MASTER 
 NEGATIVE 
 
 NO. 94-82231 
 
 1 
 
COPYRIGHT STATEMENT 
 
 The copyright law of the United States (Title 17, United States Code) 
 governs the making of photocopies or other reproductions of copyrighted 
 materials including foreign works under certain conditions. In addition, 
 the United States extends protection to foreign works by means of 
 various international conventions, bilateral agreements, and 
 proclamations. 
 
 Under certain conditions specified in the law, libraries and archives are 
 authorized to furnish a photocopy or other reproduction. One of these 
 specified conditions is that the photocopy or reproduction is not to be 
 "used for any purpose other than private study, scholarship, or research." 
 If a user makes a request for, or later uses, a photocopy or reproduction 
 for purposes in excess of "fair use," that user may be liable for copyright 
 infringement. 
 
 The Columbia University Libraries reserve the right to refuse to accept a 
 copying order if, in its judgement, fulfillment of the order would involve 
 violation of the copyright law. 
 
Author: 
 
 Ware 
 
 J 
 
 William Powell 
 
 Title: 
 
 Prof. Ware's $10,000 
 
 prize rule for the... 
 
 Place: 
 
 Philadelphia 
 
 Date: 
 
 1873 
 
x.t 'Kkcm [IV *'4ii 
 
 qu-93a^\ - \ 
 
 MASTER NEGATIVE * 
 
 COLUMBIA UNIVERSITY LIBRARIES 
 PRESERVATION DIVISION 
 
 BIBLIOGRAPHIC MICROFORM TARGET 
 
 ORIGINAL MATERIAL AS FILMED • EXISTING BIBLIOGRAPHIC RECORD 
 
 •MINIM 
 
 480 
 
 mz 
 
 ¥*are, William Powell 
 
 Prof. Vfare's XlO»000 prize rule for the equa- 
 tion of payments ... To which is appended Ran- 
 kin's perpetual manual. Philadelphia, Claxton, 
 Remsen & Haffelfinger, 1873. 
 
 47, c8| p. lejom. 
 
 RESTRICTIONS ON USE: 
 
 TECHNICAL MICROFORM DATA 
 
 FILM SIZE: ?:hiT(\TC\ 
 
 DATE FILMED: 
 
 TRACKING # : 
 
 REDUCTION RATIO 
 
 : q^ 
 
 IMAGE PLACEMENT: lA 
 
 IB IIB 
 
 \o-S-^M 
 
 INITIALS 
 
 = % 
 
 ffiJM Olt>M. 
 
 FILMED BY PRESERVATION RESOURCES. BETHLEHEM. PA. 
 
 I 
 
'V? 
 
 A^ 
 
 
 
 •v? 
 
 v^^ 
 
 X*^ 
 
 
 > 
 3D 
 
 O 
 
 m 
 
 CO 
 
 c^ 
 
 >p- 
 
 
 ^ 
 
 > 
 
 > 
 
 a^ 
 
 > 
 
 A^' 
 
 
 ^. 
 
 
 'V? 
 
 ^..-^, 
 
 y* 
 
 '^, 
 
 >.. ^ 
 
 
 ^p- 
 
 
 1.0 mm 
 
 1.5 mm 
 
 2.0 mm 
 
 Ul 
 
 o 
 
 3 
 3 
 
 g 
 
 3 
 3 
 
 
 ^ 
 
 O 
 
 ff^i^i^PKisisiJ 
 
 is| 
 
 CO 
 
 CO 
 
 K3 
 00 
 
 O^ 
 
 00 
 
 o 
 
 
 ro 
 
 In 
 
 ABCDEFGHIJKLMNOPQRSTUVWXYZ 
 abcdefghijklmnopqrstuwvxyzl234567890 
 
 ABCDEFGHIJKLMNOPQRSTUVWXYZ 
 abcclefghijklmnopqrstuwvxyzl234567890 
 
 ABCDEFGHIJKLMNOPQRSTUVWXYZ 
 
 abcdefghijklmnopqrstuvwxyz 
 
 1234567890 
 
 2,5 mm 
 
 ABCDEFGHIJKLMNOPQRSTUVWXYZ 
 
 abcdefghijklmnopqrstuvwxyz 
 
 1234567890 
 
 rV 
 
 
 ^S 
 
 * 
 
 V 
 
 ^' 
 
 
 f^ 
 
 ^<s> 
 
 ^O 
 
 fp 
 
 ^ 
 
 
 « 
 
 ^* 
 
 ■i 
 
 « 
 
 ■« 
 
 ^<^ 
 
 ■* 
 
 ^o 
 
 ^ 
 
 m 
 
 3 
 O 
 
 ■o m "o 
 
 O 
 
 O 
 O 
 
 3D 
 
 > 
 
 O 
 
 C CO 
 30 5 
 
 CO - 
 
 m 
 
 > 
 
 3D 
 

 .t:^^^yv: 
 

 W22 
 
 THE LIBRARIES 
 
 School of Business 
 
 Given by 
 
 Ilnion Theological Sem 
 
 t 
 
 i\' 
 
 '' 
 
 ! 1 
 
 
 
 II 
 
iv 
 
 ( J 
 
 PROF. WARE'S 
 
 $10^000 
 
 If>RIZE RULE 
 
 FOK THE 
 
 Umim 0f llaatn^ttb. 
 
 Two-thirds of the time and labor saved — requiring only 
 one division in debit and credit aecoiints. 
 
 TO WHICH IS APPENDED 
 
 RANKIN'S PERPETUAL ALMANAC. 
 
 »; '> -V 
 
 -00^ '00- . . 
 
 a 00a ''-i ^ 
 
 » »t «!J • 
 
 o 
 
 <L> *> 
 
 ^PBlIii^DELeHCA: 
 CLAXTON, REMSEN & II.> FFELriNGER, 
 624, 626&ti28 IkJAtlkEC STH^.iPrr ' ' 
 1873. 
 
 '( 
 
nl 
 
 
 /I 
 
 Entered, according to Act of Congress, in the year 1872, by 
 
 Prop. W. Powell Ware, in the Office of the Librarian 
 
 of Congress, at Washington, D. C. 
 
 \AlZZ 
 
 1 
 
 « s * • 
 
 • • • 
 
 « * . 
 
 • • 
 
 c < 
 
 • « • 
 
 c . 
 
 «• 
 
 - c 
 
 i CO c 
 
 e b 
 
 ■ e c c li 
 
 « « CO 
 
 • • • s 
 
 e 
 t 
 
 L. 
 
 1 
 
 INDEX. 
 
 PAGE 
 
 Q. 
 CO 
 
 Author's Preface, ^ 
 
 General Rules of Equation, 7 
 
 Dr. and Cr. Accounts, ^ 
 
 Bills on Unequal Time 1^ 
 
 Bills on Equal Time, ^^ 
 
 Monthly Statements, ^^ 
 
 Balance Falling Due prior to First Transaction,.. ..19 
 Computation of Interest for 360 Days per Annum,. 20 
 
 ** ** 365 '• " 21 
 
 Interest by Cancellation, 22 
 
 To Calculate Interest for Days, 24 
 
 Computing Percentage, 25 
 
 Multiplication 27 
 
 Diamond or Cliain Rule, 29 
 
 Multiplication of Fractions, 31 
 
 Division of Fractions, • 32 
 
 Guide in Addition, 33 
 
 Conversion of Sterling Money, 34 
 
 Barter ^^ 
 
 Discount, 36 
 
 Wood Measure, &c 37 
 
 Names of Coins, 39 
 
 Yalue of Foreign Money, 40 
 
 Prof. Ware's Challenge, 45 
 
 Decision of the Judges, 46 
 
 Magic Square, ... . » 47 
 
PREFACE. 
 
 The author of tliis inestimable little book 
 has spent several years as a teacher in schools 
 in different States. He has found it a very 
 difficult task (in all cases) to make pupils 
 thoroughly understand and fully comprehend 
 the rules in mathematics as they are generally 
 laid down in the arithmetics of the past and 
 present, and if understood at all by them, 
 would be forgotten almost before leaving 
 school, or at least a very short time after. He 
 also spent several years as book-keeper, in 
 which vocation he experienced the great need 
 of short, simple, and comprehensive rules by 
 which time and labor could be saved in all 
 cases, and especially in that most important 
 in the whole routine of commercial transac- 
 tions—viz. : '' Equation of Payments.'' The 
 idea occurred to him that improvements might 
 be made in mathematics as well as in me- 
 chanics. He resolved to try, and after long 
 and ardent study, succeeded in devising and 
 bringing to light a plan so simple that the 
 ordinary mind can fully comprehend and 
 understand. After perfecting his system or 
 rule, he sought to impart the same to book- 
 keepers and business men. He succeeded^ in 
 giving over 2,000 private lessons, each of 15 to 
 25 minutes, and in all cases gave perfect sat- 
 
mmtrnm 
 
 6 
 
 PROP, ware's system op 
 
 isfaction, after which he offered a premium of 
 $10,000 for a better system than his own; 
 failing to get any better, he then put his system 
 in book form, which is now being rapidly sold 
 at $3 per copy in commercial circles. He has 
 from nearly twenty-five years experience 
 among business men and book-keepers, ob- 
 served the difficulty they have in recollecting 
 the ordinary rules, and if remembered, a vast 
 amount of time and labor has been lost by 
 using them ; he has also seen the many efforts 
 made to devise shorter and simpler methods, 
 and the disposition to ignore the rules as taught 
 in the arithmetics of the day. Believing the 
 time and money spent in the schools of the 
 present day in that particular branch to be a 
 useless expenditure, and knowing from expe- 
 rience that simple things learned in school 
 can be easily remembered in after life, he has, 
 at the suggestion of friends, consented to put 
 his system in a cheap form, that can be intro- 
 duced into all the public and other schools 
 throughout the whoie country, that the rising 
 generation may save a great amount of hard 
 study, waste of time, labor, and money, and 
 learn something that will prepare them for the 
 vicissitudes of business, and can be remem- 
 bered all their after life at a mere nominal 
 expense. If such be the case, then his mission 
 will have been fulfilled in which he has long 
 sought to be a benefactor to the whole com- 
 munity. 
 
 W. POWELL WAEE. 
 
 GENERAL RULES 
 
 or 
 
 EQUATION 
 
 Start at the first of the month in which the 
 first transaction takes place, instead of the 
 date of the first bill. Call the first month 0, 
 then number the following months in their 
 regular order, setting the number in the mar- 
 gin, or elsewhere. 
 
 Each bill then shows at sight the time for 
 which the interest must be obtained. 
 
 Note. — Compute interest at 1 per cent, per 
 month. Any amount of dollars shows its own 
 interest (in cents) for one month. Point off 
 the right hand figure, and the interest is shown 
 (in cents) for one-tenth of a month (or 3 
 days). 
 
sma^ 
 
 8 
 
 r.> 
 
 PliOF. WARE S SYSTEM OP 
 
 EULE. 
 
 Multiply tlie tuJiole amount of dollars by the 
 number of months required. Multiply one- 
 ienth of the dollars by one-tMrd the number 
 of days required,* setting the products under 
 each other until all the interest is obtained ; 
 add up the interest, annex two ciphers to the 
 right, and divide by the footing of the bills 
 (in dollars only) ; the answer will be in months 
 and hundredths of months. Multiply the 
 hundredths by 30 to bring it into days. 
 
 N. B. — Add the month in the margin to 
 those in the face of the bills in all cases of 
 unequal time. 
 
 *NoTE. — One-third of any number of days 
 shows how many tenths are contained therein. 
 
 EXAMPLE. 
 
 24 days contain 8 tenths, 25 days 8|^ tenths, 
 20 days 8f tenths, 27 days 9 tenths, &c. 
 
 k 
 
 EQUATION OF PAYMENTS. 
 
 9 
 
 DEBIT AND OEEDIT ACCOUNTS 
 
 0? ALL CLASSES. 
 {To find tnlwri f.ie balance is due) 
 
 KULE. 
 
 Arrange the time, commencing at the first 
 of the month on which the first transaction 
 took place, whether debit or credit. Then 
 compute the interest on both sides of the ac- 
 count for the time called for in each bill; 
 subtract the smaller amount of interest from 
 the larger, annex two ciphers to the right of 
 the difference in interest (read so many cents), 
 and divide by the balance of the account. As 
 many months and days as are obtained in the 
 quotient, or answer, so long will the balance 
 fbe falling due, from the cipher or starting 
 ' point. 
 
10 
 
 PROF, ware's system OF 
 
 1871 
 
 1872 
 
 EXAMPLE. 
 Dr. 
 
 0, July 27, Mds. 4 mos 1350 I ?!?? 
 
 4, Nov. 12, " 6 " 2531 p-JJ {^ 
 
 6, Jan. 18, '• 5 " 1940 [^JJJJ 
 
 9 Apr. 21, Cash 117o[l^|-|J 
 
 16991 $667.90 
 
 1^1 
 
 w 
 III 
 
 Cr. 
 
 1871 
 
 1872 
 
 l.Aug. 9, Cash 750 I- I [^ 
 
 3, Oct. 5 *Dft. 90 days 961 !^ ^J ^^H 
 
 9, Apr. 6, Cash 850 ^- "^' ^^ 
 
 ^^"i 1.70 
 
 \ 2.50 
 
 13, Aug. 15, Note 60 days 500 [ '^? ^^ 
 
 $3061 $221.71 
 
 I 
 
 Br. Int 66.790 
 
 Cr. Int 22.471 
 
 13930 
 
 Balance .... 3930)443 1 9 . 00(1 1 . 27 
 
 30 
 
 8.10 
 11m. 8^ from July Ut. 
 
 Balance due June 8, 1872. 
 
 % K 
 
 5 days If tenths, or ^ of 961, 
 
 j 
 
 1' 
 
 ^ 
 
 EQUATION OF PAYMENTS. 
 
 11 
 
 Commence July 0. From July 1st to No- 
 vember 1st, is 4 months ; to January, 6 months ; 
 to April, 9 months. From July to August, 1 
 month; to October, 3 months; to April, 9 
 months ; to August next year, 13 months. 
 
 Eead the bills :— 1st, you want the interest 
 for 4 months and 27 days ; 2d, 10 months and 
 12 days; 3d, 11 months and 18 days; 4th, 9 
 and 21 days; 5th, 1 month and 9 days; 6th, 
 6 months and 5 days ; 7th, 9 months and 6 
 days ; 8th, 15 months and 15 days. 
 
 Now obtain the interest : — 
 
 1 month, at 1 per cent, per month, is $13.50 ; 
 4 months is four times as much, $54.00 ; one- 
 tenth of a month is one-tenth of $13.50, which 
 is $1.35; 27 days being nine-tenths, is nine 
 times $1.35, which is $12.15; 10 months is 
 ten times $25.31, which is $253.10; 12 days is 
 four times $2.53=$ 10.12; and so on through 
 the whole account. 
 
 Add up the interest of the Dr., then the Cr.; 
 subtract the smaller from the larger amount, 
 bringing down the difference, omitting the 
 point between the dollars and cents ; place a 
 point to the right of whole amount, then add 
 two ciphers to the right of the point, and di- 
 
.' 
 
 I 
 
 vide the difference of interest by the balance 
 ot the account. As often as the divisor is 
 contained in the dividend, up to the point, so 
 many months you get ; add one cipher and 
 divide, that will give you tenths of months : 
 add the other cipher and divide, that will 
 give you hundredths of months. Your an- 
 swer will read 11 months and 27 hundredths 
 of a month. Multiply the hundredths bv 30 
 which will bring the time into days, 37x30 
 —8 days and ten one-huudredths, which is 
 never counted unless fifty one-hundredths or 
 upward. Thus the answer is 11 months and 
 8 days from July 1 (inclusive), 1871, balance 
 due June 8, 1873. 
 
 N. B.— Now comes in the regular rate per 
 cent. Any number of days that the balance 
 IS paid hefore the 8th of June, the interest is 
 taken off at the legal rate. Any number of 
 days after the 8th of June the interest is added 
 at the legal rate. 
 
 1873. 
 
 1872. 
 
 EQUATION OV PAYMENTS. 
 
 18 
 
 EXAMPLE. 
 Dr. 
 
 10.92 
 
 0,Jau. 9,Mds.6mos 181.7.j*| "^g^ 
 
 0. " 21, 
 3, Mar. 1, 
 
 2, " 24, 
 
 3, Apr. 22, 
 
 i.i <( ( 
 
 ~*^"-"^ / 1.75 
 " " ** 380.50 ] ^^-^3 
 
 150.10 ^ ^^^ 
 
 L 27.00 
 
 800.00 \ 2.10 
 .10 
 
 U (( u 
 
 « << ii 
 
 Cr. 
 
 $1262 60 $101.22 
 
 1, Feb. 6, Cash ^^^ | "^ . 
 
 2, Mar. 16, 30 clays 200 1 ^; 
 
 2, 
 
 << 
 
 27,60 
 
 (< 
 
 50 
 
 30 
 
 6.00 
 
 07 
 
 "^"^ I 1.80 
 
 $550 $18.67 
 
 Dk. Int 10122 
 
 Cr. Int 18.67 
 
 Bal. $712 60 
 
 713)8255:00(11.57 
 
 30 
 
 17.10 
 11m. lid from Jan, 1st. 
 
 Balance due Dec. 17, 1872. 
 
 * Bills containing Dollars and Cents, the cents are omirted 
 if under fifty; and counted as one dollar if fifty or upward. 
 
 rT"^^"^'^™^^^" 
 
BILLS BOUGHT ON UNEQUAL TIME, 
 
 {without credit.) 
 
 EULE. 
 
 Compute the interest on each bill for the 
 time called for in the several bills ; add up the 
 interest ; annex two ciphers to the right of the 
 whole amount, and divide by the footing of 
 the bills, (the dollars only). The number of 
 months and days obtained in the quotient, 
 will show how long the amount will be in 
 falling due from the 0, or starting point. 
 
 EXAMPLE. 
 
 Dr. 
 
 1871. 0, May 6, Mds. 3 mos $931 j 27.93 
 
 \ 1.86 
 0, " 13, 
 
 2, July 9, 
 4, Sept. 1, 
 
 1872. 8, Jan. 27, 
 
 (( 
 
 (( 
 
 i( 
 
 4 
 5 
 
 a o/>/v I 17.20 
 
 ^^^\ 3.44 
 
 ( .29 
 
 " 432J25.92 
 
 / 1.29 
 
 ** 384 j 34.56 
 
 2928)14118.00(4.82 
 11712 30 
 
 i .13 
 Cash 321 (25.68 
 
 ( 2.88 
 $2928 141.18 
 
 24060 24.60 
 23424 
 
 6360 4 mos. 25 d.from May 1. 
 Due Sept. 25, 1871. 
 
 
 EQUATION OF PAYMENTS. 
 
 15 
 
 Commence May 0— July, 2 months; Sep- 
 tember, 4 months ; January, 8 months. 
 
 Eead the bills— 1st bill, 3 months, 6 days; 
 2d bill, 2 months, 13 days ; 3d bill, 2 and 4 are 
 6 months, 9 days; 4th bill, 4 and 5 are 9 
 months, 1 day; 5th bill, 8 months, 27 days. 
 
 Compute the interest — 3 months is 3 times 
 $9.31=$27.93; 6 days is twice 93c.=$1.86 ; 2 
 months is twice $8.60=117.20; 13 days is 4^ 
 times 86c., &c., &c. 
 
 N. B. — Multiply the whole amount of dollars 
 by the number of months; one-tenth the 
 dollars by one-third the days. 
 
 \\ 
 
BILLS BOUGHT ON EQUAL TIME. 
 
 EULE. 
 
 Compute the interest for tlie time that each 
 bill calls for, up to the date of purchase. Add 
 up the interest, annex two ciphers, and divide 
 by the footing of the bills (the dollars only). 
 
 The months and days obtained in the quo- 
 tient will show the average date of purchase, 
 from the 0. 
 
 Add the time of credit (whatever it may be) 
 to the average date, and that will show the 
 date of maturity. 
 
 N.B. — The answer always comes in months 
 and hundredths of months. Multiply the 
 hundredths by 30, which will give the number 
 of days. 
 
 " 
 
 B^adhiriftaMb*dfiM*H 
 
 =n 
 
 EQUATION OF PAYMENTS. 
 
 17 
 
 EXAMPLE. 
 
 Dr. 
 1871. Feb. 0, Omos $430 j 1-^^ 
 
 2 Apr. 13, " " 384J ^-^ 
 
 5 July G, ^' '' ^'^^j^^'46 
 
 5 July 21, - - ^^M^2:66 
 
 7 Sept. 2, ** '' 431 i 30.17 
 
 $1856 74.74 
 
 1856)7474.00(4.02 
 
 30 
 
 .60 4m. Id, from Feb, Ist. 
 Average date, June 1st — due 6 mos. 
 
 Head— 1st bill, 9 days; 2d bill, 2 months, 
 13 days ; 3d bill, 5 months, 6 days ; 4th bill, 5 
 months, 21 days; 5th bill, 7 months, 2 days. 
 
 4 
 
 Compute the interest — 9 days is 3 times 
 43c.; 2 months is twice $3.84 ; 13 days is 4^ 
 times 38c.; 5 months is 5 times $2.30 ; 6 days 
 is twice 23 ; 5 months is 5 times $3.81 ; 21 
 days is 7 times 38c.; 7 months is 7 times $4.31 ; 
 2 days is f of 43. 
 
_22^ 
 
 18 PROF, ware's system of 
 
 MONTHLY STATEMENTS. 
 
 KULE. ' 
 
 Compute the interest on each bill for the 
 number of days tliat each bill calls for. 
 
 Acid up the interest, annex two ciphers, and 
 divide by the footing of the bills. 
 
 N. B. — In a monthly statement the answer 
 will always be in hundredths of months. 
 
 EXAMPLE. 
 
 1871. Jan. 9, I87j .54 
 
 " 10, ^^^y'it 
 
 " 11, 231^ -^^ 
 
 / .15 
 
 " 13,... 438ll.75 
 
 " 18, .. 217J1.30 
 
 " 32, ^llj^S 
 
 " 34, 221^ 1176 
 
 '' 37, 407^ 3.66 
 
 " 30, 386^3.86 
 
 *' 31, 999J^J^ 
 
 4078 28.57 
 4078)2857. 00(. 70 
 
 30 
 
 21.00 21 daps. 
 Due January 21. 
 
 Compute the interest for 9 days, 10 days, 
 11 days, &c. 9 days is 3 times 18c. ; 10 days 
 is 3^ times 68c. ; 1 1 days is 3f times 23c. ; 12 
 days is 4 times 43c., &c. 
 
 EQUATION OF TAYMENTS. 19 
 
 Balance Falling Due Prior to the Pirst Transaction. 
 
 EXAMPLE. 
 
 N. B.— Work as before. 
 
 Dr. 
 
 { 3 75 
 1870. 0, July 4, Mds $3750 ] ^;25 
 
 '' 21 " 2000^ 14.00 
 
 O', *' 27^ " 1850^ 11). 65 
 
 2!sept3; - 1220J^J:g 
 
 3,Oct.i6, " 90o|^J;J5 
 
 .30 
 
 $9720 93.07 
 Cr. 
 
 1870. 4, Nov. 24, Cash, |500 j ^J; JJ 
 
 5, Dec. 1, Dft. 30 days, 850 j ^^'^ 
 
 IS71. 8,Mar. 6, Cash, ^^j 1.20 
 
 ( 104- 00 
 10, May 1, Note 90 days, 800 1 ^"*;27 
 
 $2750 238.75 
 
 Bal $6970 
 
 238 . 75 — greater interest. 
 93 . 07 — smaller interest. 
 
 1970)13568.00(1.94 
 6970 30 
 
 65980 28.20—1 m. 28d, back of July 1. 
 62730 
 
 32500 Balance due May 2d, 1870. 
 
 -4 
 
If Ihe interest of the smaller side of the ac- 
 count exceeds that of the larger side, the time 
 counts loch from the starting point. In the 
 above example, the smaller exceeds the greater 
 by $130.68, throwing the balance, 1 month 
 and 28 days, back of July 1st. 
 
 -N". B.— The interest must be paid from May 
 2d up to the day of settlement, at the legal 
 
 COMPUTATION OF INTEREST. 
 
 (For 360 days per annum,) 
 
 EULE. 
 
 First obtain the interest at 12 per cent, per 
 annum for the required time ; then divide the 
 product by 13, which will give the interest at 
 1 per cent, per annum. Multiply this quo- 
 tient by the rate per cent, required. The re- 
 sult will be the answer in cents. 
 
 EXAMPLE. 
 
 What is the interest on $1850 for 7 months 
 and 27 days, at 9 per cent, per annum. 
 
 EQUATION OP PAYMENTS. 
 
 21 
 
 SOLUT10l!f. 
 
 $1850 7 mos., 37 days, at 9 per cent. 
 
 12950 
 1665 
 
 12)146.15 
 
 12.18 
 9 
 
 $109.62— ^7W. 
 
 One month is $18.50 ; 7 months is 7 times 
 as much; one-tenth is $1.85; 27 days (being 
 nine-tenths) is nine times as much. 
 
 Add up and divide the product by 12, which 
 is $12.18, at 1 per cent, per annum; 9 per 
 cent, is 9 times $12.18; 8 per cent, would be 
 8 times $12.18 ; 5 per cent., 5 times, &c., &c. 
 
 COMPUTATION OF INTEREST. 
 
 (For 365 days per annum.) 
 
 RULE. 
 
 Multiply the principal by the number of 
 days ; then add one one-tenth of the product 
 to itself; then add one-half of the one-tenth; 
 add up the whole amount. If 7 per cent, is 
 required, divide the product by 6. If 6 per 
 cent, is required, divide by 7. 
 
 J^^ Point one for mills. 
 
22 
 
 PROF, ware's system OF 
 
 EXAMPLE. 
 
 What is the interest on $875 for 120 days, 
 at 7 per cent, per annum (of 365 days) ? 
 
 SOLUTIOI^. 
 
 $875 120 days at 7 per cent. 
 
 105000 
 
 10500—1 tenth. 
 5250— i of 1 tenth. 
 
 6)120750 
 
 $20. 12.5—^72^. 
 
 ' 
 
 FOR COMPUTING INTEREST 
 
 BY CANCELLATION. 
 
 EXAMPLE. 
 
 What is the interest on $180 for 3 years, 7 
 months, and 18 days, at 8 per cent, per annum. 
 
 i 
 
 4 
 
 SOLtJTIOX. 
 
 i$0 Principal, 60 
 316 time. 
 
 120 
 $ per cent. 2 
 
 Ans.—%37.92.0 
 
 '• 
 
 EQUATION OF PAYMENTS. 
 
 23 
 
 1st. — Draw a perpendicular line, place the 
 principal on the right, bring the years and 
 months, to months, take i of the days and 
 place to the right of the months, setting the 
 time under the principal, and the rate per 
 cent, (whatever it may be) under the time ; on 
 the left (in all cases) place 3 and 4.* 
 
 2d. — Divide with the numbers on the left, 
 through any number on the right which they 
 will divide without a remainder, cancelling 
 each number as you use them ; then multiply 
 all the uncanceled numbers together on the 
 right, and divide (if any) by those on the left. 
 The answer will come i:i mills, if days be in 
 the time; if no days, in cents. 
 
 3d. — If there be one over in taking the jV of 
 the days, place a 3 to the right of a decimal 
 point; thus 2 years, 7 months, 19 days, equal 
 31G.3 ; if two, place a G ; thus 1 year, 5 months, 
 20 days, equal 176.G— working as a whole 
 number until done. Cut off in your answer 
 o:ie figure for each figure to the right of a 
 decimal point or points. 
 
 4th.— For days only, place the principal, whole number of 
 days, and the rate per cent, on the right, placing 3, 3 and 4 on 
 the tleft, working by rule 2d; the answer will be in mills. 
 
 ♦ The 3 and 4 stand for the 12 months In the year. 
 t The 3, 3 and 4 stand for 360 days in the year. 
 
 ^ 
 
24 
 
 PROF, ware's system OP 
 
 EXAMPLE FOE DAYS. 
 
 What is the interest on $720 for 36 days at 
 9 per cent, per annum. 
 
 3 
 
 720 
 3$ 
 
 9 
 
 Ans.—%^A^S) 
 
 If the numbers will not divide, multiply all 
 the right hand side together, and divide by the 
 left multiplied together, the quotient will be 
 the answer. 
 
 If fractional rates per cent, occur, bring it 
 to an improper fraction, placing the numerator 
 on the right, the denominator on the left, 
 working as before. 
 
 SHOET METHOD TO OALOULATE INTEEEST. 
 
 EULE. 
 
 Multiply the principal by half the number 
 of days ; that product divided by 30 will give 
 the answer in cents. 
 
 
 EQUATION OF PAYMENTS. 
 
 25 
 
 EXAMPLE. 
 
 What is the interest on $165 for 16 days at 
 6 per cent. ? 
 
 165 dollars. 
 
 8 half the number of days. 
 3.0)132.0 
 
 . 44 cents. 
 Divisors for Different Bates Per Gent. 
 
 Any amount multiplied by the time in days, 
 
 as per example : $200 for 19 days, and divide 
 
 by 72, will give you the interest at 5 per cent. 
 
 per annum. 
 
 Ans. $.52.7. 
 
 At 6 per cent, as above, divide by 60 
 
 '' 7 per cent, 
 
 ♦ • 
 
 
 u 
 
 
 52 
 
 *• 8 per cent, 
 
 
 
 u 
 
 
 45 
 
 *• 9 per cent, 
 
 
 
 i< 
 
 
 40 
 
 *' 10 per cent. 
 
 
 
 i( 
 
 
 ae 
 
 ** 12 per cent, 
 
 
 
 4( 
 
 
 ao 
 
 " 15 per cent, 
 
 
 
 « 
 
 
 24 
 
 " 20 per cent. 
 
 
 
 (( 
 
 
 18 
 
 *' 24 per cent. 
 
 
 
 ii 
 
 
 15 
 
 *' 40 per cent, 
 
 
 
 t( 
 
 
 09 
 
 COMPUTING- PERCENTAGE. 
 
 To ascertain what is gained or lost by selling 
 ail ARTICLE for which a specified sum has been 
 paid. 
 
EuLE. — Annex two ciphers to the selling 
 PRICE, divide by the cost. The difference 
 between the quotient and 100 will be the 
 gain or loss per cent. 
 
 Example. — Paid 5 dollars for a book, and 
 sold it for 8 dollars. AVhat per cent, did I gain ? 
 
 Operation — 5)800 
 
 1 . GO Ans. — 60 per cent. 
 
 Example.— Paid, 10 dollars for a hat, and 
 sold it for 8 dollars. What per cent, did I lose ? 
 
 Operation— 10)800 
 
 80 
 Ans. — 100 less 80=20 per cent. 
 
 To ascertain what an article should be sold 
 for, which cost a specified sum, so as to gain 
 a proposed per cent. 
 
 EuLE.— Multiply the cost by 100, with the 
 per cent, added ; cut off two figures to the 
 right. The figures at the left will show the 
 PEICE for which the article must be sold. 
 
 Example. — Paid 30 cents per yard for 
 CLOTH ; for how much must I sell it so as to 
 realize 20 per cent, profit ? 
 
 Operation — dO^cost. 
 
 120 — 100 per cent added. 
 
 36.00 I must sell it for 36 cents. 
 
 , 
 
 ' 
 
 EQUATION OF PAYMENTS. 
 
 27 
 
 MULTIPLICATION. 
 
 EXAMPLES. 
 
 In multiplying, it is easier to multiply by 
 2, 3, 4, and 5, than by 7, 8, or 9, &c. 
 
 I shall now present examples in Multipli- 
 cation. 
 
 1. Multiply 428 by 15. 
 
 428X15 ^ place the 15 at the 
 
 2140 right of 428, and use the sign 
 
 of Multiplication ; but this 
 
 6420 is iiot necessary, from the 
 
 fact that it may be placed anywhere or not 
 written at all ; this of course is left to the 
 choice of the operator. 
 
 I first multiply by 5, placing the first 
 product figure one place to the right; 5 times 
 8 is 40 ; then 5 times 2 equal 10, and the 4 
 that I carried=14, write the 4 under the 8 ; 
 thus proceed ; then add the two products for 
 the answer. 
 
38 
 
 PROF, ware's system OP 
 
 2. Multiply 8844 by 14. 
 
 8844X14 
 35376 
 
 123816 
 
 3. Multiply 64827 by 36. 
 
 64827X36 ^^ 
 § Commence with 3, then 
 
 194481 multiply that product by 2, 
 
 388962 placing the first product figure 
 
 ^^~rr" in the place of units. 
 
 4. Multiply 87234 by 39. 
 
 87234X39 
 
 261702 
 785106 
 
 3402126 
 
 I 
 
 )■ 
 
 
 EQUATION OF PAYMENTS. 
 
 29 
 
 THE DIAMOND OE CHAIN EULE. 
 
 1st. Draw a perpendicular line. 
 
 2rf. Arrange the numbers on opposite sides 
 of the line, a^irected. 
 
 M. Then cancel on opposite sides of this 
 line all equal figures and numbers. 
 
 Uh, If there are ciphers on both sides of the 
 line, cancel the same number on each side. 
 
 bth. If any number on one side will divide 
 any number on the opposite side, cancel both 
 numbers, placing the quotient on the side of 
 the larger number. 
 
 Qtli, If any two or more numbers multiplied 
 together equal one or more numbers on the 
 opposite side, cancel all those numbers. 
 
 "Hth. If any number greater than unity will 
 divide two numbers, one on each side, without 
 a remainder, cancel both numbers, placing the 
 quotients on the right and left of the numbers 
 divided. 
 
Sth. Then multiply the figures that remain 
 on the right hand for a dividend, and those 
 on the left for a divisor. 
 
 Wi. Then divide the product of those on 
 the right by the product of those on the left ; 
 the quotient arising from this division will be 
 the answer. 
 
 EEMARKS. 
 
 Should the divisor exceed the dividend, the 
 answer will be a fraction. 
 
 If the numbers will not cancel, then multi- 
 ply those together that are on the right for a 
 dividend, and those on the left for a divisor. 
 Then divide, and the quotient arising from 
 this division, gives the answer. 
 
 This rule may be considered as a pair of 
 scales when exactly counterpoised; for we 
 may add or subtract, multiply or divide — in 
 fact, may do any thing to one side, so long as 
 we do the same to the other side ; for our ob- 
 ject will be, not to destroy the balance or 
 equilibrium. 
 
 In this rule, also, the same principle acts as 
 in the scales; for we take those things, the 
 value of which we know, to ascertain the 
 value of those which we do not know. 
 
 :l 
 
 \ 
 
 N. 
 
 EQUATION OF PAYMENTS. 
 
 31 
 
 MULTIPLTOATION 01 lEAOTIONS. 
 
 Place the numerators, both of the multi- 
 pliers and multiplicand, on the right, and the 
 denominators of both on the left of the line, 
 then proceed to cancel all figures of equal 
 value on the right and left ; those uncanceled 
 show the answer. 
 
 Examples.— 1. Multiply ^^ by| of | off of 
 I of f of I of I and show the answer. 
 
 t 
 
 9 
 
 $ 
 
 1 
 
 t 
 
 -Ans. \ 
 
 2. Multiply 
 
 3. Multiply 
 
 4. Multiply 
 
 5. Multiply 
 
 6. Multiply 
 
 7. Multiply 
 
 8. Multiply 
 
 9. Multiply 
 
 10. Multiply 
 
 11. Multiply 
 
 12. Multiply 
 
 ibyfoffoffofT^V 
 
 ioff of|-byxVofi|• 
 l of i of i by U of H- 
 
 I of I by f 
 
 I of ^s by tV of tV 
 
 lofxVofAbyiiof^off 
 -^ of f of I of I by i of T^. 
 i of I of I of -I by f of |. 
 
 iofiofTiVoffof|byf. 
 ioffbyf ofj-Vofi 
 
 A. \. 
 A. i. 
 
 A. f 
 
 A. -j^. 
 
 A. ^. 
 
 A. ^. 
 
 A. ^V 
 
 ^■^' 
 A. f 
 
I 
 
 1 
 
 DIVISION OF FRACTIONS. 
 
 Place the numerators of the divisor on the 
 lelt, and the denominators on the right, but 
 place the dividend as in multiplication. If 
 whole numbers are joined to a fraction, reduce 
 as in multiplication. 
 
 PEOBLEMS. 
 1. Divide i of | of f by | of -/g- of f 
 
 
 
 1 
 
 $ 
 
 
 
 7 
 
 4 
 
 t 
 
 $ 
 
 $ 
 
 n 
 
 
 
 t 
 
 4- Ans. 
 
 2. Divide \\>j \. 
 
 3. Divide \\>^ \. 
 
 4. Divide f by \. 
 
 5. Divide \ by |. 
 
 6. Divide \ by |. 
 
 7. Divide ^ by |. 
 
 8. Divide | of | by f of |. 
 
 9. Divide I < f I off l)v | of ||. 
 
 10. Divide 1 of I by 1 ' 
 
 11. Divide 1 of i by |. 
 
 12. Divide i of ^ by i of \. 
 
 A. \. 
 A. If 
 
 A. |. 
 A. If 
 A. If 
 A. f. 
 A. 1. 
 A. \. 
 A. 1. 
 
 13. Divide-|of I byf of5. 
 
 14. Divide \ o: J- by f of 10. 
 
 15. Divide I of I by f of 12. 
 K;. Dividj J-of2 by ^ of 4. 
 
 17. Divide J- of 4 by I of 8. 
 
 18. Divide liby4. 
 
 10. Divide 'l\ by ^ of 5. 
 
 •-^0. Divide I'ofG by2f of3. 
 
 A. f. 
 A. ^. 
 
 A- -5^. 
 A. 1. 
 
 A. 1. 
 
 A. |. 
 
 A. 1. 
 
 A. \. 
 
 SAFE GUIDE IN ADDITION. 
 
 RULPl 
 
 111 addition put down the Avhole amount 
 until done. The left hand figure shows the 
 amount to be carried to the next column, the 
 right shows the answer. 
 
 EXAMPLE. 
 
 13467 
 
 34 1st column 
 
 46329 
 
 23 ...2d 
 
 72548 
 
 28. . . .3cl 
 
 9302 
 
 25....4tli 
 
 57831 
 
 4 last " 
 
 46357 
 
 Q H it 
 
 /^ • • • • 
 
 245834 Ans, 
 
 N. B. — In the last addition put the figure 
 in the right hand column. 
 
I i 
 
 ■r>Tk¥l 
 
 34 
 
 PROF, ware's system OF 
 
 OOKVEESION OF STEELING MONET. 
 
 EULE. 
 
 Place a cipher to the right of the pence, di- 
 vide by 12; add the shillings, divide by 20; 
 then add the i^onnds. Multiply the whole by 
 40, and divide the product by 9. Point off in 
 the answer one figure for each decimal. 
 
 EXAMPLE. 
 How many dollars are there in £50 7s. 6d ? 
 
 12)00 
 2,0)7, 5 
 
 50 375 
 40 
 
 9)2015000 
 
 $223.88.8 par value. 
 
 SOLUTIOX. 
 
 Multiply by 40, because in £1 there are 40 
 ! sixpences ; divide by 9, because $1 is equiva- 
 lent to 4s. Gd. at par. In 4s. 6d. there are 9 
 sixpences. 
 
 I- 
 
 EQUATION OF PAYMENTS. 
 
 35 
 
 BARTER. 
 
 ^ 
 
 Place the given quantity of the commodity 
 and the price at which it is valued, on the 
 right of the line. Place on the left the con- 
 stituents of the commodity whose value is 
 required. 
 
 EXAMPLES. 
 
 1. How much cloth at 22 cents per yard, 
 must be given in exchange for 4400 lbs. of 
 cotton, at 3^ cents per pound ? 
 
 ^ 
 
 MOO 
 
 7 
 
 700 
 
 Ans. 700 yds. 
 
 2. How much tea, at 64 cents per pound, 
 must be given for 448 pounds of coffee, at 20 
 cents per pound ? * Ans. 140 lbs. 
 
 3. How much wheat at $1.25 cents per 
 bushel, must be given for fifty bushels of rye, 
 at 70 cents per bushel ? Ans. 28 bush. 
 
 4. How many bushels of rye worth 70 cents 
 per bushel, must I give for 28 bushels of 
 wheat, the wheat valued at $1.25 per bushel ? 
 
 Ans. 50 bush. 
 
I 
 
 30 
 
 piioF. wake's system of 
 
 5. How many pounds of coffee can I have in 
 exchange for 28 lbs. of butter, valued at 21 
 cents per lb.; the value of the coffee is 12 cts. 
 V^Y lb ? Ans. 49. 
 
 G. How many sheep at H per head, must I 
 give for G cows, at $12 a piece ? Ans. 18. 
 
 7. Sold 28 bushels of wheat at 75 cents per 
 bushel; how many barrels of salt can I have 
 in exchange at $2 per barrel ? Ans. 10|. 
 
 8. How much coffee at 20 cents per pound, 
 must I give for 120 yards of cloth, at 64 cents 
 per yard ? Ans. 384. 
 
 9. How many bushels of wheat will pay for 
 40 barrels of pork at $8 per barrel, when wheat 
 is worth 80 cts. per bushel ? Ans. 400 bush. 
 
 DISCOUNT. 
 
 Diacaunt is an alhwance made far prompt payment 
 BISCOUKT WITHOUT TIME. 
 
 Place the sum on which the discount is to 
 be made, and the rate per cent, on the right, 
 and one hundred on the left. 
 
 Example. — What is the discount on $400, 
 at G per cent Ans. $24. 
 
 '' 
 
 i 
 
 I QUATIOX OP PAYMENTS. 
 
 37 
 
 WOOD MEASURE, &c. 
 
 liULE. 
 
 Place the length, height, and width, on the 
 right; on the left place the dimensions of one 
 cord. 
 
 EXAMPLE. 
 
 HoAv many cords cf Avood in a pile 120 feet 
 long, 12 feet high, and 4 feet wide ? 
 
 .^10 15 
 
 1$ 3 
 
 ,4 _ 
 
 Ans. 45 Cords. 
 
 SOLUTIOIS'. 
 
 4 equals 4; 4 into 12 three times; 8 into 
 120, 15 times; 3 times 15 is 45 cords. 
 
 How many cords of wood in a pile 32 feet 
 long, 12 high, and 4 Avide ? 
 
 n 4 
 
 It 3 
 
 A — 
 
 
 15 
 
 Ans. 12 Cords. 
 
 How many yards of carpeting will it take 
 to carpet a hall 18 l)y 20 feet ? 
 
 1^ 2 
 
 20 — 
 
 Ans. 40 Yards. 
 Note. — Divide by 9, because 9 squaic feet 
 make 1 square yard. 
 
38 
 
 PROF, ware's system OP 
 
 If i of 6 be 3, what will the i of 20 be ? 
 
 3 
 3 
 1 
 
 20 
 
 Ans. 74. 
 
 1 
 6 
 4 
 
 
 How many bricks in a wall 40 feet long, 12 
 feet high, and 1 ' feet thick ? Size of brick, 8 
 by 4 by 2 inches. 
 
 8 
 4 
 3 
 2 
 
 4C 
 
 12 
 4 
 
 1728in.= l cubic ft. 
 
 Answer 17,280 5ricA:s. 
 
 How many feet board measure in the floor 
 joists of a building 18 by 40 feet, joists 3 by 8 
 inches, placed 16 inches apart from the centre 
 of each ? 
 
 40 
 
 18 
 
 16 3 
 
 8 
 
 Answer lOSO feet. 
 
 How many dollars will it cost to carpet a 
 hall 24 by 15, carpet one yard wide, at 11 
 shillings per yard? 
 
 9 
 
 8 
 
 24 
 15 
 11 
 
 Aaswer $55 
 
 EQUATION OF PAYMENTS. 39 
 
 BRAZIL. D c M 
 
 Johannes, (half in proportion) 17 06 8 
 
 Dobraon 32 71 4 
 
 J^obra 17 30 5 
 
 Moidore, Oialf in proportion) 6 56 
 
 Crusado g^ g 
 
 ENGLAND. 
 
 Guinea, half in proportion 5 n g 
 
 Sovereign, do 4 ^5 
 
 Seven Shilling Piece. ... 1 70 6 
 
 FRANCE. 
 
 Double Louis, coined bcf 1^80 9 69 3 
 
 Louis, coined before 1786 4 84 4 
 
 Double Louis, coined since 178G 9 IG 3 
 
 Louis, coined since 1786 4 58 1 
 
 Double Isapoleon, or forty francs 7 71 3 
 
 Kapoleon, or twenty francs 3 86 6 
 
 COLUMBIA. 
 Doubloons 15 53 g 
 
 MEXICO. 
 Doubloons, shares in proportion 15 53 8 
 
 PORTUGAL. 
 
 Dobraon 32 71 4 
 
 ^obra 17356 
 
 Johannes 17 qq 8 
 
 Moidore, lia.lf in proportion 6 56 
 
 Piece of 16 testoons, or 1600 rees 2 12 5 
 
 Old Crusado of 400 rees 58 6 
 
 New Crusado of 480 rees 63 7 
 
 Millree, coined in 1755 78 
 
 i h 
 
40 
 
 PROF, ware's system OF 
 
 SPAIN. 
 
 D C M 
 
 Quadruple pistol, or Doubloon, 1772, double 
 
 and single, and shares in proportion 16 03 3 
 
 Doubloon, 1801 15 53 8 
 
 Pistole, 1801 3 88 8 
 
 Coronilla, gold doll., or vintem, 1801 98 2 
 
 U. S. AMERICA. 
 
 Eagle, coined before July 31, 1834 *. . .10 66 8 
 
 Eagle, coined after July 31, 1834 10 . . . 
 
 Shares in proportion. 
 
 VALUE OF FOREIGN MONEY. 
 
 CANADA, NOVA SCOTIA, &c. 
 
 A Farthing. . 
 4 Farthings = 
 12 Pence 
 60 Pence 
 20 Shillmgs 
 30 Shillings 
 40 Shillings 
 50 Shillings 
 
 a penny 
 
 a shilling 
 
 a dollar 1 
 
 a pound 4 
 
 a moidore 6 
 
 a half Joe 8 
 
 a Fed. Eagle 10 
 
 1 
 20 
 
 4.1 
 
 T 
 
 11 
 
 EQUATION OF PAYMENTS. 
 
 41 
 
 NORTHERN PARTS 
 
 ENGLAND & SCOTLAND. 
 
 LONDON, LIVERPOOL, BRISTOL, EDINBURGH, GLASGOW, AC. 
 
 D C M 
 
 A Farthing 4.6 
 
 2 Farthings = a half-penny 9i 
 
 2 Half-pence a penny 1 Si 
 
 4 Pence a groat 7 4 
 
 6 Pence a half shilling 11 1.1 
 
 12 Pence a shilling 22 2.2 
 
 54 Pence an Ame. dol 1 . . 
 
 5 Shillings a crown 1 11 1.1 
 
 20 ShilliRgs a pound ster 4 44 4.4 
 
 21 Shillings an English guinea. . . 4 66 6.7 
 
 BREMEN. 
 
 3 Grotes == a double shilling. . 3 2 
 
 24 Grotes a mark 25 5i 
 
 48 Grotes a double mark 51 1 
 
 72 Grotes or 3 marks a rix dollar 76 6^ 
 
 Accounts are kept in Rix-doUars and Grotes. 
 
 HANOVER, 
 
 LUNENBURG, ZELL, &C. 
 
 A Pfenning . . . . 2.7 
 
 3 Pfennings = a dreyer 8 .2 
 
 8 Pfennings a marien 2 1.9 
 
 12 Pfennings a grosh 3 2.8 
 
 8 Groshen a half guilden 26 2i 
 
 10 Groshen a guilden 52 5 
 
 24 Groshen a rix dollar 78 7i 
 
 32 Groshen a double guilden . . 1 5 
 
 34 Groshen a ducat 1 10 
 
 Accounts are kept in Rix- dollars, Groshen s, and 
 Pfennings. 
 
 w iii-UJWaB 
 
•^■^^mhM^ 
 
 42 
 
 L 
 
 PROP, ware's system of 
 
 ETJEOPE. 
 
 SOUTHERN PARTS. 
 
 PO RTU GAL. 
 
 D 
 
 A Rhea. 
 10 Reas 
 20 Reas 
 5 Vintins 
 4 Testoons 
 24 Vintins 
 10 Testoons 
 48 Testoons 
 64 Testoons 
 
 = a half vintin 1 
 
 a vintin 2 
 
 a testoon 12 
 
 a crusad of exchange ... 50 
 
 a new crusado 60 
 
 a milrea 1 25 
 
 amoidore 6 .. 
 
 a Johannes 8 .. 
 
 M 
 
 n 
 
 5 
 5 
 
 Accounts are kept in Millreas and Reas. 
 
 FRANCE AND NAVARRE. 
 
 PARIS, LYONS, MARSEILLES, BORDEAUX, BAYONNE, &C. 
 
 Of 
 
 A Denier 
 3 Deniers 
 2 Liards 
 
 12 Deniers 
 
 20 Sols 
 
 60 Sols 
 6 Livres 
 
 10 Livres 
 
 24 Livres 
 
 = a Hard... 2.3 
 
 adardene 4.6 
 
 a sol 9j 
 
 a livi-e toumois 18 5 
 
 an ecu of exchange. ... 55 5 
 
 an ecu or crown 1 11 1.1 
 
 a pistole 1 85 . . 
 
 a Louis d'or 4 44 4.4 
 
 Accounts are kept in Livres, Sous, and Deniers. 
 
 SPAIN. 
 
 32 Reals = a pistole of exchange. ... 3 18 5 
 
 36 Reals a pistole 3 72 2 
 
 Accounts are kept in Dollars, Reals, & Maravedis. 
 
 i 
 
 EQUATION OF PAYMENTS. 
 
 43 
 
 SPAIN— Continued. 
 
 GIBRALTAR, MALAGA, DENIA, &C. 
 
 Velon. 
 
 D C M 
 
 A Maravedi '. . 1.6 
 
 2 Maravedis = an ochavo 3.2 
 
 4 Maravedis a quartil 6.4 
 
 o4 Maravedis a real velon 5 3.2 
 
 15 Reals a piastre of ex 79 6.3 
 
 512 Maravedis a pistole 77 6.3 
 
 GO Reals a pistole of ex. ... 3 18 5 
 
 2043 Maravedis a pistole of ex. .. . 3 18 5 
 
 70 Reals a pistole 3 72 2 
 
 Accounts are kept in Dollars, Reals, ifc Maravedis. 
 
 BARCELONA, SARAGOSSA, VALENCIA, &C. 
 
 A Maravedi 3.9 
 
 16 Maravedis = a soldo 6 2i 
 
 2 Soldos a rial, old plate 12 5 
 
 16 Soldos a dollar 1 
 
 20 Soldos a libra 1 25 
 
 24 Soldos a ducat 1 50 
 
 60 Soldos a pistole 3 60 
 
 There are also Ducats of 21 and 22 Soldos. 
 
 Accounts are kept in Dollars, Reals & Maravedis. 
 
 ATo^^?.— Although 60 Soldos are equal to 3 dollars 
 and 75 cents, the Spanish Pistole is worth but 3 doll- 
 ars and 60 cents. 
 
 ' 
 4 
 
44 
 
 PROF, ware's system OF 
 
 ITALY. 
 
 GENOA, NOVA, CORSICA, BASTEA, &C. 
 A r. • DOM 
 
 A Denari g* 
 
 12 Denari = a soldi 7,9 
 
 4 Soldi a clievalet 3 1.8 
 
 20 Soldi a lira 15 9.2 
 
 30 Soldi a testoon 23 8^ 
 
 5 Lires a croisade 79 6.3 
 
 115 Soldis apezzoofex 92 5.9 
 
 6 Testoons a genoinc i 44 4 
 
 20 Liers a pistole. 3 18 5 
 
 Accounts are kept in Lier?, Soldis, and Denaris. 
 
 CHINA. 
 
 PEKTN, CANTON, &C. 
 
 A Cash 14 
 
 10 Cash = a candareen l 4.8 
 
 10 Candareens a mace 14 8 
 
 10 Mace, 1 oz. G dwt. 6 grs. = a tale. 1 48 
 
 Accounts are kept here in Tales, Mace, Candareens, 
 and Cash. 
 
 EQUATION OF PAYMENTS. 
 
 45 
 
 PROF. WARE'S CHALLENGE. 
 
 From N. Y. Herald, Oct. 30, 1870. 
 
 $10,000 has been deposited with Greenbaum Bros & Co., 
 Bankers, National Park Bank Building, by Prof. W Powell 
 Ware, 21 West 124th Street, for the best Rule for Equation of 
 Payments. To be decided by competent judges on December 
 1st, 1870* 
 
 From N. Y. Standard, Nov. 4tli, 18 TO. 
 
 A Chance for Mathematicians. - The problem of the 
 Equation of Payments is receiving at present the attention of 
 the best mathemaricians, an announcement having been re- 
 cently made by Prof W Powell Ware, of21 West 124th Street 
 of this city that he wouldpay$10 000 for the best rule." The 
 money has been deposited for the purpose with Messrs. Green- 
 baum Bros &Co., Bankers* National Park Bank Building, to 
 whom competitors may send their rules. On Deoember 1st the 
 successful competitor will receive payment for his rule. 
 
 From N. Y. ITorld, Nov. 13, 1870. 
 
 The mathematicians have become very enthusiastic in their 
 race for the $10,000 offered by Prof. Ware, of this city, for the 
 best rule for the Equation of Payments. The plans already 
 received come from almost every seetion of the country, and 
 include eom^ very good and some very preposterous solutions. 
 All partie*^ interes ed will meet at 12 o'clock, on December 1, 
 1870, at the Astor House, at which time the successful compet- 
 itor will receive the reward for his labor. 
 
 From !V. Y. Times, Nov. 15, 1870. 
 
 Equatiox op Payments.— Prof. Ware's offer of $10,000 
 for the best rule for the equation of payments has drawn out a 
 very excitini( competition between the mathematicians all over 
 the country. The rules already received by Prof. Ware and 
 thoMe^*sr8. Greenblm Brothers, in whose hands the money 
 IS dopo>ited, come from every section of the country, and in- 
 clude pome marvelous mathematical efforts. The award for the 
 best plan will be made December 1, 1870, at the Astor House, at 
 which place all interested parties will assemble at 12 o'clock. 
 
 Numerous extracts from different sections of the country 
 omitted for want of space. 
 
46 
 
 PROF, ware's system OF 
 
 DECISION OF THE JUDGES. 
 
 [true copy.] 
 
 "We, the undersigned committee selected to decide 
 upon the different plans submitted in the contest for 
 the best rule for the Equation of Payments, after ma- 
 ture and careful examination and test of plans offered 
 by fifty-seven competitors (made conjointly and per- 
 sonally) do declare this to be our positive and final 
 decisions, viz : 
 
 That the Rule presented by Prof. W. Powell 
 Ware, of New York City, is the shortest, simplest, 
 and best, possessing the greatest utility and general 
 adaptation, not only of the plans now bofore us, but 
 of any that has ever come to our knowledge, and 
 which in our j udgment is mathematically correct. 
 
 We therefore declare that Prof W. Powell Ware, 
 
 of New York, is duly entitled to the award offered. 
 
 Signed : 
 
 Jos. C. Atwood, with Landers, Frary & Clark, 53 
 Chambers Street. 
 
 A. O. Field, with Jordan, Marsh & Co., 184 and 186 
 Church Street. 
 
 John G. Huhn, with Hoover, Calhoun & Co., 362 
 Broad wa5\ 
 
 Edward F. Choate, with E. K Dibble and Co.. 53 
 and 55 Worth Street. 
 
 B. F. Blake, with Manning, Glover & Co., 109 and 
 111 Worth Street. 
 
 We fully concur in the above decision — 
 
 H. E. Phelps, book-keeper of H. B. Claflin & Co, 
 John P. Gaul, with Tetft, Griswold & Kellogg. 
 
 443 and 445 Broadwav 
 Anthon J. Kruger, with Duncan, Sherman & Co., 
 
 Banker?. 
 Wm. H. Clark, with Henry Clewes & Co., Bankers, 
 
 32 Wall Street. 
 Matthew Bunker, of Benedict, Hall & Co., 134 and 
 
 136 Grand Street. 
 
 X 
 
 EQUATION OF PAYMENTS. 
 
 47 
 
 I 
 
 I 
 
 Prof. W. POWELL WAEE'S 
 
 MAGIC SQUARE 
 
 : t 
 
 These columns (added) make 100, forty-two 
 
 different ways. 
 
 J 3 7 
 
 9 
 
 6 
 
 2 
 
 8 
 
 4 
 
 1 3 
 
 7 
 
 9 
 
 6 
 
 2 
 
 8 4 1 3 7,9 
 
 3 9 1 
 
 7 
 
 2 
 
 4 
 
 6 
 
 8 
 
 3 9 
 
 1 
 
 7 
 
 2 
 
 4 
 
 6 8 3 9 17! 
 
 7 19 
 
 3 
 
 8 
 
 6 
 
 4 
 
 2 
 
 7 1 
 
 9 
 
 3 
 
 8 
 
 6 
 
 4 2 7 19 3 
 
 9 7 3 
 
 1 
 
 4 
 
 8 
 
 2 
 
 6 
 
 9 7 
 
 3 
 
 1 
 
 4 
 
 8 
 
 2 6 9 7 3 1 
 
 6 2 8 
 
 4 1 
 
 3 
 
 7 
 
 9 
 
 6 2 
 
 8 
 
 4 
 
 1 
 
 3 
 
 7 9 6 2 8 4 1 
 
 2 4 6 
 
 8 
 
 3 9 
 
 1 
 
 
 2 4 
 
 6 
 
 8 
 
 3 
 
 9 
 
 17 2 4 6 8 
 
 8 6 4 
 
 2 
 
 7 
 
 1 
 
 9 
 
 3 
 
 8 6 
 
 4 
 
 2 
 
 7 
 
 1 
 
 9 3 8 6 4 2 
 
 4 8 2 
 
 6 
 
 9 
 
 7 
 
 3 
 
 1 
 
 4 8 
 
 2 
 
 6 
 
 9 
 
 7 
 
 3 14 8 2 6 
 
 1 3 7 
 
 9 
 
 6 
 
 2 
 
 8 
 
 4 i 3 
 
 7 
 
 9 
 
 6 
 
 2 
 
 8 4 1 3 7,9 
 
 3 9 1 
 
 7 
 
 2 
 
 4 
 
 6 
 
 8 
 
 3 9 
 
 1 
 
 7 
 
 2 
 
 4 
 
 6 8 3 9 17 
 
 7 19 
 
 3 
 
 8 
 
 6 
 
 4 
 
 2 
 
 7 1 
 
 9 
 
 3 
 
 8 
 
 6 
 
 4 2 7 1 9 3 
 
 9 7 3 
 
 1 
 
 4 
 
 8 
 
 2 
 
 6 
 
 9 7 
 
 3 
 
 1 
 
 4 
 
 8 
 
 2 6 9 7 3 1 
 
 6 2 8 
 
 4 
 
 1 
 
 3 
 
 7 
 
 9 
 
 6 2 
 
 8 
 
 4 
 
 1 
 
 3 
 
 7 9 6 2 8 4 1 
 
 2 4 6 
 
 8 
 
 3 
 
 9 
 
 1 
 
 7 
 
 2 4 
 
 6 
 
 8 
 
 3 
 
 9 
 
 1 7 2 4 6 8 1 
 
 8 6 4 
 
 2 
 
 7 
 
 1 
 
 9 
 
 3 
 
 8 6 
 
 4 
 
 2 
 
 7 
 
 1 
 
 9 3 8 6 4 2 
 
 4 8 2 
 
 6 
 
 9 
 
 7 
 
 o 
 O 
 
 1 
 
 4 8 
 
 2 
 
 6 
 
 9 
 
 7 
 
 3 14 8 2 6 
 
 13 7 9 
 
 6 
 
 2 
 
 8 
 
 4 
 
 1 3 
 
 7 
 
 9 
 
 6 
 
 2 
 
 8 4 13 7 9 
 
 3 9 i 
 
 7 
 
 2 
 
 4 
 
 6 
 
 8 
 
 3 9 
 
 1 
 
 
 2 
 
 4 
 
 6 8 3 9 17 
 
 7 19 
 
 3 
 
 8 
 
 6 
 
 4 
 
 2 
 
 7 1 
 
 9 
 
 3 
 
 8 
 
 6 
 
 4 2 7 19 3 
 
 9 7 3 
 
 1 
 
 4 
 
 8 
 
 2 
 
 6 
 
 9 7 
 
 3 
 
 1 
 
 4 
 
 8 
 
 2 6 9 7 3 1 
 
1 
 
 46 
 
 PiiOF. ware's system of 
 
 DECISION OF THE JUDGES. 
 
 [true copy.] 
 
 We, the undersigned committee selected to decide 
 upon the different plans submitted in the contest for 
 the best rule for the Equation of Payments, after ma- 
 ture and ciireful examination and test of plans offered 
 by fifty-seven competitors (made conjointly and per- 
 sonally) do declare this to be our positive and final 
 decisions, viz : 
 
 That the Rule presented by Prof. W. Powell 
 Ware, of New York City, is the shortest, simplest, 
 and best, possessing the greatest utility and general 
 adaptation, not only of the plans now before us, but 
 of any that has ever come to our knowledge, and 
 which in our j udgment is mathematically correct. 
 
 We therefoi^ declare that Prof W. Powell Ware, 
 
 of New York, is duly entitled to the award offered. 
 
 Signed : 
 
 Jos. C. Atwood, with Landers, Frary & Clark, 58 
 Chambers Street. 
 
 A. O. Field, with Jordan, Marsh & Co., 184 and 186 
 Church Street. 
 
 John G. Huhn, with Hoover, Calhoun cfe Co., 362 
 Broadway. 
 
 Edward F. Clioate, with E. R. Dibble and Co., 53 
 and 55 Worth Street. 
 
 B. F. Blake, with Manning, Glover & Co., 109 and 
 111 Worth Street. 
 
 We fully concur in the above decision — 
 
 H. E. Phelps, book-kpeper of H. B. Claflin & Co, 
 John P. Gaul, with Teifr, Griswold & KeUogg. 
 
 44.3 and 445 Broadwav 
 Anthon J. Kruger, with Duncan, Sherman & Co., 
 
 Bankers. 
 Wm. H. Clark, with Henrv Clewes & Co., Bankers, 
 
 32 Wall Street. 
 Matthew Bunker, of Benedict, Hall & Co., 134 and 
 
 136 Grand Street. 
 
 ( 
 
 EQUATION OP PAYMENTS. 
 
 47 
 
 Prof. W. POWELL WAEE'S 
 
 MAGIC SQUAKE. 
 
 These columns (added) make 100, forty-two 
 
 different ways. 
 
 1 
 
 3 
 
 7 
 
 9 
 
 6 
 
 2 
 
 8 
 
 4 
 
 1 
 
 3 
 
 7 
 
 9 
 
 6 
 
 2 
 
 8 
 
 4 
 
 1 
 
 3 
 
 7 
 
 f) 
 
 3 7 9 
 
 9 1 
 
 7 
 
 19 3 
 
 7 3 JT 
 
 2 8 4 
 
 6 8 
 
 4 
 G 
 
 8 
 3 
 9 
 1 
 
 7 
 
 2 
 
 6 2 8 
 
 2 4 6 
 8 6 4 
 4 8 2 
 1 
 
 3 9 
 
 3 7 
 
 4 2 
 
 2 6 
 
 7 9 
 1 7 
 9 3 
 
 3 1 
 
 8 4 
 6 8 
 
 4 2 
 
 4 
 
 6 
 
 8 2 6 
 
 3 7 9 
 
 9^7 
 
 i 9 3 
 
 7 3 1 
 
 7 1 .9 
 9 7 3 
 
 6 2 8 
 
 2 4 6 
 
 8 6 4 
 4 8 2 
 13 7 
 
 3 9 J 
 
 7 i 9 
 
 9 7 3 
 6 2 8 
 2 4 6 
 
 8 6 4 
 
 4 8 2 
 
 4 1 
 
 8 3 
 
 2 7 
 
 6 9 
 
 9 6 
 
 7 2 
 
 3 8 
 1 4 
 
 4 1 
 
 8 3 
 
 2 7 
 
 6 9 
 
 9 6 
 
 7 2 
 
 3 8 
 
 1 4 
 
 4 1 
 
 8 3 
 
 2 7 
 6 9 
 
 7 
 1 
 9 
 3 
 8 
 6 
 4 
 
 3 
 
 9 
 1 
 
 i 
 
 2 
 4 
 6 
 
 8 2 
 
 3 7 
 
 9 1 
 1 9 
 
 7 3 
 
 2 8 
 
 4 6 
 
 6 4 
 
 8 2 
 
 3 7 
 
 9 1 
 1 9 
 
 7 3 
 
 9 6 
 
 7 2 
 
 3 8 
 
 1 4 
 
 4 1 
 
 8 3 
 
 2 7 
 
 6 9 
 
 9 6 
 
 7 2 
 
 3 8 
 
 1 4 
 
 4 1 
 
 8 3 
 
 2 7 
 
 6 9 
 
 9 6 
 
 7 2 
 
 3 8 
 1 4 
 
 2 8 
 4 6 
 6 4 
 8 2 
 
 3 7 
 
 9 
 1 
 7 
 2 
 4 
 6 
 
 1 
 9 
 3 
 8 
 6 
 4 
 
 4 1 
 
 8 3 
 2 7 
 
 6 9 
 
 9 6 
 
 7 2 
 
 3 
 1 
 4 
 8 
 2 
 
 8 
 4 
 1 
 3 
 
 7 
 
 8 2 
 
 3 7 
 
 9 1 
 
 1 9 
 
 7 3 
 
 2 8 
 
 4 6 
 6 4 
 
 8 2 
 
 6 9 
 9 6 
 
 7 2 
 
 3 8 
 
 1 4 
 
 4 1 
 
 8 3 
 
 2 7 
 6 9 
 
 3 
 9 
 1 
 
 7 
 
 2 
 
 4 
 
 6 
 
 8 
 
 3 
 
 9 
 
 1 
 
 i 
 
 2 
 
 4 
 
 6 
 
 8 
 
 3 
 
 9 
 
 1 
 
 
 7 9 
 
 1 7 
 9 3 
 
 3 1 
 
 8 4 
 6 8 
 
 4 2 
 
 2 6 
 9 
 
 ry 
 i 
 
 1 
 
 9 
 3 
 
 8 
 
 7 
 3 
 1 
 4 
 
 6 8 
 4 2 
 2 6 
 
 7 9 
 1 7 
 
 9 3 
 3i 
 
< ■ 
 
 RANKIN'S PERPETUAL ALMANAC, 
 
 BOOK FORM, 
 
 TWO MONTHS TO A PAGE. 
 
 -OO^^OO- 
 
 PHILADELPHIA : 
 CLAXTON, REMSEN & HAFFELFINGER, 
 
 624, 626 & 628 MARKET STREET. 
 
I 
 
 Entered according to Act of Congress, in the year 1873, by 
 
 A. N. RANKIN, 
 In the Office of the Librarian of Congress, at Washington. 
 
 ELECTROTYPED BT J. FAUAN k SON, PHILADELPHIA. 
 
 • 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Mo. 
 
 1 Tu. 
 
 1 We. 
 
 |Th. 
 
 Fr. 
 
 1 Sat. 
 
 18. 
 
 1 7|14 
 
 21 |28 
 
 
 
 Tu. 
 
 1 We. 
 
 |Th. 
 
 IFF. 
 
 1 Sat. 
 
 18. 
 
 |Mo. 
 
 1 1 8 1 15 
 
 22| 29 
 
 
 We. 
 
 |Th. 
 
 1 Fr. 
 
 1 Sat. 
 
 IS. 
 
 1 Mo. 
 
 |Tu. 
 
 2 1 9 1 16 
 
 23|30 
 
 
 Th. 
 
 1 Fr. 
 
 j Sat. 
 
 18. 
 
 |Mo. 
 
 |Tu. 
 
 j We. 
 
 3 1 10 1 17 
 
 24|31 
 
 
 Fr. 
 
 1 Sat. 
 
 18. 
 
 1 Mo. 
 
 |Tu. 
 
 1 We. 
 
 |Th. 
 
 4 111 1 18 
 
 25 1 
 
 
 Sat. 
 
 IS. 
 
 1 Mo. 
 
 1 Tu. 
 
 1 We. 
 
 |Th. 
 
 1 Fr. 
 1 Sat. 
 
 5 1 12 1 19 
 
 26 1 
 
 
 s. 
 
 1 Mo. 
 
 1 Tu. 
 
 1 We. 
 
 jTh. 
 
 |Fr. 
 
 6 1 13 1 20 
 
 27 1 
 
 
 1771 
 
 1 1772 
 
 1 
 
 1 1773 
 
 1 1774 I 
 
 1775 
 
 11776 
 
 Janua 
 
 ry. 
 
 
 
 1 1777 
 
 1 1778 
 
 1 i77J 
 
 1<80| 
 
 
 11781 
 
 
 
 
 1782 
 
 1 1783 
 
 1784 
 
 
 1 1785 1 
 
 1786 
 
 11787 
 
 
 
 1788 
 
 
 1 1789 
 
 1 1790 
 
 1791 1 
 
 1792 
 
 1 
 
 
 1793 
 
 1 1794 
 
 1 1795 
 
 1 1796 
 
 
 17H7 
 
 1 1798 
 
 
 1799 
 
 11800 
 
 1 1801 
 
 1 1802 
 
 1803 1 
 
 1804 
 
 1 
 
 
 1805 
 
 1 1806 
 
 1 1807 
 
 1 1808 
 
 
 1809 
 
 1 1810 
 
 
 1811 
 
 1 1812 
 
 1 
 
 1 1813 
 
 1814 1 
 
 1816 
 
 11816 
 
 
 
 1 1817 
 
 1818 
 
 1 1819 
 
 18.:0 1 
 
 
 1 1821 
 
 
 1822 
 
 1 1823 
 
 1824 
 
 
 1825 j 
 
 1826 
 
 1 1827 
 
 
 18 J8 
 
 
 1829 
 
 1 1830 
 
 1831 1 
 
 1832 
 
 1 
 
 
 183;^ 
 
 1834 
 
 1 1835 
 
 1 1^36 
 
 
 1837 
 
 1 1838 
 
 
 1839 
 
 1840 1 
 
 
 1 1841 1 
 
 1842 1 
 
 1843 
 
 11844 
 
 
 
 1845 1 
 
 1846 
 
 1 1847 1 
 
 1848 1 
 
 
 1 1849 
 
 
 1850 
 
 1851 1 
 
 1852 
 
 
 1N53 1 
 
 1854 
 
 1 1865 
 
 
 1856 
 
 
 1857 
 
 1 1858 1 
 
 1859 1 
 
 1860 
 
 1 
 
 
 1861 
 
 1862 
 
 1863 
 
 1 1864 1 
 
 
 1866 
 
 1866 
 
 
 1867 
 
 1868 1 
 
 
 1869 1 
 
 1870 
 
 1871 
 
 1872 
 
 
 
 1873 1 
 
 1874 
 
 1S75 1 
 
 1876 1 
 
 
 1877 
 
 
 1878 1 
 
 1879 1 
 
 1880 
 
 1 
 
 1881 1 
 
 1882 
 
 1^83 
 
 
 1884 1 
 
 
 1885 
 
 18-6 1 
 
 1887 1 
 
 1888 
 
 
 
 1889 1 
 
 1890 1 
 
 1891 
 
 1892 1 
 
 
 1893 
 
 189 
 
 
 1895 1 
 1901 1 
 
 1896 1 
 
 
 1897 1 
 
 1898 1 
 
 1899 
 
 1900 
 
 
 1902 1 
 
 1903 
 
 1904 1 
 
 
 1905 1 
 
 1906 
 
 
 1907 1 
 
 1908 1 
 
 
 1909 
 
 1910 1 
 
 1911 1 
 
 1912 
 
 
 
 1913 1 
 
 1914 
 
 1915 1 
 
 1916 1 
 
 1 
 
 1917 
 
 
 191S I 
 
 1919 1 
 
 1920 1 
 
 1 
 
 1921 1 
 
 1922 1 
 
 1923 
 
 
 1924 1 
 
 
 1925 1 
 
 1926 1 
 
 1927 1 
 
 1928 1 
 
 
 
 1929 1 
 
 19:i0 1 
 
 1931 1 
 
 1932 1 
 
 
 1933 1 
 
 1934 
 
 
 1935 
 
 1936 1 
 
 
 1937 1 
 
 1938 1 
 
 1939 1 
 
 1940 
 
 
 
 1941 1 
 
 194'^ 
 
 1943 1 
 
 1944 1 
 
 1 
 
 1945 
 
 
 1946 1 
 
 1947 1 
 
 1948 1 
 
 1 
 
 1949 1 
 
 1950 
 
 1951 
 
 
 
 
 1952 1 
 
 
 1953 1 
 
 1954 1 
 
 1955 1 
 
 1956 i 
 
 
 February. | 
 
 
 
 Mo. 1 
 
 Tu. 1 
 
 We. 
 
 Th. 1 
 
 Fr. 1 
 
 Sat. 
 
 8. 
 
 1 4|11| 
 
 18 1 2.M 
 
 
 Tu. 1 
 
 We. 1 
 
 Th. 1 
 
 Fr. 1 
 
 Sat. 
 
 S. 
 
 1 Mo. 
 
 1 6|12| 
 
 19 1 26 
 
 
 We. ( 
 
 Th. 1 
 
 Fr. 
 
 Sat. 1 
 
 8. 1 
 
 Mo. 
 
 Tu. 
 
 1 6|13| 
 
 20 1 27 
 
 
 Th. 1 
 
 Fr. 1 
 
 Sat. 1 
 
 8. 1 
 
 Mo. 1 
 
 Tu. 1 
 
 We 
 
 1 7|14| 
 
 21 (28 
 
 
 Fr. 1 
 
 Sat. 1 
 
 8. 1 
 
 Mo. 
 
 Tu. 1 
 
 We. 1 
 
 Th. 
 
 1| 8|15j 
 
 22 1 29 
 
 
 Sat. 1 
 
 s. 
 
 Mo. 1 
 
 Tu. 1 
 
 We. I 
 
 Th. 1 
 
 Fr. 
 Sat. 
 
 2 1 9 1 16 1 
 
 23 1 
 
 
 8. 1 
 
 Mo. 1 
 
 Tu. 1 
 
 We. 1 
 
 Th. 1 
 
 Fr. I 
 
 3 j 10 1 17 1 
 
 24| 
 
 
 The Year and Days of the Week for both Months are in the same cohimn 
 
 
4 1 11 
 
 ill 
 
 March. 
 
 April. 
 
 25 
 
 5 I 12 j 19 I 26 
 
 6 I 13 I 20 I 27 
 
 7 I 14 I 21 I 2S 
 
 I I 8 I 15 I it I v9 
 
 2 I 9 I 16 I 23 I 3() 
 
 3 I 10 I 17 I 24 I 31 
 
 1 I 8 I lo I 22 I 29 
 
 2 1 9 I 16 I 23 I 30 
 
 3 I 10 I 17 I 2H 
 
 4 I 11 I 18 I 2o I 
 
 5 I 12 I 19 I 2r, I 
 
 6 I 13 I 2(» I 27 I 
 
 7 IIH 21 I J8 I 
 
 Mo. \ Tu. I We. I Th. | Fr. | Sat. 
 
 1811 
 
 1839 
 
 1867 
 
 1895 
 
 1907 
 
 Tu. I We. I Th. I Fr. | Sat. | S- 
 
 Sat. I S, \ Mo. i Tu. I We. | Th. 
 S. I Mo. I Tu. I We. I Th. | Fr. 
 1771 
 
 I 1772 I 1773 I 1774 ( 1775 
 
 1782 j 1783 I 
 
 1788 I 17S9 I 1790 | 1791 | 
 
 1793 I 1794 I 1795 
 
 1799 I 1800 I 1801 I 1802 | 1803 | 
 
 1805 I 1806 I 1807 
 
 I 1812 I 1813 I 1814 I 1815 
 
 1828 I 1829 I 1830 | 1831 ( 
 
 18:^3 I 1834 I 1835 
 
 I 1840 I 1841 I 1842 J 1843 
 
 1844 I 1845 I 1846 | 1847 I 
 
 1850 I 18ol I 
 
 1856 I 1857 I 1858 | 1859 | 
 
 1861 I 1862 I 1863 
 
 I 1868 I 1869 I 1870 | 1871 
 
 1872 I 1873 I 1874 | 1875 | 
 
 1878 I 1879 I 
 
 1884 I 1885 I 18-6 | 1887 | 
 
 1889 I 1890 I 1891 
 
 1901 I 190 J I 1903 
 
 I 1908 I 1909 I 1910 I 1911 
 
 I91« I 1919 I 
 
 1924 I 1925 I 1926 | 1927 | 
 
 1929 I 1930 I 1931 
 
 1935 
 
 1936 I 1937 I 1938 | 1^39 
 
 s. 
 
 Mo 
 
 We. I Th. I Fr. | Sat. | S. I Mo. | Tu. 
 Th. i Fr. I Sat. | S. | Mo. | Tu. jlVe. 
 
 Fr. I Sat. I S. I Mo. | Tu. | We. | Th. 
 
 Fi\ 
 Sat. 
 
 1776 I 1777 I 1778 | 1779 | | 17bO | 1781 
 
 ~ 1784 I 1785 i 1786 | 1787 
 
 1792 
 
 I 1796 I 1797 I 1798 
 
 1804 
 
 I 1808 I 1809 I 1810 
 
 1816 I 1817 I 1818 I 1819 | | ISiO j 1821 
 1822 I 1823 I I 1824 { 1825 | 1826 | 1827 
 
 1832 
 
 I lb36 I 1837 I 1838 
 
 I 1848 I 1849 
 
 1852 I 1853 I 1854 | 1855 
 
 i860 
 
 I 1864 I 1865 I 1866 
 
 I 1876 I 1877 
 
 1880 I 1881 I 1882 | 1883 
 
 1888 
 
 I 1892 I 1893 I 1894 
 
 I 1896 \ 1897 I 1898 I 1899 | 1900 
 
 I 1904 I 1905 I 1906 
 
 1912 I 1913 I 1914 \ 1915 | | 1916 | 1917 
 
 1920 I 1921 I 1922 I 1923 
 
 192^ 
 
 I 1932 I 1933 j 1934 
 
 1940 I 1941 I 1942 | 1943 | | 1944 I 1945 
 
 1946 I 1947 I 
 
 1948 I 1949 I 1950 | 1951 
 
 1952 I 1953 I 1954 | 1955 | 
 
 1966 
 
 Mo. I Tu. \ We. I Th. | Fr. | Sat. | g. 
 
 Tu. I We. I Th. I Fr. | Sat. | JS. | Mo. 
 
 VVeJTh. I Fr. ( Sat. | S. ' Mo. ( Tu. 
 
 Th. I Fr. I Sat. | g. | Mo. | Tu. | We 
 
 Fr. I Sat. I S. I Mo. | Tu. | We. | Th. 
 
 Sat. I S- I Mo. I Tu. I We. | Th. I Fr. 
 
 8. I Mo. I Tu. I W e. I Th. | Fr. | Sat. 
 
 The Year and Days of the Week for both Months are in the same column. 
 
 
 Mo. 1 Tu. 1 We. 1 Th. | Fr. | Sat. | g. 
 
 1 6 1 13 1 20 1 27 
 
 
 
 Tu. I We. 1 Th. 1 Fr. | Sat. | g. | Mo. 
 
 1 7 1 14 1 21 1 28 
 
 
 We. 1 Th. 1 Fr. | Sat. | g. | Mo. | Tu. 
 
 1 1 8 1 15 1 22 1 29 
 
 
 Th. I Fr. 1 Sat. | g. | Mo. | Tu. | We. 
 
 2 1 9 1 16 1 23 1 30 
 
 
 Fr. I Sat. 1 g. 1 Mo. | Tu. | We. | Th. 
 
 3 1 10 1 17 1 24 1 31 
 
 
 Sat. 1 g. 1 Mo. 1 Tu. 1 We. | Th. | Fr. 
 
 4 1 11 1 18 1 25 1 
 
 
 g. 1 Mo. 1 Tu. 1 We. 1 Th. | Fr. | Sat. 
 
 5 12 1 19 1 26 1 
 
 
 1771 1 1 1772 1 1773 | 1774 j 1775 | 
 
 May. 
 
 
 1776 1 1777 1778 | 1779 | j 1780 | 1781 
 
 
 
 
 1782 1 1783 1 1 1784 ( 1785 | 1786 | 1787 
 
 • 
 
 
 1 1788 1 1789 1 1790 | 1791 | | 1792 
 
 
 1793 1 1794 j 1795 | | 1796 | 1797 | 1798 
 
 
 1799 1 1800 1 1801 I 1802 | 1803 | | 1804 
 
 
 1805 1 1806 1 1807 | | 1808 | 1809 | 1810 
 
 
 1811 1 1 1812 1 1813 1 1814 | 1816 | 
 
 
 1816 1 1817 1 1818 1 1819 | | 1820 ( 1821 
 
 
 1822 1 1823 1 j 1824 | 1825 j 1826 | 1827 
 
 
 1 1828 1 1829 J 1830 | 1831 | | 1832 
 
 
 1833 1 1834 1 1835 1 | 1836 | 1837 | 1838 
 
 
 1839 I I 1840 1 1841 | 1842 | 1843 | 
 
 
 1844 1 1845 j 1846 | 1847 | | 1848 | 1849 
 
 
 1850 1 1851 1 1 1852 | 1863 | 1854 | 1855 
 
 
 1 1856 1 1857 1 1858 | 1859 | | 1860 
 
 
 1861 I 1862 I 1863 | | 1864 | 1866 | 1866 
 
 
 1867 I I 1868 1 1869 j 1870 1871 | 
 
 
 1872 1 1873 1 1874 | 1875 | | 1876 | 1877 
 
 
 1878 1 1879 1 1 1880 | 1881 | 1882 | 1883 
 
 
 1 1884 1 1885 1 18^6 | 1887 | | 1888 
 
 
 1889 1 1890 1 1891 | | 1892 | 1893 | 1894 
 
 
 1895 1 1 1896 1 1897 | 1898 | 1899 1900 
 
 
 1901 1 1902 1 1903 1 1 1904 1 1905 | 1906 
 
 
 1907 J I 1908 1 1909 | 1910 | 1911 | 
 
 
 1912 1 1913 1 1914 1 1915 | | 1916 | 1917 
 
 
 1918 1 1919 1 1 1920 1 1921 | 1922 | 1923 
 
 
 1 1924 1 1925 1926 | 1927 [ | 1928 
 
 
 1929 1 1930 1 1931 ( | 1932 | 1933 | 1934 
 
 
 1935 1 1 1936 j 1937 | 1938 1939 | 
 
 
 1940 1 1941 1 1942 | 1943 | 1944 | 1945 
 
 
 1946 1 1947 1 1 1948 1949 | 1950 | 1951 
 
 
 
 
 1 1952 1 1953 1 1954 | 1956 | 1966 
 
 June. 
 
 
 
 Mo. 1 Tu. 1 We. 1 Th. | Fr. | Sat. | g. 
 
 1 3 1 10 ! 17 1 24 
 
 
 Tu. 1 We. 1 Th. 1 Fr. | Sat. g. | Mo. 
 
 1 4|11 |18|26 
 
 
 We. 1 Th. 1 Fr. | Sat. | g. | Mo. Tu. 
 
 1 6 1 12 1 19 1 26 
 
 
 Th. 1 Fr. 1 Sat. | g. | Mo. | Tu. | We. 
 
 1 6 1 13 1 20 1 27 
 
 
 Fr. 1 Sat. 1 g. 1 Mo. I Tu. | We. | Th. 
 
 1 7 1 14 1 21 1 28 
 
 
 Sat. 1 g. 1 Mo. 1 Tu. We. | Th. I Fr. 
 
 1 1 8 1 15 1 22 1 29 
 
 
 g. 1 Mo. 1 Tu. 1 We. 1 Th. | Fr. | Sat. 
 
 2 1 9 1 16 1 23 1 30 
 
 
 The Year and Days of the Week for both Months are in the same column. 
 
 
 

 1 1 8 1 15 1 22 1 29 
 
 Mo. j Tu. 1 We. 1 Th. | Fr. | Sat. | S. 
 
 
 2 1 9 1 16 1 23 1 30 
 
 Tu. 1 We. 1 Th. 1 Fr. | Sat. | g. | Mo. 
 
 3 1 10 1 17 1 24 1 31 
 
 We. 1 Th. 1 Fr. | Sat. | S. 1 Mo. | Tu. 
 
 4 1 11 1 18 1 2.) 1 
 
 Th. 1 Fr. 1 Sat. | g. | Mo. | Tu. | We. 
 
 5 1 12 j 19 I 26 1 
 
 Fr. 1 Sat. 1 S. 1 Mo. | Tu. | We. | Th. 
 
 6 1 13 1 20 1 27 1 
 
 |Sat. 1 S. Mo. 1 Tu. 1 We. | Th. | Fr. 
 
 7 1 14 1 21 1 28 1 
 
 S. Mo. 1 Tu. 1 We. 1 Th. | Fr. | Sat. 
 
 July. 
 
 1771 1 1772 1 1773 | 1774 | 1775 | 
 
 
 
 1776 1 1777 1 1778 | 1779 | j 1780 | 1781 
 
 
 1782 1 1783 1 1 1784 | 1785 | 1786 | 1787 
 
 1 1788 1 1789 1 1790 | 1791 | | 1792 
 
 1793 1 1794 1 1795 j | 1796 | 1797 | 1798 
 
 1799 1 1800 1 1801 1 1802 | 1803 | j 1804 
 
 1805 1 1806 1 1807 | | 1808 | 1809 | 1810 
 
 1811 1 1 1812 1 1813 1 1814 | 1815 | 
 
 1816 1 1817 1 1818 1 1819 | | 1820 | 1821 
 
 1822 1 1823 1 1 1824 | 1825 | 1826 | 1827 
 
 1 1828 1 1829 1 1830 1831 | | 1832 
 
 1833 1 18;U 1 1835 | | 1836 | 1837 | 1838 
 
 1839 1 1 1840 1 1841 | 1842 | 1843 | 
 
 1844 1 1845 1 1846 | 1847 | | 1848 | 1849 
 
 1850 1 1851 1 1 1852 | 1853 | 1854 | 1855 
 
 1 1856 1 1857 1 1858 | 1859 | | 1860 
 
 1861 I 1862 1 1863 | | 1864 | 1865 | 1866 
 
 1867 1 1 1868 1 1869 | 1870 | 1871 | 
 
 1872 1 1873 1 1874 | 1875 | | 1876 1877 
 
 1878 1 1879 1 1 1880 ( 1881 | 1882 | 1883 
 
 1 188H 1885 1 18^6 | 1887 | | 1888 
 
 1889 1890 1 1891 | | 1892 | 1893 | 1894 
 
 1895 1 1 1896 1 1897 | 1898 | 1899 ( 1900 
 
 1901 1 1902 1 1903 1 1 1904 1 1905 | 1906 
 
 1907 1 1 1908 1 1909 | 1910 | 1911 | 
 
 1912 1 1913 1 1914 1 1915 | | 1916 | 1917 
 
 1918 1 1919 1 1 1920 1 1921 | 1922 | 1923 
 
 1 1924 1 1925 1 1926 [ 1927 | | 1928 
 
 1929 1 19;i0 1 1931 1 1 1932 1 1933 ( 1934 
 
 1935 1 1 1936 1 1937 | 1938 f 1939 | 
 
 1940 1 1941 1 1942 | 1943 | | 1944 | 1945 
 
 
 
 1946 1 1947 1 1 1948 | 1949 \ 1950 | 1951 
 
 
 August. 
 
 1 1952 1 195:3 1 1954 1 1955 1 | 1956 
 
 1 5 1 12 1 19 1 26 
 
 Mo. 1 Tu. 1 We. 1 Th. ( Fr. | Sat. | g. 
 
 1 6 1 13 1 20 1 27 
 
 Tu. 1 We 1 Th. 1 Fr. | Sat. | S. 1 M« 
 
 1 7 1 14 1 21 1 28 
 
 We. ! Th. 1 Fr. Sat. | S. 1 Mo. j Tu 
 
 1 1 8 1 15 1 22 1 '29 
 
 Th. 1 Fr. 1 Sat. | g. Mo. | Tu. | W e 
 
 2 1 9 1 10 23 1 30 
 
 Fr. 1 Sat. 1 S. ( Mo. | Tu. ( We. f Th. 
 
 3|10|17|2t 31 
 
 Sat. 1 S. 1 Mo. Tu 1 We. | Tli. 1 Fr. 
 
 4 1 11 ! 18 1 25 1 
 
 S. 1 Mo. 1 Tu. 1 We. Th | Fr. | Sat. 
 
 The Year and Days of the Week for both Months are in the same column 
 
 • 
 
 Mo. iTu. I We. |Th. | Fr. | Sat. | g . 
 
 Tu ^j We. I Th. I Fr. | Sat. | g, | M^ 
 
 We. I Th. I Fr. | S at. | g. | Mo. I Tu. 
 
 Th. ~ 
 
 Fr. 
 
 I Fr. j Sat. I g, I Mo. | Tu. | We. 
 T«at. I g. I M o. I Tu. I We. | Th. 
 
 Sat. I g, I Mo. I Tu. I We. | Th. | Fr. 
 
 g. 
 
 1771 ( 
 
 I Mo. I Tu. I We. I Th ^|Fr~fs^- 
 I 1772 I 1773 I mTjlTTSl 
 
 1776 I 1777 j 1778 I J 779j__|T7^ | i7«i 
 1782^ 1 1783 I [17841 1785 | 178 6 j 1787 
 I 1788 I 1789 I 1790 | 1791 | \vm 
 
 1793 I 1V94 I 1795 | | 1796 | 1797 I 1798 
 
 1799 I 1800 J 1801 I 1802 | 1803 | fl804 
 
 1805 I 1806 I 1807 | | 1808 | 180 9 i 1810 
 1811 I i 1812 I 1813 I 1814TT8151 
 
 1816 I 1817 I 1818 I 1819 | 
 
 1822 I 1823 I [ 1824 | 1825 | 1826 | 1827 
 
 I 1820 I 1821 
 
 I 1828 I 1829 I 1830 | 1831 | ~ (1832 
 
 183;^ I 1834 I 1835 | | 1836 | 1837 I 1838 
 
 1839 I 
 
 1840 I 1841 I 1842 | 1843 | 
 
 1844 I 1845 j 1846 | 1847 | | 1848 I 1849 
 
 1850 I 1851 i I 1852 j 1853 | 1854 | 1855 
 
 I 1856 ( 1857 I 1858 | 1859 | 
 
 1864 
 
 1861 I 186 2 I 1863 | 
 1867 I 
 
 I 1860 
 
 1865 I 1866 
 
 I 1H68 I 1869 I 1870 | 1871 | 
 
 1872 I 1873 I 1874 | 1875 | | 1876 | 1877 
 ^878 I 1879 I I 1880 | 1881 | 1882 I 1883 
 
 1889 
 
 I 1884 I 1885 I 18>'6 | 1887 | 
 1890 I 1891 I 
 
 I 1888 
 
 I 1892 I 1893 I 1894 
 
 1895 I I 1896 I 1897 | 1898 | 1899 | 1900 
 1901 I 1902 I 19031 I 1904 | 1905 | 1906 
 
 1907 I I 1908 I 1909 | 1910 | 1911 | 
 1912 I 1913 I 1914 I 1915 | | 1916 j 1917 
 1918 I 1919 I j 1920 I 1921 | 1922 | 1923 
 I 1924 I 1925 I 1926 \ 1927 | fl928 
 
 1929 I 1930 I 1931 | | 1932 | 1933 | 1934 
 
 1935 I 
 
 1936 I 1937 I 1938 | 1939 | 
 
 1940 I 1941 I 1942 | 1943 | | 1944 | 1945 
 
 1946 I 1947 I I 1948 | 1949 | 1950 | 1951 
 
 i 1952 I 1953 I 1954 | 1955 | | 1956 
 
 Mo. I Tu. \ We. I Th. | Fr. | Sat. | g. 
 
 Tu. I We I Th. I Fr. | Sat. | g. ) Mo. 
 
 We. ( Th. I Fr. | Sat. | g. | Mo. | Tu. 
 'Hi. I Fr. I Sat. | g . | Mo. i Tu. I We 
 
 Fr. i Sat. I g. I Mo. | Tu. ( We. | Th. 
 
 Sat. I g. I Mo. I Tu. I We. | Th. | Fr. 
 "g. I Mo. I Tu. I We. I Th. | Fr. | Sat. 
 
 i 2 I 9 1 16 I 23 I 30 
 
 3 1 10 1 17 I 24 1 
 
 i 4 1 11 1 18 I 25 I 
 
 6 I 12 I 19 j 26 I 
 
 6 1 13 I 20 I 27 I 
 
 I 7 1 14 I 21 I 28 I 
 
 1 1 8 1 15 I 22 I 29 
 
 September. 
 
 October. 
 
 I 7 I 14 I 21 I 28 
 
 1 I 8 I 15 I 22 I 29 
 
 2 I 9 I 16 I 23 I 30 
 
 3 I 10 I 17 I 24 I 31 
 
 4 I 11 I 18 I 25 I 
 
 5 I 12 I 19 I 26 I 
 
 6 I 13 I 20 I 27 I 
 
 The Year and Days of the Week for both Months are in the same column. 
 
- ' .M il ■ 
 
 I 
 
 fr 
 
 ^. i 
 
1 
 
 COLUMBIA UNIVERSITY LIBRARIES 
 
 This book is due on the date indicated below, or at the 
 expiration of a definite period after the date of borrowing, as 
 provided by the rules of the T-iibrary or by special arrange- 
 ment with the Liibrarian in charge. 
 
 DATE BORROWED 
 
 DATE DUE 
 
 DATE BORROWED 
 
 1 
 DATE DUE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 C28(i141)m100 
 
 
 
 
 '^ 
 
 ( 
 
 D486 
 
 Ware, W. Powell 
 
 W22 
 
 Prof. Ware's $10,000 prize rule 
 for the equation of payments. 
 
 rP<^<^ 
 
 U/yy 
 
 Al9l 0\\oV\ 
 
 WAY nt|1994 
 
 I 
 
 COLUMBIA UNIVERSITY LIBRARIES 
 
 004141 
 
 7240 
 
 i 
 
 SEP 28 19** 
 
^■ 
 
 
 *^.>--' . : 'lS 
 
 W: 
 
 "-"««* 
 
 
 
 
 ■^■'^^f'ij^ii 
 
 ■m-i 
 
 s\: 
 
 
 
 ^ i^il 
 
 
 ^^# 'Jul 
 
 tr. V*. i 
 
 ^ 
 
 7S 
 
 > I* 
 
 t^'-i 
 
 #■:¥• 
 
 s^ 
 
 ^iS~*-"