scale, fir&s;t cutting off one Figure to the Right-hand, gives what <HI>per Diem.</HI></P>
</DIV3>
<DIV3 TYPE="example">
<HEAD>Example.</HEAD>
<P>At <HI>l.</HI> 3.17.6. <HI>per</HI> Month, what one Day?</P>
<P>3.17.6&equals;5051[2&equals;<HI>l.</HI> 0. 2. 9.</P>
</DIV3>
</DIV2>
<DIV2 TYPE="part">
<HEAD>Simple Intere&s;t for Quarters.</HEAD>
<LIST>
<ITEM>For a Quarter of a Year &times; by 91,25</ITEM>
<ITEM>For Six Months &times; by 182,5</ITEM>
<ITEM>For Nine Months &times; by 273,75</ITEM>
</LIST>
</DIV2>
<TRAILER>FINIS.</TRAILER>
<PB REF="22">
<PB REF="23">
<PB REF="23" MS="y">
<PB REF="24">
<PB REF="24" MS="y">
</DIV1>
</BODY>
</TEXT>
</GROUP>
</EEBO>
</ETS>
