Ex Librh 
 ■ C. K. OGDEN

 
 '.V^^' 
 
 \v>«r<ntM.AN
 
 RATIONAL 
 
 RECREATIONS 
 
 IN WHICH THE PRINCIPLES OF 
 
 NUMBERS 
 
 AND 
 
 NATURAL PPIILOSOPHY 
 
 ARE CLEARLY AND COPIOUSLY ELUCIDATED, 
 BY A SERIES OF 
 
 EASY, ENTERTAINING, INTERESTING 
 EXPERIMENTS. 
 
 AMONG WHICH ARK 
 
 ALL THOSE COMMONLY PERFORMED WITH 
 THE CARDS. 
 
 By W. HOOPER, m» d, 
 V O L. L 
 
 THE FOURTH EDITION, CORRECTED. 
 LONDON: 
 
 JfXiWTED FOR B. LAW AND SON, AVE-MARI A-LA NE ; AN» 
 e. C. A.HU J. KOa^NSON, PATER-NOSTER-ROW, 
 
 1794. , ^
 
 stack 
 
 Annex 
 
 ^ A 
 
 v.l 
 
 RATIONAL 
 
 R E C R E A T I O N S. 
 
 VOLUME THE FIRST. 
 
 ARITHMETICAL and MECHANICAL 
 EXPERIMENTS. 
 
 A %
 
 ADVERTISEMENT. 
 
 yf S the dejign of this work is to render ufe- 
 
 ful knowledge eafy and ejitertaining^ the 
 
 author has feleded the principal part of the 
 
 experiments from the writers on recreative 
 
 Philofophy of the laji and prefent centuries ; 
 
 from Baptifta Porta to Ozanam and Guyot ; 
 
 the laji, efpecially^ has furnijhed a large num^ 
 
 ber of reereations that are new and pleafng^ 
 
 and from him alfo are copied feveral figures 
 
 that the authors of the experiments they ex- 
 
 plain have only defcribed. 'The writers on 
 
 fleSlricity have alfo contributed a confidcrahle 
 
 quantity of recreations^ and fuch as for pie a- 
 
 fure and furprize are inferior to none. 'Though 
 
 this work is, in general, a compilation, fome 
 
 original experiments will be here found, and 
 
 the whole, perhaps, will appear to be delivered 
 
 with more perfpicuity and conci/iony and di' 
 
 » gefied
 
 u ADVERTISEMENT. 
 
 gejied In a manner more regular than has been 
 hitherto attempted, 1'he principles of each 
 
 fcience are, moreover, here latddozvn in afeiv 
 
 plain aphorlfmsj fuch as require no previous 
 knowledge, andvery little capacity or attention 
 to comprehend', fo that the reader will readily 
 dif cover, at the faine time that he admires the 
 
 phcenotnena, the fource from whence they prO" 
 ceed, and learn, that far from being marvellous 
 or incomprehenfible, they are the regular and 
 necejfary ejfe&s of the laws of nature* 
 
 INTRO.
 
 ■MnnamnMnDn 
 
 INTRODUCTION. 
 
 A MONG the various productions of 
 the prefs, thofe that are intended 
 for inftru (Stive entertainment feem to 
 deferve fome degree of attention, and 
 that as well from the difficulty as the 
 utility of the enterprize ; for though to 
 offer ufeful knowledge be fufficiently 
 eafy, yet to render that knowledge en- 
 gaging is oftentimes extremely difficult. 
 Man, carelefs, froward, ftubborn, vain, 
 impetuous, difdains the imputation of 
 a 2 igno-
 
 iv INTRODUCTION. 
 
 ignorance, and loaths the authoritative 
 di(51:ates of afTuming fuperiority. 
 
 Should wc not, therefore, endea- 
 vour to render ufeful learning, not 
 dull, tedious, and difguftful, not rug- 
 ged and perplexing, not auftere and 
 imperious, but facile, bland, delightful 
 alluring, captivating ? that Philofophy, 
 with his fober garb and folemn afpe6l, 
 when led by the hand of the fportive 
 nymph Imagination, decked in all the 
 glowing ever- varying colours of the Ikies, 
 may gain admittance to the parties of 
 the gay and carelefs; and while his 
 awful eye retrains the exuberance of 
 her fallies, the beams that dart from 
 her radiant front may play upon his 
 countenance, and diffipate the cloud 
 
 that
 
 INTRODUCTION. f 
 
 that too frequently hangs over his 
 brow. 
 
 Thus will the mind of man be pleaf- 
 ingly enlarged and fortified ; he will 
 unavoidably acquire a knowledge of his 
 own ignorance ; and by finding the fal» 
 lacy of what he thought moil certain, 
 the evidence of the fenfes, he will leani 
 to determine with caution on the feem- 
 ing convi£lions of the mind, and divefl 
 himfelf of thofe prepofTeffions, from 
 whence fo many of the evils of life 
 proceed. 
 
 Thus may he advance with tranquil 
 fleps through the flowery path of in« 
 veftigation, till arriving at fome noble 
 eminence, he beholds, with awful a- 
 ftonifhment, the inimenfe riches in the 
 a ^ boiu^d-^
 
 vl INTRODUCTION'. 
 
 boundlefs regions of fcience, and be- 
 comes animated to attain a ftill more 
 lofty ftation ; while his heart is incef- 
 fantly rapt with joys of which the gro- 
 velling herd have no conception, com- 
 pared with whofe ignorance, the infenfi- 
 bility of the blind and deaf, to the mofl 
 brilliant harmony of colours, or enchant- 
 ing melody of founds, are but trifling 
 imperfedlions. 
 
 Though this work is principally in- 
 tended for the rifing generation, yet 
 they whom a criminal indulgence of 
 their guardians, or a flavifh fubmif- 
 fion to their oWn tyrannic paiiions, have 
 plunged into fenfuality, till inceiTant fru- 
 ition hath produced an unconquerable 
 loathing, or till age hath deprived them 
 of appetite, and nought remains of 
 
 life
 
 INTRODUCTION. vii 
 
 life but a wretched hankering after en- 
 joyments they can never more obtain ; 
 even they will here find an entrance 
 to new pleafures ; they will fee, with 
 grateful admiration, that all-bounteous 
 Providence has flill in llore for them, 
 joys poignant yet tranquil, perpetually 
 increafing, yet never cloying, and that 
 it depends on themfelves ftill to pur- 
 fue, even to the utmoft verge of life, 
 a continual round of variegated plea- 
 fures. 
 
 To each volume is prefixed, a fhort 
 defeription of the plates contained there- 
 in, with a reference to the page where 
 they may be found ; and to the figures 
 in each plate, is annexed the page where 
 fuch figure is fully defcribed in the 
 work. 
 
 a 4 At
 
 viii INTRODUCTION. 
 
 At the end of each volume is added a 
 table of contents, in which is given a 
 regular abfl:ra6l of every article ; fo that 
 the reader, after having once perufed 
 the whole, by looking over the contents, 
 will readily remember how every recre» 
 ation is to be performed. 
 
 Dj:SCRIP-
 
 DESCRIPTION of the PLATES. 
 
 PLATE I. p. 20. 
 
 Fig. I. Neper's rods. There are eleven 
 of thefe rods placed perpendicular and 
 clofe to each other : on the firfl: is wrote 
 the nine digits, and on the lafl nine cy- 
 phers : the other nine contain a multi- 
 plication table. 
 
 Fig. 2. Exampleof the manner of plac- 
 ing the rods for multiplying and dividing. 
 
 Fig. 3. The Chinefe fwan pan. The 
 
 perpendicular lines within the fquare 
 if 
 
 A BCD reprefent bars, that divide it into 
 feven divilions. The five horizontal lines 
 in the upper divifions, and the feven hori- 
 zontal lines in the lower divifions, on 
 which are fmall black circles, reprefent 
 4 wires ;
 
 X DESCRIPTION of 
 
 wires ; the circles are balls moveable on 
 thofe wires, and by bringing them up to 
 the middle bar they exprefs the fum re- 
 quired. 
 
 PLATE II. p. 148. 
 
 The myflical dial. The inner circle 
 ILMN turns round on its center O, within 
 the other circle EFGH, fo that any letter 
 of the former may be placed ^gainft the 
 flrft letter of the latter, as fhall be agreecj 
 on. The letters of the one are then wrote 
 for thofe of the other, as in the example 
 under the figure. 
 
 PLATE III. p. 153. 
 
 The mufical cypher. The inner cir^ 
 cle ILMN, on which the notes are wrote, 
 turns round within the other circle, as in 
 the laft Plate, and the notes are here 
 wrote for the letters, as in the example 
 under the figure, 
 
 PLATE
 
 THE PLATES. xi 
 
 PLATE IV. p. i66. 
 
 Fig. I . The machine for vifual corre^ 
 {pondence ABCD, Fig. i, is a circle of 
 wood which turns on the centre G : «, b^ 
 r, d^ are pins by which it turns round. 
 Through its circumference are cut the 
 letters of the alphabet, and between A 
 and Z is an open Ipace, 
 
 Fig. 2, is the pole to which the circle 
 juft mentioned is placed by its centre, 
 near P. The board EF, at top, prevents 
 any letter from being leen, except that 
 diredly oppofite the Ipace in its middle, 
 
 Fig. 3, is the machine for auricular 
 correfpondence. The firings to the two 
 bells A and B, which are moveable on the 
 crofs-piece C D, are pulled one or more 
 times, according to the letter that anfwers 
 to the number of founds, 
 
 PLATE V. p. 178. 
 
 This plate contains the primary mecha-t 
 nic inftruments, or jnechanic powers. 
 
 Fig,
 
 xli DESCRIPTION of 
 
 Fig. 1,2,3,4, are levers of different kinds; 
 each of the other figures have their names 
 annexed to them. 
 
 PLATE VL p. 186. 
 
 Fig. I and 2. A dial to go without 
 wheels, Ipring, or weight. CD, Fig. i, 
 is the cylinder, the ends of whofe axis, as 
 they defcend, point to the hours marked 
 on the columns EF. 
 
 Fig. 2, reprefents the internal flruflure 
 of the cylinder, which confifts of five di- 
 vifions, in three of which there is water, 
 expreffed by the fhade. 
 
 Fig. 3 and 4. A dial to fhow the hour 
 ^y defcending an inclined plane. A B, 
 Fig. 3, the external appearance of the 
 dial : gy a hemiiphere, on which a figure 
 fits that points to the hour. 
 
 Fig. 4, the internal firudlure of the dial. 
 
 PLATE VII. p. 194. 
 
 Fig. I and 2, the infcru table lock. AB, 
 Fig. I , the fcutcheon to the lock ; C the 
 pinion by which it is fixed in any pofitlon. 
 
 ABCD,
 
 THE PLATES. xiii 
 
 ABCD, Fig. 2, the twelve wards of the 
 key, which turn round the pipe and are 
 fixed together by the fcrew E. 
 
 Fig. 3, the hand-mill to grind corn, 
 &c. inceflantly, without any animal force, 
 ABCD a fmoke-jack, that turns the rope 
 EF, by which the mill is kept in continu- 
 al motion, 
 
 PLATE VIII. p. 196. 
 
 Fig. I , a carriage to go without any ex- 
 ternal force. ABCD, the figure of the 
 carriage, with the perfon who rides in it, 
 and the footman who drives it. 
 
 Fig. 2, reprefents the machinery by 
 which it is moved, and which is concealed 
 in a box behind the carriage. C D are 
 two treddles that are pufhed down alter- 
 nately by the man behind the carriage, 
 and by means of the ropes C A, DA, 
 turn the wheels H, H, which being fixed 
 on the fame axis with the great wheels 
 I, I, turn them alfb. 
 
 PLATE
 
 j^iv DESCRIPTION of 
 PLATE IX. p. 200. 
 
 Fig. I. The catapulta. ABCD, the 
 frame in which the arrows are placed ; 
 E F the. fpring by which they are forced 
 out. G the poft to which the rope that 
 bends the fpring is faftened* 
 
 Fig. 2. The faiUng chariot; AB the 
 body of the chariot ; CD the fails ; E the 
 rudder, guided by the man at the helm A. 
 
 PLATE X. p. 206. 
 
 Fig. I. A carriage to fail againft the 
 wind. ABCD the body of the carriage ; 
 M the maft : GEFH the fails ; K the cog- 
 wheel, that takes the teeth placed perpen- 
 dicular to the fides of the fore-wheels ; 
 R the rudder by which it is guided. 
 
 Fig. 2. The uninvertible carriage. AB 
 the body of the carriage ; C the weight by 
 which it is kept always upright : FGDE 
 are iron circles in which it moves ; P the 
 door ; O the window, and Q^ the ihafts. 
 
 PLATE
 
 THE PLATES. XV 
 
 PLATE XL p. 212. 
 Fio;. I . The cafe of the columnar dial. 
 
 AC the capital, that contains the ftriking 
 part of this dial ; GH is the fhaft on which 
 are marked the hours ; H the index, that 
 by its defcent Ihows the hour. The hand 
 in the circle on the bafe B, points to the 
 minute. 
 
 Fig. 2, fhowsthe machinery of this dial. 
 A is the wheel that moves the minute 
 hand, and which is turned by the weicrht 
 B, to which is fixed the hour hand H. 
 F and G are two brafs wheels fixed on the 
 axis D E. The wheel F raifes the end M 
 of the lever MNO, and makes the other 
 end, to which the hammer P is fixed, to 
 ftrike the bell (^ 
 
 PLATE XII. p. 222. 
 
 Fig. I , is an air chronometer. AB is a 
 glafs tube ; CD the frame in which it is 
 placed ; E a pifton to let out the air ; F the 
 firing by which the piilon is drawn up ; 
 G the handle that confines the ftrine of 
 the piilon. Flo-.
 
 xvi DESCRIPTION, &c. 
 
 Fig. 2. Shows the form of the piflon in 
 the tube. 
 
 Fig. 3. A conical roller to receive the 
 firing to the index of a dial, when placed 
 over the tube. 
 
 Fig. 4. A lamp chronometer. A is a 
 fmall glafs lamp, placed in the fland B, 
 C the handle that fupports the ftyle H, 
 and frame DEFG, which is covered 
 with oiled paper, and on which are wrote 
 the figures for the hours. 
 
 Fig. 5. A no£lurnal dial. A and B are 
 two wheels of the fame dimenfion, and 
 concentral ; C a pinion : D and E two 
 wheels placed on the fame axis ; F a lamp 
 fixed on the edge of the wheel B ; G the 
 weight that gives motion to the whole 
 machine. 
 
 Fig. 6. Is a hollow cone, by which the 
 flame of the lamp F is confined to a par- 
 ticular part of the wheel A. 
 
 RATIONAL
 
 RATIONAL RECREATIONS. 
 
 ARITHMETIC. 
 DEFINITIONS. 
 
 WE fhall not here define the pri- 
 mary principles of numbers, as 
 our readers are fuppofed to underfland 
 the four firft rules of arithmetic, addition, 
 llibtra<5lion, multiplication, and divifion ; 
 we (hall therefore begin with arithmetic 
 powers. 
 
 I. By the powers of any number. Is 
 meant the feveral times that number is 
 multiplied into itfelf. Thus, if 4 be mul- 
 tiplied into itfelf, the product 1 6 will be 
 its lecond power, or fquare ; and if that 
 fum be multiplied by four, the produd 
 64 is the third power, or cube of 4, &c. 
 
 Vol. I. B 2. The
 
 2 RATIONAL 
 
 2. The root of any power is that num- 
 ber from whence it firft Iprung, or was 
 multiphed : fo the fquare root of 1 6 is 4 ; 
 and the cube root of 27 is 3. 
 
 3. When two numbers are compared 
 together, the firft is called the antecedent, 
 and the fecond the confequent ; and the 
 proportion thefe numbers bear to each 
 other is called their ratio. Thus, the ratio 
 of 27 to 9, is that of 3 to i. 
 
 4. When three numbers are compared 
 together, if the difference between each of 
 them be equal, as 2, 4, 6, or, 9, 6, 3, they 
 are faid to be in arithmetic proportion. 
 
 5. If three numbers be compared to- 
 gether, and they have one common ra- 
 tio, that is, the fame multiplier or divifor, 
 as 3, 9, 27, or 64, 16, 4, they are in geo- 
 metric proportion. 
 
 6. Whenever the confequent is double 
 the antecedent, they are faid to be in du- 
 plicate proportion ; but if the antecedent 
 -be double the confequent, they are in fub- 
 duplicate proportion. 
 
 7. When 
 
 2
 
 RECREATIONS. 3 
 
 7. When any feries of numbers conti- 
 nually increafes or decreafes by an equal 
 addition or fubtra£lion, as 2, 4, 6, 8, &c, 
 or 18, 15, 12, 9, &c. they arefaid to be in 
 arithmetic progreffion. 
 
 8. When a feries of numbers, continual- 
 ly increafes or decreafes by one common 
 multiplier or divifor, that is, by one com- 
 mon ratio, as 4, 8, 16, 32, &c. or 81, 27, 
 9, 3. they are in geometric progreffion. 
 
 9. If over a feries of numbers, in geo- 
 metric progreffion, there be placed an- 
 other in arithmetic progreffion, whofe 
 
 common difference is i, as thus ' ' ^' 
 
 J. S1.C., He ,..,„„„.„.:::: 
 
 16,32,) 
 
 dices or exponents of the former : and if 
 the geometric feries begin with i, the 
 other mufl begin with a cypher, thus, 
 
 1,2,4,8, 16, i 
 
 I o. The feveral different ways that one 
 
 number of quantities can be taken out of 
 
 another greater number, of the fame ort, 
 
 B 2 are
 
 4. RATIONAL 
 
 are called the combinations of the former 
 in the latter. Thus the different ways, 
 that three balls can be taken out of fix, 
 are the combinations of 3 in 6. 
 
 1 1 . All the different ways the whole of 
 any number of quantities can be taken or 
 difpofed, are called the permutations of 
 that number ; fo all the different ways 
 that fix counters can be placed in a line, 
 are the permutations of the number 6. 
 
 APHORISMS. 
 
 1 . If two even numbers be added toge- 
 ther, or fubtraded from each other, their 
 lum or difference will be an even number. 
 
 2. If two uneven numbers be added or 
 fubtra£led, their fum or difference will be 
 an uneven number. 
 
 3. The film or difference of an even 
 and uneven number will be an uneven 
 number, 
 
 4. The product of two even numbers 
 will be an even number ; and the product 
 of two uneven numbers will be an uneven 
 number. 
 
 5. The
 
 RECREATIONS. 5 
 
 5. The produd of an even and un- 
 even number will be an even num- 
 ber. 
 
 6. If two different numbers be divifi- 
 ble by any one number, their fiim and 
 their difference will be aifo divifible by 
 that number. 
 
 7. If feveral different numbers, di- 
 vifible by three, bemadded or multiplied 
 together, their fum and their produd 
 will alfo be divifible by 3. 
 
 8. If two numbers, divifible by 9, be 
 added together, the fum of the figures in 
 the amount will be either 9, or a number 
 divifible by 9. 
 
 9. If any number be multiplied by 9, 
 or by another number divifible by 9, the 
 amount of the figures of the produft 
 will be either nine, or a number divifible 
 by 9. 
 
 10. In every arithmetic progrefHon, if 
 double the fum of all the terms in any 
 feries be divided by the firft and lafl 
 term added . together, the quotient will 
 
 B 3 be
 
 6 RATIONAL 
 
 be the number of all the terms in that 
 feries*. 
 
 II. In 
 
 * This and the following aphorifm.^., relating to 
 progreflions, may be applied to many ufeful pur- 
 pofes befides thofe mentioned in the courfe of this 
 work. For example. 
 
 1. A man is to go a journey of ii2o miles, 4d 
 of which he propofes to ride the firft day, and to 
 increafe the number, by an equal addition, every 
 day to the laft, when he intends to ride loo miles. 
 How long will he be going his journey ? 
 
 You have here the firft term 40, the laft term 
 100, and the fum of all the terms 1200, to find the 
 number of terms: therefore, byaphorifm 10, if the 
 double of 1 1 20, that is 2240, be divided by 40 added 
 to 100, the quotient, which is 16, will be the num- 
 ber of terms, or days he will be going. 
 
 But> by the nth aphorifm, if the difference be- 
 tween the firft and laft term, that is 60, be divided by 
 the number of terms lefs i, which is 15, the quotient 
 4 will be the common difference, or number of 
 miles he muft add each day. 
 
 2. A father intends to lay up lol. toward his 
 daUgMer's portion, the day fhe is a year old, and to 
 increafe the fum as much every year as fhall make 
 her fortune, at the end of 20 years, loool. What 
 will he have to lay up the laft year ? 
 
 Here the firft term, number of terms and fum of 
 the feries are given, to find the laft term ; there- 
 fore,
 
 RECREATIONS. 7 
 
 II. In every fuch feries, if the difference 
 between the firfl and lafl term be divided 
 
 by 
 
 fore, by aphorifm I2, is from double the fum of the 
 feries, which is 2000, you fubtrad the produ6t of 
 the firft term, multiply by the number of terms, that 
 is 200, and divide the remainder, which will be 
 1800, by the number of terms, the quotient 90 is 
 the laft term, or number of pounds he muft lay up 
 the laft year. 
 
 3. A gentleman propofes to plant a number of 
 trees in his grounds, for 20 years together, in regu- 
 lar progreflion, 20 the firft year, and loo the laft. 
 How many trees will he plant ? 
 
 By aphorifm 13, if you multiply the firft and laft 
 term by the number of terms, and divide the fum 
 of the two products, which is 24.00, by 2, the quo- 
 tient 1200 is the number of trees he muft plant. 
 
 4. A landlord alks 5I. a year for an acre of land, 
 which the farmer thinking too much, the landlord 
 offers to let him a leafe of it, for 21 years, at id. 
 the firft year, 2d. the fecond year, 4d. the third, and 
 fo on, doubling the fum every year. What would 
 the farmer pay the laft year ? and what would be 
 the average rent for the whole term ? 
 
 Here the 20th term (which is to be confidered as 
 
 the laft, the firft term being one, which neither 
 
 multiplies nor divides) will be found by the 14th 
 
 aphorifm to be 1,048,576 pence, or 4369I. is. 4d. 
 
 B 4 which
 
 8 RATIONAL 
 
 by the number of terms, lefs i , the quo- 
 tient will be the common difference be- 
 tween each term of that feries, 
 
 12. If the produ<£l of the number of 
 terms multiplied by the firft term, be fub- 
 traded from double the fum of the feries, 
 and the remainder be divided by the num- 
 ber of terms, the quotient will be the lafl 
 term. 
 
 13. If the firfl and laft term be each 
 multiplied by the number of terms, and the 
 fum of the two products be divided by two, 
 the quotient will be the fum of the feries. 
 
 14. In every geometric progrellion, if 
 any two terms be multiplied together 
 
 which is the rent he will pay the laft year. But, 
 by aphorifm 15, to find the fum of the feries, the laft 
 term muft be multiplied by the ratio 2, which will 
 make it 2,097,152, and from that fum, the firft term 
 I, muft be dedu6led, when it will be 2,097,151, and 
 that fum is to be divided by the ratio 2 lefs i, that 
 is by I ; therefore it will remain the fame, and con^ 
 fcquently be the fum of the feries. Then dividing 
 2,097,151 by 21, the number of years, the quotient 
 99,864, or 41 61. 2s, will be the average rent for each 
 year. 
 
 their
 
 RECREATIONS. 9 
 
 their product will be equal to that terra 
 which anfwers to the fum of their two in- 
 dices. Thus, in the feries ' ' §' f ' ^* 
 
 2,4,8,16,32, 
 
 if the third and fourth terms, 8 and 16, 
 be multiplied together, the product 128 
 will be the feventh term of that feries. In 
 like manner, if the fifth term be multi- 
 plied into itfelf, the produ£l will be the 
 tenth term ; ajid if that fum be multiplied 
 into itfelf the produ£l will be the twentieth 
 term, &c. Therefore, to find the laft, or* 
 any other term of a geometric feries, it is 
 not neceffary to continue the feries be- 
 yond a few of the firft terms. 
 
 15. In any geometric feries, if you mul- 
 tiply the lafl term by the common ra- 
 tio, from the produd fubtra£l the firft 
 term, and divide the remainder by the 
 ratio, lefs i , the quotient will be the fum 
 of that feries. 
 
 16. In all combinations, if from an 
 arithmetic decreafuig feries, whofe firfl 
 ^erm is the number out of which the com- 
 binations
 
 lo RATIONAL 
 
 bitiatioiis- are to be formed, and whofc 
 common difference is i, there be tak' n as 
 many terms as there are quantities :o be 
 combined ; and thoie terms be mulciphed 
 into each other : and if from the feries, 
 I, 2, 3, 4, &c. there be taken the fame 
 number of terms, and they be multiphed 
 into each other, and the firft produdl be di- 
 vided by the fecond, the quotient will be 
 the number of combinations required. 
 Therefore, if you would know how many 
 ways four quantities can be combined in 
 feven, multiply the firft four terms of the 
 feries, 7, 6, 5, 4, &c. together, and divide 
 the product, which will be 840, by the 
 produd of the firft four terms of the fe- 
 ries, 1,2, 3, 4, &c. which is 24, and the 
 quotient 35 will be the combinations of 
 
 4 ii^ 7- 
 
 17. In all permutations, if the feries 
 I, 2, 3, 4, &c. be continued to as many 
 terms as there are quantities to be changed, 
 and thofe terms be multiplied into each 
 other, the produ£l will be the number of 
 permutations fought. Thus, if you would 
 
 know
 
 RECREATIONS. it 
 
 know how many permutations can be 
 formed with five quantities, multiply the 
 terms, i, 2, 3, 4, 5, together, and the 
 produd 1 20 will be the number of all the 
 permutations*. 
 
 Previous to the numerical Recreations, 
 we fhall here defcribe certain mechanical 
 methods of performing arithmetical opera- 
 tions, fuch as are not only in themfelves 
 entertaining, but will be found ufeful on 
 (everal occafions. 
 
 The ROMAN ABACUS. 
 
 ON a board about a foot long, and of 
 the form of ABCD in the follow- 
 ing figure, draw feveral lines, as ab^ cdy 
 efy ghy &c. the number of thefe lines 
 may be increafed at pleafure. 
 
 B 
 
 b 
 
 d 
 
 f 
 CL ID 
 
 * For farther examples of con b'nations and per- 
 inutations, fee Recreations XVIII. XIX. &c. 
 
 On 
 
 A 
 a 
 c 
 
 e 
 
 • 
 
 ''!'!!! '•'* 
 
 -•- 
 
 
 A A A ^ 1 
 
 • • w • ' -^ ^ w w "
 
 12 RATIONAL 
 
 On each of thefe lines, and on the fpaces 
 between them, there are to be placed a 
 certain number of counters, according to 
 the fum or quantity that is to be fet down. 
 The counters on the loweft line fland for 
 units, thofe on the fecond line for tens, 
 thofe on the third for hundreds, &c. and 
 the counters between the lines fland al- 
 ways for half the value of thofe on the 
 line next above. Therefore if you would 
 iet down 7684, you place four counters 
 on the loweft line, eight on the next 
 above, fix on the next, and feven on the 
 uppermofl line. Or you may fet down, 
 the lame fum by placing part of it on the 
 lines, and the reft between them, as 
 you fee in the figure. 
 
 To add or fubtradl by this iuftrument 
 is very eafy, as nothing more is neceffary 
 than to fet on, or take off, a certain num- 
 ber of counters ; or place thofe already on, 
 higher or lower, according to the fum 
 that is to be expreffed. 
 
 By
 
 RECREATIONS. 13 
 
 By this invention a perfon who has not 
 learned to write may fet down any fiim of 
 money, or other quantity whatever ; for 
 the counters on the feveral lines inflead 
 of tens, hundreds, &c. may ftand for hun- 
 dred weights, quarters, pounds ; or for 
 years, months, days, hours, &c. and, ac- 
 cording to the length of the board, feve- 
 ral fums of different denominations may 
 be fet down at the fame time. 
 
 N E P E R's RODS. 
 
 DIVIDE a fquare piece of brafs, ivory, 
 orpafteboard, as A BCD, (PI. I. 
 Fig. I.) iuto ninety-nine equal parts, as 
 
 in the figure : in the nine parts next the 
 left hand write the nine digits ; in thole 
 next the right hand write nine cyphers, 
 and in thofe at top the nine digits. Se- 
 parate the remaining divifions into two 
 parts, by a line drawn from the upper 
 angle on the right fide, to the lower angle 
 on the left, and on thefe divifions write 
 
 the
 
 14 RATIONAL 
 
 the multiplication table, obferving when 
 there are two figures, to place the units in 
 the right hand diviiion, and the tens in the 
 left. Then feparate the eleven columns by 
 cutting them afunder from top to bottom, 
 and you will have Neper's rods or bones*. 
 
 Thefe rods are to be placed in a box of 
 the length and depth of the fquare ABCD, 
 and wide enough to hold fix., nine, or as 
 many more of each fort as you pleafe. The 
 uppermofl figure of each rod mufi {land out, 
 above the box, that it maybe eafily diflin- 
 
 cmifhed. The rods have fometimes fi- 
 
 o 
 
 eures on each of their four fides to anfwer 
 
 o 
 
 different purpdes. On the front of the 
 box there mufl be a ledge to fupport the 
 rods as they are taken out and placed in 
 order. 
 
 To multiply any fum by thefe rods, 
 fuppofe 5487 by 273, firft, take out the 
 
 * So called from the inventor J. Neper, baron of 
 Merchifton in Scotland. 
 
 index
 
 RECREATIONS. 15 
 
 index rod of digits next the left hand, and 
 place it againfl the ledge ; then take each 
 of thofe rods that have at top one of the 
 figures of the multiplicand, beginning with 
 the figure 5, and place them in order as you 
 will fee in PI. I. Fig. 2. You are then to fet 
 down the fum that ftands againft each figure 
 of the multiplier, with this caution, that 
 when there are two figures in any fquare, 
 you are to add that in the left divifion to the 
 figure in the right divifion of the follow- 
 ing fquare, beginning with the right hand 
 column. For example, in the column 
 that ftands againfl 3 in the digits (Fig. 2.) 
 you firfi: fet down the 8, and carrying the i 
 to the 4 in the next divifion, you fet down 
 5 ; then adding the 2 on the fecond divi- 
 fion to the 2 in the third, you fet down 
 4; then adding i to 5, you fet down 
 6, and laflly the figure i. This may be 
 done almoft as fafi: as you can copy the 
 figures ; and fo of the other figures in the 
 multiplier, and the operation will ftand as 
 follows : 
 
 5486
 
 i(^ RATIONAL 
 
 5486 
 273 
 
 16458 
 38402 
 10972 
 
 1497678 
 
 To divide by thefe rods, iuppofe 
 748524 by 2793, place the rods that con- 
 tain the feveral figures of the divifor, with 
 the index rod, in the fame manner as in 
 the lafl example, and you will have the 
 product of that divilbr by each of the 
 nine digits. Then take the firfl four fi- 
 gures of the dividend 7485, and look for 
 that number on the rods which is the next 
 lefs to it ; which you will find to be 
 5586, that ftands againfl the figure 2 ; you 
 therefore put 2 for the quotient, and fub- 
 trading the lad number from the firfl, 
 bring down another figure from the divi- 
 dend. You then look again for the nearefl 
 fum to that, and fo on till you have taken 
 down all the figures of the dividend, 
 
 when
 
 J 
 
 RECREATIONS. 17 
 
 when you will find the whole quotient to 
 be 268. 
 
 The CHINESE SWAN PAN. 
 
 TN the fquare frame of wood, ABCD, 
 (PI. I. Fig. 3.) make four divifions by 
 the bars, EF and GH ; and feparate three 
 of thefe divifions into two parts by the 
 lefTer bars, a b. In each of the fmaller 
 divifions place wires, to be taken out at 
 pleaHire ; and on each of the wires in the 
 left-hand divifions, firing a fmall ivory 
 ball, or large bead ; and on the wires on 
 the right hand divifion, place four fuch 
 balls, or beads. 
 
 The balls in the left hand divifions, 
 when brought up to the middle bar, 
 ftand each for five ; and thofe in the 
 right divifions, when brought to the bar, 
 ftand for unit^. 
 
 The balls ih the two lower divifions 
 
 reprefent integers, or the whole of any 
 
 Vol. I. G quan-
 
 ta RATIONAL 
 
 quantity ; thofe on the uppermoil: wire 
 fland for tens of fuch integers, the next 
 for hundreds, and fo on, as is exprefled, 
 in the figure. The wires in all the divi- 
 fions, may be increafed to any number 
 yoii' think proper. 
 
 The balls in the four upper divifions 
 f eprefent parts of integers ; thofe in the 
 two divifions next the left hand ftand for 
 tens ; and thofe in the two other divi- 
 fions^ for units of fuch parts.* 
 
 Now if the fum you would fet down be 
 integers, begin with the balls in the two 
 lower divifions ; for example, on the 
 third row from the top bring tVx'o balls, 
 of the right hand divifion, up to the mid- 
 dle bar (fee the Figure) ; then bring up 
 two on the next row, and one on the fame 
 row in the left divifion ; next four on the 
 
 top 
 
 * This is not the original Swan Pan mentioned 
 by Du Halde, in his Hiltory of China, but an im- 
 provement on that by M. G. Smethurft, of Man- 
 thcfter. publillieJ in the Gent. Mag. for 1748.
 
 RECREATIONS. 19 
 
 top row, and one on the other fide of the 
 fame row ; then in the firfl row of units, 
 from the bottom, and in the right hand 
 divifion, place two balls, on the fecond 
 row one, and one alfo on the fame line in 
 the right hand divifion of tens : laftly, on 
 the third row of units place three balls. 
 The balls being thus placed, if the inte^ 
 gers be pounds flierling, they will exprefs 
 279I. 28. ii|d. If the integers be hundred 
 weights, the fum will be 279 cwt. 2 qrs. 
 1 1 lb. 30Z. or if they be years, they will de- 
 note 279 years, 2 months, 1 1 days, 3 hours. 
 
 A part of thefe balls may reprefent frac- 
 tions, either vulgar or decimal ; the balls 
 in the iirft two divifions of parts may 
 fland for the numerators, and thofe in 
 the other two for denominators ; or the 
 numbers' in either of thefe divifions may 
 be added to thofe in the integers, as de- 
 cimals.* 
 
 * There may alfo be holes made in the bars where 
 the dots are placed, in which pegs may be occafionally 
 put, to ftiew that thofe numbers fland for fradions. 
 
 C2 By
 
 20 RATIONAL 
 
 By this inftrument all the operations of 
 arithmetic may be readily performed : fup- 
 poie, for example, you would multiply the 
 fum fet down in the divifion of inteo:ers, 
 that is 279 by 3. Begin with the lowed 
 line, and fay 3 times 2 is 6, therefore fet 
 that number up ; then on the next row, 
 fay 3 times 7 is 21, therefore inftead of 7 
 fet up I on that line, and carry the 
 two tens to the line below, which will 
 mrke the number there 8. Then at the up- 
 per line fay 3 times 9 is 27, therefore fet 
 7 on that line, and carry 2 .to the next line 
 below, which will make that number 3. So 
 that the balls on the three lines will then 
 exprefs 837. 
 
 . If you would divide 279 by 3, begin in 
 like manner with the lowefh line ; but as 
 3 cannot be taken in 2, you add the next 
 number to it, and fay the threes in 27 
 are 9, therefore fet back the 2 on the loweft 
 line, and place 9, inftead of 7, on the 
 next line above; then at the uppermoll: 
 
 line
 
 Plat E.I. 
 
 F/^ . /./il3
 
 "1 
 
 />-/,/ 
 
 
 Fa,. 
 
 - r 
 
 ,i 
 
 / 
 
 5\S\a\ '! 
 
 2 
 3 
 
 
 J 
 
 2,„''„-;'3e|-_, 
 
 J! 
 
 J,. 
 
 \^^^ 
 
 .i J 
 
 6 
 
 'V 
 
 ''4 
 
 ■^3 
 
 ?ff 
 
 7 
 
 '-''.5 
 
 % 
 
 % 
 
 % 
 
 8 
 
 fo 
 
 % 
 
 % 
 
 % 
 
 9 
 
 ^i 
 
 3/ 
 
 % 
 
 % 
 
 F.'/.r, 
 
 r
 
 RECREATIONS. 21 
 
 line fay, the threes in 9 are 3 ; therefore 
 inftead of 9 place 3 on that hne, and con- 
 fequently the quotient will be 93. When 
 there is a remainder it may be placed with 
 the divifor, as a fradlion, in the upper di- 
 viiions. When there are many figures in 
 the multiplicand and multiplier, the latter 
 may be placed in the two firfl divifions of 
 parts, and the former and products in the 
 divifions of integers. In like manner, when 
 there are feveral figures in the dividend 
 and divifor, the former may be placed in 
 the divifion of integers, the latter in the 
 firfl two divifions of parts, and the figures 
 of the quotient as they rife, in the re- 
 maining two divifions. 
 
 Iris well worth obferving, that by means 
 of this inflrument a blind man may be 
 taught to add, fubtrad, multiply, divide, 
 and perform all the other operations of 
 arithmetic, with as much certainty as an- 
 other perlbn can by figures. 
 
 C3 RECRE=
 
 22 RATIONAL 
 
 RECREATION I. 
 
 Any number being named^ by adding a figure 
 to that number to make it diviftble by 
 nine, 
 
 TF the number named be, for example, 
 72,857, you tell him whc names it to 
 place the number 7 between any two fi- 
 omres of that fum, and it will be divifible 
 by 9. For by aphorifm 9, if any number 
 be multiplied by 9, the fum of the figures 
 of the product will be either 9, or a num- 
 ber divifible by 9. But the Him of the 
 figures named is 29, therefore 7 muft be 
 added to it to make it divifible by 9. 
 
 You may diverfify this recreation, by 
 fpecifying, before the fum is named, the 
 particular place where the figure fhall be 
 inferted, to make the number divifible 
 by 9. 
 
 RECRE-
 
 RECREATIONS. 23 
 
 RECREATION IL 
 
 A per/on having an even riumber of counters 
 in one hand^ and an odd number in the 
 other ^ to tell in which hand the odd or even, ■ 
 number is, 
 
 T ET the perfoii multiply the number 
 in his right hand by an odd number, 
 and the numl>er in his left hand by an even 
 number, and tell you if the flim of the 
 products added together be odd or even. 
 If it be even, the even number is in the 
 right hand ; but if it be odd, the even 
 number is in the left hand : as is evident 
 from the firfl five aphorifms, 
 
 iLxample, 
 I. Number in the 7 o t ^t, 1 r 
 right hand V^ I« the left 7 
 
 Multipliers 3 2 
 
 54 H 
 
 14 
 
 Their fum 68 
 
 C 4 2. Num-
 
 24 RATIONAL 
 
 2. Number in thej j^ ^j^^ j^^^ ^g 
 right hand 3 ' 
 
 Multipliers 3 2 
 
 21 36 
 
 36 
 
 Their fum 5 7 
 
 RECREATION III. 
 
 A perfon making choke of fever al numbers^ 
 another fhall name him the number by 
 'which the fum of thofe numbers is divi- 
 fible, 
 
 pROVIDE a fmall bag, divided into 
 two parts : in one part put feveral 
 tickets, on each of which is wrote a num- 
 ber divifible by three, as 6, 9, 15, '2^(^^ 62,^ 
 120, 213, 309, &c. and in the other part 
 put tickets marked with the number 3 only. 
 From the firft part draw a handful of 
 tickets, and after fhewing them, put them 
 in again ; then open the bag, and defire 
 any one to take out as many tickets as he 
 
 thinks
 
 RECREATIONS. 25 
 
 thinks proper ; fhut the bag, and when 
 you open it again offer the other part to 
 another perfon, tellfng him to take out 
 one ticket only : you then pronounce that 
 ticket to contain the number by which the 
 amount of the other numbers is divifible. 
 For each of thofe numbers being diviiible 
 by 3, their fum alfo, by aphorifm 7, mufl 
 be diviiible by the fame number. 
 
 R E C R E A T I O N IV. 
 
 To find the difference between two numbers ^ 
 the greatefi of which is unknown, 
 
 ^ I ^ A K E as many nines as there are 
 figures in the fmallefl number, and 
 fubtracl that fum from the number of 
 nines. Let another perfon add that dif- 
 ference to the largeft number, and taking 
 away the frfl figure of the amount, add 
 it to the iaft figure, and that fum will be 
 the difference of the two numbers.* 
 
 * S'.e the eighth aphorifm. 
 
 For
 
 26 RATIONAL 
 
 For example, Matthew, who is 22, tells 
 Henry, who is older, that he can difcover 
 the difference of their ages ; he therefore 
 privately deducts 22 from 99, and the dif- 
 ference, which is 77, he tells Henry to 
 add to his age, and to take away the firfl: 
 fisrure from the amount, and add it to the 
 laft figure, and that lad fum will be the 
 difference of their ages. As thus : 
 
 The difference between Matthew's? 77 
 
 age and 99 is , 3 
 
 To which Henry adding his age 35 
 
 The fum is 1 1 ^ 
 
 I 
 
 Then by taking away the firft fi-^ 
 
 gure I and adding it to the lafl > 13 
 figure 2, the fum is J 
 
 Which added to Matthew's age 22 
 
 Gives the age of Henr^-, which is 25 
 
 RECRE^
 
 RECREATIONS. 27 
 
 RECREATION V. 
 
 To /<?//, by the dial of a ivatcb, at what hour 
 any perfon intends to rife. 
 
 T ET the perfon fet the hand of the 
 dial to any hour he pleafe, and tell 
 you what hour that is, and to the number 
 of that hour you add, in your mind, 12. 
 Then tell him to count privately the num- 
 ber of that amount upon the dial, begin- 
 ning with the next hour to that on which 
 he propofes to rife, and counting back- 
 wards, firft reckoning the number of the 
 hour at which he has placed the haiKl, 
 An example will make this plain. 
 
 Suppofe the hour at which he intends to 
 rife be 8, and that he has placed the hand 
 at 5. You add 12 to 5, and tell him to 
 count 17 on the dial, firft reckoning 5, 
 the hour at which the index flands, and 
 counting backwards from the hour at 
 which he intends to rife, and the number 
 
 17
 
 28 RATIONAL 
 
 17 will neceflarily end at 8, which fhews 
 that to be the hour he chofe. 
 
 That the hour at which the countingr 
 
 o 
 ends muil: be that on which he propofed 
 
 to rife, will be evident on a little refledlion ; 
 for if he had began at that hour and count- 
 ed 12, he would neceflarily have come to 
 it again; and calling the number 17, by- 
 adding 5 to it, only ferves to difguife the 
 matter, but can make no fort of difference 
 in the counting-. 
 
 RECREATION VI. 
 
 A per/on chiiftng any two, out of feveral 
 given numbers, and after adding them to- 
 gether Jir iking out one of the figures from 
 the amount, to tellyouwhat that figure was, 
 
 CUCH numbers mufl be offered as are 
 
 divifible by 9 ; and when any two of 
 
 them are added together there mufl be no 
 
 cypher in the amount : the figures of that 
 
 amount,
 
 RECREATIONS. 29 
 
 amount, moreover, mufl: make either 9 or 
 18. Such are the numbers following; 
 36,63, 81,117, 126, 162, 207, 216, 252, 
 261, 306, 315, 360, and 432. 
 
 Thefe numbers mufl: be wrote on cards ; 
 and when any two of them are added to- 
 gether, if a figure be flruck out of the 
 fum, it will be what would make the other 
 figures either 9 or 18. For example; if a 
 perfon chofe 126 and 252, their fum will 
 be 378, from which if heftrikes out the 7, . 
 the remaiiiing figures 3 and 8 will make 
 1 1, to which 7 mufi: be added to make 18. 
 
 RECREATION VII. 
 
 'Two perfons chufmg two numbers^ a?id mul- 
 tiplying them together, by knowing the lajl 
 figure of the product to tell the other 
 figures, % 
 
 T F the number ^2> ^^ multiplied by the 
 
 numbers of the following arithmetical 
 
 progreffions, 3, 6, 9, 1 2, 1 5, 1 8, 2 1 , 24, and 
 
 27, 
 
 4
 
 30 RATIONAL 
 
 27, their produ6ls will terminate with the 
 nine digits in this order, 9, 8, 7, 6, 5, 4, 
 3, 2, I ; the numbers being as follows, 219, 
 
 438, (ssh S76, 1095, 1314, 1533' ^nS''-^ 
 1971 ; therefore put into one of the divi- 
 iions of the little bag, mentioned in the 
 third Recreation, feveral tickets marked 
 with the number ^-^-i '^^^ '^^ the other 
 part of the bag the numbers 3, 6, 9, 12, 
 15, 18, 21, 24, and 27. 
 
 Then open that part of the bag where 
 are the numbers 73, and defire a perfon 
 to take out one ticket only, then dex- 
 troufly change the opening, and defire 
 another perlbn to take a ticket from that 
 part, and when you have multiplied their 
 two numbers together, by knowing the 
 lafl figure of the produd you will readily 
 tell them by the foregoing feries, what 
 the other figures are. 
 
 RECRE-
 
 RE CREATIONS. 31 
 
 RECREATION VIIL 
 
 'J be Magical Century, 
 
 T F the number 1 1 be multiplied by any 
 one of the nine digits, the two figures 
 of the produd will always be fimilar. As. 
 follows : 
 
 II II II II II II II II II 
 123456789 
 
 II 22 -2,-2, 44 SS 66 77 88 99 
 Place a parcel of counters on a table, 
 and propofe to any one to add, alternate- 
 ly, a certain number of thofe counters, 
 till they amount to a hundred, but never 
 to add more than 10 at one time. You 
 tell him, moreover, that if you flake firfl 
 he fhall never make the even century, but 
 you will. In order to which you muft firfl 
 flake I, and remembering the order of the 
 above feries, 11, 22, '2^2^^ &c. you con- 
 flantly add, to what he flakes, as many as 
 will make one more than the numbers of 
 that feries, that is, as will make 1 2, 23, 34, 
 6 &c.
 
 32 RATIONAL 
 
 Sec. till you come to 89, after which the 
 other party cannot make the century him- 
 felf or prevent you from making it. 
 
 If the other parly has no knowledge of 
 numbers, you may flake any other num- 
 ber firft, under 10, provided you take 
 care to fecure fome one of the lafl terms, 
 as 56, 6y, 78, &c. 
 
 This Recreation may be performed with 
 other numbers ; and in order to fucceed, 
 you mufl divide the number to be attain- 
 ed, by a number that has one digit more 
 than what you can flake each time, and 
 the remainder will be the number you 
 mufl firft flake. Obferve that, to be fure 
 of fuccefs, there mufl be always a re- 
 mainder. Suppofe for example, the num- 
 ber to be attained is 52, making ufe of a 
 pack of cards, inflead of counters, and that 
 you are never to add more than 6 ; then 
 divide 52 by the next number above 6, 
 that is, by 7, and the remainder, which 
 
 is
 
 RECREATIONS. 33 
 
 is 3, will be the number you mufl: ftake 
 firft ; and whatever the other ftakes, you 
 mull: add as much to it as will make it 
 equal to the number by which you di- 
 vided, that is, 7. Therefore if his firil 
 flake be i, you muft ftake 6, &c. fo that 
 your fecond flake will make the heap 10, 
 your third ftake will make it 17, and fo 
 on, till you come to 45, when as he can- 
 not flake more than 6, you mufl make 
 the number 52. 
 
 In this, as in the former cafe, if the 
 other perlbn have no knowledge of num- 
 bers, you may ftake any number firfl un- 
 der 7 ; or you may let him ftake firft, only 
 taking care to fecure either of the num- 
 bers 10, 17, 24, 31, &c. after which he 
 cannot make 52, if you conftantly add as 
 many to his ftake as will make it 7. 
 
 Vol. I. D RECRE-
 
 34. M A T I O isr A L 
 
 IlECHEATION IX. 
 
 ne Cotjfcdcrate Counters, 
 
 pRESENT to three perfons a ring, a? 
 leal, and a IhufF-box, of which defire 
 each perfon to chufe one, privately. The 
 three perfons you difcriminate in your 
 mind by the letters A, E, I, and by the 
 fame letters you diflinguifh the ring, the 
 feal, and the box. Provide 24 counters, 
 of which give the firll perfon A, i, the fe- 
 cond perfon E, 2, and the third perfon I, 
 "1, Put the 18 rertiainino- counters on the 
 table ; and let him that has the ring take 
 as many counters more as he already has ; 
 liim that has the feal take twice as many 
 as he has, and him that has the box four 
 times as many. While they are taking 
 the counters you retire out of fight, and 
 when they have done you return, and 
 cafling your eye on the table, take notice 
 how many counters are left, 
 
 Thf
 
 RECREATIONS. 35 
 
 The remaining counters will be either 
 I, 2, 3, 5, 6, or 7, which you are to re- 
 fer to the vowels in the fyllables of the 
 following verfe : 
 
 1235 6 
 
 J^arfer — Cefar — ^ja dis — de vint — si grand 
 7 
 prince. 
 
 If there be but one counter left, the two 
 vowels in the fyllables par fer denote that 
 the firft perfon has the ring, to which you 
 have affigned the letter A ; the fecond 
 perlbn has the feal, to which you have 
 affigned the letter E ; and coniequently 
 the third perfon muft have the box. In 
 like manner, if there be fix counters re- 
 maining^, the two vowels in the fvllables 
 Ji grand ^ fhew that the firft perfon has the 
 box, denoted by the letter I ; the fecond 
 perfon has the ring, to which the letter A 
 is affigned ; and confequently the third 
 perfon has the feal : and fo of the reft. 
 
 D 2 It
 
 ^6 RATIONAL 
 
 It appears by aphorifm i6, that the 
 three articles can be taken only fix dif- 
 ferent ways. Now each of thefe ways 
 lecefTarily changes the number of counters 
 to be taken by the three perfons : from 
 whence it follows, that the counters re- 
 maining on the table will alfo be of ftx 
 different numbers ; the vowels in the fyl- 
 lables of the verfe ferve only to aid the 
 memory in difcovering the manner in 
 which the three articles are taken. 
 
 RECREATION X. 
 
 A pcrfon privately fixing on miy nwnher^ to 
 tell h'lm that number. 
 
 FTER the perfon has" fixed on a num- 
 ber, bid him double it and add 4 to 
 that fum, then multiply the whole by 5 j 
 to the product: let him add 12, and mul- 
 tiply the amount by 10. From the fum 
 of the v/hole let him dedud 320, and tell 
 you the remainder, from which, if you 
 
 cut
 
 RECREATIONS. 37 
 
 cut off the two laft figures, the number 
 that remains will be that he fixed on. 
 
 Example, 
 
 Let the number chofe be — — ■ 7 
 
 Which doubled is — — 14 
 
 And 4 added to it makes — — 18 
 
 Which multiplied by 5, gives — 90 
 
 To which 12 being added, it is 102 
 
 That multiplied by 10, makes 1020 
 
 From which dedutlinfj; ^20, the] 
 
 remanider is — — \ ' 
 
 And by ftriking off the two cy-l 
 
 phers, it becomes the original \ 7 
 
 num.ber — ' — J 
 
 RECREATION XL 
 
 'Three dice being thrown on a table^ to tell the 
 number of each of thetn, and the order in 
 which they f and. 
 
 ET the perfon who has thrown the dice 
 double the number of that next his 
 left hand, and add 5 to that ilim ; then mul- 
 tiply the amount by 5, and to the produ6l 
 adcl the nuiinber of the middle die ; then let 
 D 3 the
 
 ^S RATIONAL 
 
 the whole be multiplied by lo, and to that 
 product add the number of the third die. 
 From the total let there be fubtradled 250, 
 and the figures of the number that re- 
 mains will anfwer to the points of the 
 three dice as they ftand on the table. 
 Example, 
 Suppofe the points of the three dice 
 thrown on the table to be 4, 6, and 2. 
 Then the double of the firft die will be 8 
 To which add — — — 5 
 
 5 
 
 That fumbe multiplied by 5 will be 65 
 To which add the number of the? >^ 
 
 middle die — — 5 — < 
 
 And multiply the fum by i o 
 
 710 
 To that produ£l add the number") 
 
 of the third die — — 5 — - 
 
 712 
 And from the total fubtra6:ing 250 
 
 The three remaining figures 462 
 
 will anfwer to the numbers on the dice, 
 
 and ihew the order in which (hey fl:and. 
 
 RECRE^
 
 RECREATIONS, 39 
 
 RECREATION XII. 
 
 To tell the number a per/on has fixed on, 
 without ajkmg him any quejiions. 
 
 npHE perfon having chofe any num- 
 ber from I to 15, he is to add 21 to 
 that number, and triple the amount. Then 
 
 1. He is to take the half of that triple, 
 and triple that half. 
 
 2. To take the half of the lafl triple, 
 and triple that half. 
 
 3. Take the half of the laft triple, 
 
 4. Tak^ the half of that half. 
 
 In this operation it appears there are 
 four cafes or ftages where th? half is to be 
 taken : the three firft are denoted by one 
 of the eight following Latin words, each 
 word being compofed of three fyllables, 
 and thofe that contain the letter /, refer to 
 thofe cafes* where the half cannot be taken 
 
 * Thefe cafes being d Liferent in all the numbers 
 tliat <;an l?e <?hole, they are thereby 4i{Unguiihed. 
 
 D 4 without
 
 40 R A T I O N x\ L 
 
 without a fradtion ; therefore in thofe cafes 
 the perfon who makes the deduction is to 
 add I to the number to be divided. The 
 fourth cafe fhews which of the two num- 
 bers annexed to every word, has been 
 chofen ; for if the fourth half can be 
 taken, without adding i, the number 
 chole is in the firrc cohimn, but if not, it 
 is in the iecond column. 
 
 The words. The numbers they denote. 
 
 Mi-fe-ris 
 
 8 
 
 
 
 Ob-tin-git 
 
 I 
 
 9 
 
 Ni-mi-um 
 
 2 
 
 10 
 
 No-ta-ri 
 
 3 
 
 II 
 
 In-fer-nos 
 
 . 4 
 
 12 
 
 Or-di-nes 
 
 13 
 
 5 
 
 Ti-mi-di 
 
 6 
 
 H 
 
 Te-ne-ant 
 
 15 
 
 7 
 
 'Example^
 
 K E C R E A T I O N S. 41 
 
 Example. 
 
 Siippofe the number choie to be 5 
 
 To which is to be added i 
 
 10 
 
 Then the triple of that number is 30 
 
 The half of which is 15 
 
 The triple of that half mufl be 45 
 
 And the half of that * 23 
 
 The triple of that half 69 
 
 The half of that * ^^ 
 
 And the half of that half* 1 8 
 
 While the perfon is performing the 
 operatioji, you remark, that at the fe- 
 cond and third fliage he is obliged to add 
 I . and confequently that the word ob-iin- 
 git, in the fecond and third fyllables of 
 which is an /', denotes that the number 
 muft be either i or 9 ; and by obferving 
 that he cannot take the laft half without 
 adding i, you know that it muft be the 
 
 * At all the ftnges thus marked, i mufi: be added 
 }|) order to take the half without a frafiion- 
 
 number
 
 42 RATIONAL 
 
 number in the fecond column. If he 
 fhould make no addition at any one of the 
 four ftages, the number he chofe muft be 
 15, as that is the only number that has no 
 fradion at either of the diyifions, 
 
 RECREATION XIIL 
 
 ^hlrty foldiers having deferted^ fifi'^^^ tf 
 whom are to be punijhed', fo to place th? 
 whole number In a ring^ that you mayfave 
 any fifteen you pleafe^ and it Jhall feem 
 to be the effed of chance, 
 
 nPHE men muft be placed according tq 
 the numbers annexed to the vowels 
 in the words of the following verfe : 
 
 Po-pu-le-am vir-gam ma-ter re-gi-na 
 
 4521 3 J ; 2 2 3 I 
 fe-re-bat. 
 
 2 2 1 
 
 Therefore you place 4 of" thofe you would 
 fave firft, then 5 ci thofe you would pu- 
 liifh, then 2 of thofe to be favcd, and i
 
 RECREATIONS. 43 
 
 to be punifhed; and fo on.* You then 
 enter the ring, and beginning with the 
 firft of the four men you intend to fave, 
 you tell 9, and the ninth man is turned 
 out to be punifhed. You go on telling g 
 more, and the fecond 9 will fall on pnq 
 you intend to punifh ; and fp of the reft. 
 
 RECREATION Xiy. 
 
 So?ne perfon in company having pit a rinz 
 privately on one of \hh fingers ; to name 
 the perfon, the hand, the fiftger, and the 
 joint, on which it is placed. 
 
 T ET a third perfon double the number 
 of the order in which he ftands who 
 has the ring, and add 5 to that number j 
 then multiply that fum by 5, and to the 
 product add 10. Let him next add i to 
 the laft number if the ring be on thg ^ight 
 hand, and 2 if on the left, and multiply 
 \\\.Q whole by 10 : to t^iis produ^^t he mufl 
 
 * You will obferve that each vowel denotes the 
 |}umber that is to be placed, as « i, f 2, i 3, &:c. 
 
 add
 
 44 RATIONAL^ 
 
 add the number of the finger (counting 
 the thumb as the firfl finger) and multiply 
 the whole again by lo. Let him then 
 add the number of the joint ; and, laflly, 
 to the whole join ^5- 
 
 He is then to tell you the amount of 
 the whole, from which you are to fubtraft 
 3<35, and the remainder will confifl of 
 four figures, the firfl of which will ex- 
 prefs the rank in which the perfon flands, 
 the fecond the hand (the number i figni- 
 fying the right hand, and 2 the left,) the 
 third number the finger, and the fourth 
 the joint. 
 
 Exmnple, 
 
 Suppofe the perfon w ho flands the third 
 in order has put the ring upon the fecond 
 joint of the thumb of his left hand ; then 
 
 The
 
 RECREATIONS. 45 
 
 The double of the rank of the 7 , 
 
 thu'd perfon is 5 
 
 To which add 5 
 
 II 
 
 Multiply the fum by 5 
 
 55 
 To which add 10 
 
 And the number of the left hand 2 
 
 67 
 
 Which being multiplied by 10 
 
 670 
 To which add the number of the thumb i 
 
 671 
 And multiply again by 10 
 
 6710 
 Then add the number of the joint 2 
 
 And laftly the number 25 
 
 ^747 
 From which deducting 3535 
 
 The remainder is 3212 
 
 Of w^hich, as we have faid, the 3 denotes 
 the third perfon, the 2 the left hand, the 
 I the thum.b, and the laft 2 the fecond joint. 
 
 OF
 
 4& RATIONAL 
 
 Of arithinetica! magic fquarcs. 
 
 A jMagical fquare of this fort conlifls of 
 numbers in arithmetic progreffion, 
 fb dilpofed in parallel and equal ranks, 
 that the fum of each row, taken either 
 perpendicularly, horizontally, or diago- 
 nally, is equal ; as in the fecond figure. 
 
 Fig. I. 
 
 Fig. 2. 
 
 
 Natural fquare. 
 
 Magical fquare 
 
 . 
 
 A G B 
 
 A 
 
 B 
 
 12345 
 
 1 1 24 7 20 
 
 
 J 
 
 6 7 8 9 10 
 
 4 12 25 8 
 
 16 
 
 E II 12 13 14 15F 
 
 17 5 13 21 
 
 9 
 
 16 17 18 19 20 
 
 10 18 14 
 
 22 
 
 21 22 23 24 25 
 
 23 6 19 2 
 
 15 
 
 C H D 
 
 C 
 
 D 
 
 Any five of the fiims in this magic fquare 
 taken in a right line, make (y^. You will 
 obferve that the five numbers in the dia- 
 gonals AD and BC of them agical fquare, 
 anfwer to the horizontal and vertical ranks 
 EF and GH in the natural fquare ; and that 
 23 is the central number of both fquares. 
 
 To
 
 RECREATIONS. 4^ 
 
 To form a magical fquare, firft tranf- 
 jjofe the two ranks in the natural fquare, 
 juft mentioned, to the diagonals of the 
 magic fquare ; then place the number i 
 tinder the central number 13, and the 
 number 2, in the next diagonal downward. 
 The number 3 fhould be placed next in 
 the fame diagonal line ; but as there is na 
 room in the fquare, you are to place it m 
 that part it would occupy if another fquare 
 were placed under this. For the fame 
 reafon the number 4, by following the 
 diagonal diredlion, falling out of the 
 fquare^ it is to be put in the part it would 
 hold in another fquare, placed by the fide 
 of this : you then proceed to the numbers 
 
 5 and 6, ftill defcending ; but as the place 
 
 6 fhould hold is already filled, you then 
 go back to the next diagonal, and confe- 
 quently place the number 6 in the fecond 
 cafe under the number 5, fo that there 
 may remain an empty cafe betsveen the 
 two numbers. The fame method is to be 
 taken whenever you find a cafe already 
 fiUed. 
 
 6 You
 
 43 RATIONAL 
 
 You proceed in this manner to fill all 
 the empty cafes in the angle where the 
 number 1 5 is placed ; and as there is no 
 place for the number 1 6 in the fame dia- 
 gonal defcending, you muft place it in the 
 part it would hold in another fquare, and 
 continue the fame method till all the cafes 
 are filled. This method will ferve equally 
 for all forts of arithmetic progreffions 
 compofed of odd numbers*; thofe com- 
 pofed of even numbers being too compli- 
 cate and abftrufe for recreations. 
 
 * IM. Ozanam, who has wrote very learnedly 
 on magical fquares, obferves, that, the Egyptians, 
 and the Pythagoreans, their difciples, held them in 
 great veneration. Tliey were dedicated by them, 
 he fays, to the feven planets. Saturn had a fquare 
 of nine cafes afligned him; Jupiter, one of 16 
 cafes ; Mars,, one of 25 ; Venus, 49 ; and Mercury, 
 64 c^fes : to the Tvlpon they gave a fquare of 81 
 cafes ; and to the Deity, one of a fingle cafe, as unify 
 can never be multiplied nor divided, tut is for ever 
 unchangeable. 
 
 RECRE-
 
 Plate,. TI. 

 
 ^ 

 
 RECREATIONS, 
 
 RECREATION XV. 
 
 49 
 
 '^e feries of numbers from i to 2^ being 
 wrote on that number of cards^ after you 
 have Jhuffed them, to deal them to five 
 perfons, either by twos or threes, at the 
 option of the parties, afid the amount of 
 the numbers on each one^s cards to be the 
 fame, 
 
 T N difpofing thefe cards you muft have 
 recourfe to the magical fquare in the 
 lad Recreation, and obferve to put the two 
 cards that have the numbers 1 1 and 4 at 
 top ; thole cards that have 24 and 12 next, 
 and fo continue, by 2 and 2, to the laft 
 number of that rank, 16, which muil: be 
 wrote on a card a Httle wider than the refti 
 You muft follow the fame method with 
 the next three numbers 17, 10, 23, and 
 fo on to the laft three 9, 22, 15, as is 
 fully explained in the following table* 
 
 Vol. t B Cards.
 
 50 
 
 K A 1 1 U i\ A J^ 
 
 Cards. 
 
 Numbers. 
 
 I 
 
 2 
 
 i Firll: perfon, 
 43 ^ 
 
 3 
 
 4 
 
 "^f Second perfon. 
 123 ^ 
 
 5 
 6 
 
 ^ ^ Third perfon. 
 
 7 
 8 
 
 q f Fourth perfon. 
 
 9 
 
 10 \v 
 
 o7 
 
 • J J 9 c Fifth perfon. 
 ^ide card 163 ^ 
 
 1 1 
 
 ^71 
 
 12 
 
 10 [Fir ft perfon. 
 
 13 
 
 ^3^ 
 
 14 
 16 
 
 5] 
 
 18 > Second perlbn. 
 
 6] 
 
 17 
 18 
 
 '31 
 
 I > Third perfon. 
 
 19 
 
 19J 
 
 20 
 
 21 ' 
 
 21 
 
 1 4 \ Fourth perfon. 
 
 22 
 
 2 
 
 23 
 
 24 
 
 91 
 
 22 [Fifth perfon. 
 
 25 
 
 15J 
 
 The cards being thus difpofcd, or be- 
 coming fo by being fhuffled in the man- 
 ner
 
 RECREATIOiSIS. 51 
 
 tier we fhall explain farther on, when we 
 treat of the combination of cards, you 
 offer to deal them by twos or threes iirfl : 
 if it be required to deal them by twos firft, 
 there is no occafion to cut them ; but 
 if they are to be dealt by threes, they 
 mull: be cut, that he who cuts them may 
 divide the pack exa6lly in that part where 
 the wide card is, and that the fifteen cards 
 that were at the bottom may be at top. 
 Obferve, you muft feel the cards before 
 you deal, in order to know if they be cut 
 at the wide card ; if not, they mull: be 
 cut again, or you may cut them yourfelf. 
 
 It is evident by the foregoing table, 
 which is formed after the magic fquare, 
 that the numbers on each perfon's cards 
 muft necelTarily amount to the fame 
 number, fixty-five. 
 
 E 2 RECRE-
 
 52 RATIONAL 
 
 RECREATION XVI. 
 
 To (kal the 3 2 caj^ds of the game of piquet to 
 four perfonSy after you have fhuffed theniy 
 
 and the parties have chofe whether you 
 fhall deal by twos or threes ; infuch man' 
 
 ner, that all the cards in each perfon's 
 
 handfloall he of the fame fuit, 
 
 THIRST, difpofe the cards in the follow- , 
 ing order, and obferve that the eighth 
 card mull: be a little larger than the reft.^ 
 
 ^ f of Hearts. Firfl perfon* 
 
 F'crhf- (spades. Second perfon. 
 6 E'o-ht c^^^'^o^^^s. Third perfonr- 
 
 i ^ , f Clubs. Foui'th perfon.- 
 
 wide card 
 
 9 King 1 
 
 10 Eight {-Hearts.- Firfl perfon. 
 
 11 Nine J 
 
 12 Ace 1 
 
 13 Knave [Spades. Second perfon^ 
 
 14 Ten J 
 
 15 Ace
 
 RECkEATIONS. 53 
 
 15 Ace 1 
 
 J 6 Seven > Diamonds. Third perfon. 
 
 17 Nine J 
 
 18 King ^ 
 
 19 Ten [Clubs. Fourth perfon. 
 
 20 Nine J 
 
 21 Queen') 
 
 22 Knave | Hearts. Firfl perfon. . 
 
 23 Ten J 
 
 24 Queen ^ 
 
 25 Nine [-Spades. Second perfon. 
 
 26 Seven J 
 
 27 King 
 
 28 Queen -Diamonds. Third perfon. 
 
 29 Ten J 
 
 30 Queen ^ 
 
 31 Eight ?Ckibs. Fourth perfon. 
 
 32 Seven J 
 
 You then follow the fame method as in 
 the preceeding Recreation : if the cards are 
 required to be dealt by twos firft, they are 
 not to be cut, but you deal, once two and 
 twice three. If they are to be dealt by 
 threes firfl, they mufl be cut at the place 
 of the wide card, and then dealt by twice 
 three, and once two. 
 
 E 3 Of
 
 54 
 
 R x\ T I O N A L 
 
 Of geometrical magic fquares. 
 
 THE fame method we have given for 
 fining up the cafes or divifons of 
 an arithmetic magic fquare, is to be fol- 
 lowed in thefe. We fhall confine ourfelves 
 here to examples of the three following 
 geometric fquares, containing nine divi- 
 fions each, which are filled up with three 
 different progreflions, applicable to the 
 follov/ins: Recreation. 
 
 Fig;. I. 
 ■ o 
 
 Fig. 2. 
 
 Fig. 3- 
 
 It 
 
 8 
 
 256 
 
 3- 
 
 4 
 128 
 
 2 
 
 64 
 
 2 J 
 
 12 
 
 ;84 
 
 768 
 48 
 
 6 
 192 
 
 96 
 
 56 
 
 179 
 
 214 
 448 
 
 224 
 
 28 
 896 
 
 1 12 
 
 7 
 
 You will obfcrve, that in every geome- 
 tric fquare, the product of the numbers 
 in each row, v/hether taken vertically, 
 horizontally, or diagonally, is conflantly 
 the fam^. 
 
 RECRE^
 
 RECREATIONS. 55 
 
 RECREATION XVII. 
 
 Several different numbers being wrote upoji 
 cards, to jhuffie them, and deal the whole, 
 or part of them, to three perfons, in fuch 
 manner that each one multiplying the num- 
 bers on his cards together, the product of 
 each perfon\ cards fh all be the fame ; and 
 to repeat the recreation after having /huf- 
 fed the cards afecond time^ 
 
 TXT' RITE upon feven-and-twenty cards 
 the numbers that are in the fore- 
 going fquares, and difpofe them in the 
 
 following order. 
 
 
 I 16 
 
 Firfl: perfbn. 
 
 2 512 
 
 Second perfon. 
 
 3 4 
 
 Third perfon. 
 
 4 8 
 
 I ft perfon. 
 
 5 32 
 
 2d perfon. 
 
 6 128 
 
 3d perfon. 
 
 7 256 
 
 I ft perfon. 
 
 8 2 
 
 2d perfon. 
 
 9 wide card 64 
 
 3d perlbn. 
 
 10 24 
 
 I ft perfon. 
 
 II 768 
 
 2d perfon. 
 
 12 6 
 
 3d perfon. 
 
 E 
 
 4
 
 56 RATIONAL 
 
 m 12 Firll: perfon, 
 
 i^ 48 Second perfan. 
 
 ic 192 Third perfqn. 
 
 16 384 I ft peribn, 
 
 } 7 3 2Q perlon, 
 
 18 wide card 96 3d perfon, ' 
 
 JO 56 ift perron, 
 
 20 179 2d perfon. 
 
 21 214 3d perfon. 
 
 22 28 I ft perfon, 
 
 23 1 1 2 2d perfon, 
 
 24 448 3d perfon. 
 
 25 896 I il: perfon. 
 
 26 72^ perfon. 
 
 27 wi4e card 224 3d perfon. 
 
 You obferve that the 9th, i8th, and 
 27th cards are to be wider than the reft, 
 that tl:ie cards being cut in thofe parts the 
 numbers may not be difarranged. It is 
 plain Hkewife, from this difpofition of 
 the cards, that if they are dealt to three 
 perfbns, one by one, or three together, 
 they muft each have one of the ranks of 
 numbers in the magic fquare. 
 
 In
 
 RECREATIONS. 57 
 
 In order to repeat this recreation it is 
 only neceflary to put the cards that have 
 been dealt on the top of the pack, and 
 jn ihufRing the cards take care not to 
 {huffle the nine bottom cards. The pack 
 being then cut at the wide card, that is at 
 the top of the loweft range of cards, they 
 are then placed at top, and ferve for the 
 fecond recreation, which will appear the 
 more extraordinary, as the produ(5l then 
 will not be the fame as before, 
 
 A recreation of the lame kind may be 
 performed with numbers in arithmetic 
 progreflion, taken, in like manner, from 
 a magical fquare ; and that will be the 
 more agreeable, as the numbers on the 
 cards will then require to be added only, 
 jjot ^nultiplied. 
 
 RECRE.
 
 58 RATIONAL 
 
 RECREATION XVIII. 
 
 'To Jind the number of changes that may be 
 
 rung on twelve bells, 
 TT appears by the 17th aphorifm, that 
 nothing more is neceflary here, than 
 to multiply the numbers from i to 12 
 continually into each other, in the follow- 
 ing manner, and the laft produd will be 
 the number fought, i 
 
 2 
 
 1 
 
 6 
 
 4 
 
 5 
 
 120 
 6 
 
 720 
 7 
 
 5040 
 8 
 
 40320 
 9 
 
 362880 
 10 
 
 3628800 
 II 
 
 39916800 
 12 
 
 479,001,600
 
 RITCREATIONS. 
 
 RECREATION XIX. 
 
 59 
 
 Suppofe the letters of the alphabet to be wrote 
 fo fmall that no one of them fhall take up 
 more fp ace than the hundredth part of a 
 fquare inch : to find how many fquare 
 yards it would require to write all the per- 
 mutations of the 24 letters In that fi%e. 
 
 T> Y following the fame method as in the 
 laft recreation, the number of per- 
 mutations of the 24 letters will be found 
 to be 
 
 62,044,840, 173,323,943,936,000 
 
 Now the inches in a fquare yard being 
 1296, that number multiplied by 100 gives 
 1 29600, which is the number of letters each 
 fquare yard will contain ; therefore if we 
 divide 62,044,840, 173,323,943,936,000 
 by 129600, the quotient, which is 
 478,741,050,720,092, 160, will be the 
 number of yards required, to contain the 
 above mentioned number of permutations. 
 
 But
 
 6o RATIONAL 
 
 'But as all the 24 letters are contained in 
 every permutation, it will requii:e a ipace 
 ?4 times as large, that is 
 
 1 1,489,785,21 7,282,21 1,840, 
 jNTow the number of fquare yards contain- 
 ed on the furface of the whole earth is 
 but 617,197,435,008,000, therefore it 
 would require a lurface of 18620 times as 
 large as that of the earth to write all the 
 permutations of the 24 letters in the {\z% 
 above mentioned. 
 
 RECREATION XX. 
 
 Jo ^nJ hoiu many different ways the elckfl 
 hand at piquet may take in his Jive cards,, 
 
 'yHE eldeit hand having twelve cards 
 dealt him, there remain twenty 
 cards, any ii^^Q of which may be in thofe 
 he takes in ; confequently we are here to 
 find how many ways five cards may be 
 taken out of 20 : therefore by aphorifm 
 J 6, if we multiply 20, 19, 18, 17, i>6» 
 inta each other, which will make 1 860480, 
 
 and
 
 RECREATIONS. 6t 
 
 and that number be divided by i, 2, 3, 4^ 
 5, multiplied into each other, which make 
 J 20 the quotient, which is 15504, will 
 be the number of Ways five cards may be 
 taken out of 20. From hence it follows, 
 that it is 15503 to i, that the eldefl hand 
 does not take in any five certain cards* 
 
 RECREATION XXI. 
 
 3o JinJ the number of deals a pej-fon may 
 play at the game of ivhifi without ever 
 holding the fame cards twice. 
 
 ' I ^ H E number of cards played with 2i% 
 whift being 52, and the number 
 dealt to each perfon being 13, it follows^ 
 that by taking the fame method as in the 
 laft recreation, that is, by multiplying 52 
 by 51, 5a, &c. fo on to 41, which will 
 make3,954, 242,643,9 1 i,239,68o,ooo,and 
 then dividing that fum by i, 2, 3, &c. to 
 13, which will make 6,227,020,800, the 
 quotient, which is 635,013,559,600, will 
 be the number of different ways thirteen^ 
 
 cards
 
 62 RATIONAL 
 
 cards may be taken out of 52, and con- 
 fequently the number fought. 
 
 (=4 
 
 
 
 
 ^ 
 
 kj 
 
 
 
 
 •^ d^ 
 
 
 
 
 
 
 w • . 
 M ON • ^C^ 
 
 < 
 
 
 
 
 M . -^^^ 
 
 •— < 
 
 
 
 
 00 ^ , VO . 
 
 oi. 
 
 
 
 
 l^ • N . On 
 
 
 w 
 
 M 
 
 hH 
 
 .^ « ^00 . f^ • 
 
 vX ^^ NO • w .ON 
 
 »— » 
 
 M 
 
 
 -^ 
 
 " 10 <N NO 
 
 
 
 CO 
 CO 
 
 4 
 
 ^o^d^^^4 
 6 ^ ^ NO ^J? o> 
 
 M . CO . <N • ^ . 
 10 NO 1-1 ^ Ct 
 
 
 
 
 
 VO 00 00 CO • 
 
 . C« (N 10 
 
 
 ' 
 
 
 
 ^ NO ^ >^3: 
 
 0^5 CO .^ ^ 
 
 < 
 
 
 
 
 
 a> 
 
 
 
 
 ^di;^^ 
 
 
 0^ 
 
 
 
 
 
 w CI 
 
 CO ^ lO^ t^OO H- C¥ 
 
 The conflru^lion of this table is very 
 fimple. The line A a confifts of the firft 
 twelve numbers. The line A b confifts 
 every where of units ; and fecond term 3, 
 
 4 of
 
 RECREATIONS. 63 
 
 of the line B r, is compofed of the two 
 terms i and 2 in the preceding rank: 
 the third term 6, in that line, is formed 
 of the two terms 3 and 3 in the preceding 
 rank: and fo of the reft; every term, 
 after the firft, being compofed of the two 
 next terms in the preceeding rank ; and 
 by the fame method it may be continued 
 to any number of ranks. To find by this 
 table how often any number of things 
 can be combined in another number, un- 
 der 13, as ftippofe 5 cards out of 8 ; in 
 the eighth rank look for the fifth term, 
 which is ^6, and that is the number 
 required. 
 
 Though we have fhewn in the forego- 
 ing recreations the manner of finding the 
 combination of all numbers whatever, yet 
 as this table anfwers the fame purpofe, 
 for fmall numbers, by infpedion only, it 
 will be found ufeful on many occafions ; 
 as will appear by the following recrea- 
 tions. 
 
 RECRE-
 
 64 RATIONAL 
 
 RECREATION XXIt* 
 
 I'd find how many different founds may be 
 produced by fr iking on a harpfichord two 
 or more of the feven natural notes at the 
 fame time^ 
 
 1. T^HE combinations of two in"] 
 
 feven, by the foregoing tri- f^* 
 angle are 
 
 2. The combinations of ^ in 7, are 35 
 
 3. The cornbinations of 4 in 7, are 3J 
 
 4. The combinations of 5, are 21 
 
 5. The combinations of 6, are 7 
 6r The feven notes all together once i 
 
 Therefore the number of all the"^ 
 ibunds will be i 
 
 RECREATION XXIIL 
 
 'Take four fqu are pieces of pafeboard, of the 
 
 fame di men/ion, and divide them diagonally^ 
 
 that is by drawing a line from two oppcfite 
 
 angles i as in tbefgure^, into 8 triangles ; 
 
 paint
 
 RECREATIONS. 
 
 65 
 
 pa'mt J ofthefe triangles with the primitive 
 colours^ red, orange, yellow, green, blue, 
 indigo, violet, and let the eighth he white. 
 'To find how many chequers or regular four- 
 Jided figures, different either inform or co- 
 lour, may be made out ofthofe eight triangles, 
 
 "plRST by combining two of thefe tri- 
 angles there may be formed either 
 the triangular fquare A, or the inclined 
 fquare B, called a rhoiPib. Secondly, by 
 combining four of the triangles ; the 
 large fquare C, may be formed ; or the 
 long fquare D, called a parallelogram. 
 
 Now the firit two fquares, confiftlng of 
 
 two parts out of 8, they may each of them. 
 
 Vol. I. F by
 
 (,(> RATIONAL 
 
 by the eighth rank of the triangle be taken 
 28 different ways, which makes 56. And the 
 laft two Iquares, confifting of four parts^ 
 may each be taken by the fame rank of the 
 triangles 70 times, which makes I40 
 
 To which add the foregoing number 56 
 
 and the number of the different^ 
 fquares that may be formed of 
 the eight triangles, will be 
 
 196 
 
 RECREATION XXIV. 
 
 A man has 1 2 different forts of flowers^ 
 and a large number of each fort. Me is 
 dtftrous of fitting them in beds or fiou- 
 rifhes, in his parterre. Six flowers infome, 
 7 in others, and 8 in others \ fo as to have 
 the greatefl variety pofjible ; the flowers in 
 no t%vo beds to be the fame. 'To flnd how 
 many beds he mufl have. 
 
 1. HP HE combinations of 6 in 121 
 
 by the laft rank of the tri- [924 
 angles, are ^ 
 
 2. The combinations of 7 in 12, are 792 
 
 3. The combinations qf 8 in 12, are 49^ 
 
 Therefore the number of beds 7 
 
 mufl be 
 
 6 
 
 I 2211
 
 RECREATIONS. 
 
 67 
 
 RECREATION XXV. 
 
 To find the number of chances that may be 
 thrown on two dice, 
 
 A S each die has 6 faces, and as every 
 face of one die may be combined 
 with all the faces of the other, it follows, 
 that 6 multiplied by 6, that is 36, will- 
 be the number of all the chances : as is 
 alfo evident from the folio win 2; table. 
 
 Points. 
 
 Numb, of Numb, of 
 chances. points. 
 
 2 I.I 
 
 3 
 
 4 
 
 5 
 6 
 
 7 
 8 
 
 9 
 10 
 II 
 12 
 
 2.1 
 
 2.2 
 
 4-1 
 
 3-3 
 6.1 
 
 4.4 
 
 6-3 
 
 5-5 
 6.5 
 
 6.6^ 
 
 1.2 
 
 3-1 
 
 1.4 
 
 5-1 
 1.6 
 
 6.2 
 
 3.6 
 
 6.4 
 5.6 
 
 1-3 
 
 3-2 
 
 5.2 
 2.6 
 
 5-4 
 4-6 
 
 2-3 
 4.2 
 
 2.5 
 
 5-3 
 4-5 
 
 2.4 
 4.3 
 3-5 
 
 3-4 
 
 I 
 
 
 2 
 
 2 
 
 
 6 
 
 3 
 
 
 12 
 
 4 
 
 
 20 
 
 5 
 
 
 30 
 
 6 
 
 
 42 
 
 5 
 
 
 40 
 
 4 
 
 
 36 
 
 3 
 
 
 3° 
 
 2 
 
 
 22 
 
 I 
 
 
 12 
 
 — — 
 
 
 
 36 
 
 
 2;j2 
 
 
 
 
 It appears by this table, i. That the 
 number of chances for each point con- 
 tinually encreafes to the point of feven, 
 F 2 and
 
 68 RATIONAL 
 
 and then continually decreafes till 1 2 : 
 therefore if two points are propofed to be 
 thrown, the equality, or the advantage 
 of one over the other, is clearly vifible *. 
 2. The whole number of chances on the 
 dice being 252, if that number be di- 
 vided by ^6, the number of different 
 throws on the dice, the quotient is 7 : 
 it follows therefore, that at every throw 
 there is an equal chance of bringing feven 
 points. 3. As there are ^^ chances on 
 the dice, and only 6 of them doublets, 
 it is 5 to I, at any one throw, againft 
 throwing a doublet. 
 
 By the fame method the number of 
 chances upon any number of dice may be 
 found : for if 36 be multiplied by 6, that 
 
 * It is eafy from hence to determine whether a 
 bet propofed at hazard, or any other game with, 
 the dice be advantageous or not ; if the dice be 
 true : which, by the way, is rarely the cafe for any 
 long time together, as it is fo eafy for thofe that are 
 poiTefled of a dexterity of hand to change the true 
 dice for falfe. 
 
 * produ6lj
 
 RECREATIONS. '69 
 
 produd, which is 216, will be the chances 
 on 3 dice ; and if that number be multi- 
 plied by 6, the produdl will be the chances 
 on 4 dice, &c. 
 
 ■if 
 
 RECREATION XXVI. 
 
 7i dlfcover the number of points on 3 cards, 
 placed under three different parcels of 
 cards. 
 
 "yj O U are firft to agree that the ace fhall 
 ' tell eleven, the picflured cards ten 
 each, and the others accordins; to their 
 number of points ; as at the game of pi- 
 quet. Then propofe to any one to choole 
 3 cards, and over each of them to put as 
 many cards as will make the number of 
 the points of that card 15. Suppole, for 
 example, he choofe a 7, a 10, and an 
 ace : then over the 7 he mufl: place eight 
 cards: over the 10, five cards ; and over 
 the ace, four. Take the remainder of the 
 cards, and feeming to look for fome card- 
 ^mong them, tell how many there are, 
 F 3 and
 
 76 RATIONAL 
 
 and adding 1 6 to that number, you will 
 have the number of points on the three 
 cards. As in this inflance, where there 
 will remain 12 cards, if you add 16 to 
 that number it will make 28, which 
 is the number of points on the three 
 cards *. 
 
 RECREATION XXVIL 
 
 I'he ten duplicates. 
 
 ' I 'AKE twenty cards, and after any 
 one has fhuffled them, lay them down 
 by pairs on the board, without looking at 
 them. Then defire feveral perfons to 
 look each of them at different pairs, 
 and remember what cards compofe them. 
 You then take up all the cards, in the 
 order they lay, and place them again on 
 the table, according to the order of the 
 letters in the following words. 
 
 * If this Recreation be performed with a pack of 
 quadrille cards, the number added to the emaining 
 cards muft be eight, 
 
 MU-
 
 RECREATIONS. 71 
 
 M 
 
 u 
 
 T 
 
 u 
 
 S 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 D 
 
 E 
 
 D 
 
 I 
 
 T 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 N 
 
 
 
 M 
 
 E 
 
 N 
 
 1 1 
 
 12 
 
 13 
 
 H 
 
 15 
 
 C 
 
 
 
 C 
 
 I 
 
 S* 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 Now you will obferve that thefe words 
 contain ten letters repeated, or ten pair 
 of letters. Therefore you aik each per- 
 fon which row, or rows, the cards he 
 looked at are in ; if he fay they are in the 
 firft row, you know that they mufl be the 
 lecond and fourth : if in the jfecond and 
 fourth rows, they muft be the ninth and 
 nineteenth, and fo of the reft. 
 
 * Thefe words convey no meaning. The laft 
 word is fometimes wrote Coecis; but that being no 
 Latin word, can make no fenfe with the others. 
 If, indeed, it was Cascis, a fort of fenfe might 
 be made out : but then the ce would by no means 
 anfwer the o in Nomen, as it muft do to perform 
 the Recreation. 
 
 F 4 RE-
 
 72 RATIONAL 
 
 RECREATION XXVIII. 
 
 To flame the number of cards that a perfon 
 Jhall take out of the pack. 
 
 *T^O perform this Recreation you muft 
 fo difpofe a piquet pack of cards, that 
 you can eafily remember the order jn 
 which they are placed. Suppofe, for ex- 
 ample, that they are placed according to 
 the words in the following line ; 
 Seven aces, eight kings, nine queens, and ten knaves. 
 
 And that every card be of a different fuit, 
 following each other in this order ; fpades, 
 clubs, hearts, and diamonds. Then the 
 eight firft cards will be the feven of 
 fpades, ace of clubs, eight of hearts, king 
 of diamonds, nine of fpades, queen of 
 clubs, ten of hearts, and knave of dia- 
 monds ; and fo of the refl *. 
 
 * This Recreation n^ay be farther diverfified, 
 by placing the cards in fuch manner, by the table 
 for ihirty-twQ numbers, that after they have been 
 fhuffled once or twice, they may come into the 
 above order. 
 
 You
 
 RECREATIONS. 73 
 
 You fhow that the cards are placed pro-, 
 mifcuoufly, and then offer them with the 
 backs upward, to any one, that he may 
 draw what quantity he pleajfe ; which 
 when he has done, you dextroufly look 
 at the card that precedes, and that which 
 follows thofe he has taken. After he has 
 well regarded the cards, you take them 
 from him, and putting them into diffe- 
 rent parts of the pack, fhuffle them, or 
 give them to him to fhuffle. Durinof 
 which you recolle6l, by the forecroinsf 
 line, all the cards he took out : and as 
 you lay them down, one fcy one, you 
 name each card. 
 
 This is a pleafing Recreation for thofe 
 tihat have a good memory ; they that 
 jiave not, fhould never attempt it, 
 
 RECRE^
 
 74 RATIONAL ^ 
 
 RECREATION XXIX. 
 
 A century of different names being wrote on 
 the cards, to tell the particular name which 
 any ferfon has thought on^, 
 
 f~\ N ten cards, write a hundred different 
 names, obferving only, that the laft 
 name on each card begin with one of the 
 letters of the word, INDROMACUS, 
 which letters, in the order they ftand, 
 anfwer to the numbers i, 2, 3, &c. to 
 10. On ten other cards write the fame 
 names, with this reftridlion, that the firft 
 name on every card muft be taken from 
 the firft of the other cards, whofe laft 
 name begins with I : the fecond name 
 mufl: be taken from that whole laft name 
 begins with N : and fb of the reft. Then 
 let any one choofe a card out of the £rft 
 ten, and after he has fixed on a name 
 
 * This is called the Impenetrable Secret; though 
 jt is one of the moft eafy Recreations with the cards. 
 
 give
 
 RECREATION'S. 75 
 
 give it you again, when you carefully 
 note the lafl name, by which you know 
 the number of that card. You then take 
 the other ten cards, and after fhufRing 
 them, fhow them to the perfon one by 
 one, and afk if he fee the name he chojfe, 
 and when he iays he does, you look to 
 that name which is the fame in number 
 from the top, with the number of the 
 card he took from the other parcel, and 
 that will be the name he fixed on. As 
 for example, fuppofe he took out the 
 card that had the word Daphnis at the 
 bottom, which is the third card, and that 
 he fixed on the name Galatea, then that 
 word will necefiarily be the third on the 
 other card. 
 
 Order
 
 7^ 
 
 RATIONAL 
 
 Order of the words on thejirji ten cards. 
 
 Firji Card Second 
 
 • nird 
 
 Fourth 
 
 Celadon 
 
 Pomona 
 
 Deucalion 
 
 Licas 
 
 Andromeda 
 
 Qmphalus 
 
 Hefiona 
 
 Calypfo 
 
 Silenus 
 
 Ariadne 
 
 Galatea 
 
 Medea 
 
 Acis 
 
 Lifis 
 
 Thetis 
 
 Adonis 
 
 Eglea 
 
 Flora 
 
 Atys 
 
 Ceres 
 
 Sirincus 
 
 Danae 
 
 Palamedes 
 
 CafTandra 
 
 Thyrfis 
 
 Alcander 
 
 Melibasus 
 
 Pales 
 
 Polyphemus 
 
 Tirefias 
 
 Orion 
 
 Menelaus 
 
 Proteus 
 
 Ifforia 
 
 Nifus 
 
 Glaucus 
 
 Jafon 
 
 JSJarcifiTus 
 
 J)aphnis 
 
 j^ophelina 
 
 Fifth 
 
 Sixth 
 
 Seventh 
 
 Eighth 
 
 Latona ■ 
 
 Icarus 
 
 Ganymede 
 
 Leander 
 
 Hilas 
 
 Clitander 
 
 Ariftea 
 
 Peleus 
 
 Thifbe 
 
 Alcinous 
 
 Hyaclnthus 
 
 Califta 
 
 Plana 
 
 Endimion 
 
 Circe 
 
 Cadmus 
 
 Palcemon 
 
 Alcldon 
 
 Mopfa 
 
 Pfyche 
 
 Hebe 
 
 Iphis 
 
 Piramus 
 
 Semele 
 
 Sappho 
 
 Achelous 
 
 Philemon 
 
 Iphigenia 
 
 A6leon 
 
 Philomela 
 
 Aftrea 
 
 Silvia 
 
 Medufa 
 
 Cephalus 
 
 Pelias 
 
 Alpheus 
 
 Qrphcus 
 
 Mirtilus 
 
 AL^rianus 
 
 Coridon 
 
 Ninth 
 
 'Tenth 
 
 Hipolitus 
 
 Efon 
 
 Dryope 
 
 Ifander 
 
 Corilas 
 
 Califtiis 
 
 NefTus 
 
 Ifidora 
 
 Procris 
 
 Arachne 
 
 Philoftetes 
 
 Melicerte 
 
 CapariHa 
 
 Pirus 
 
 Marfias 
 
 Riblis 
 
 Arcthufus 
 
 Vertumnus 
 
 Licas 
 
 ^ilvander 
 
 Orde.
 
 RECREATIONS. 
 
 17 
 
 Order of the words on the lafi 
 
 ten cards. 
 
 F'lrft Car 
 
 -d Second 
 
 nird 
 
 Fourth 
 
 Celadon 
 
 Andromeda 
 
 Silenus 
 
 Acis 
 
 Pomona 
 
 Omphalus 
 
 Ariadne 
 
 Lifts 
 
 Deucalion 
 
 Plefiona 
 
 Galatea 
 
 Thetis 
 
 Licas 
 
 Calypfo 
 
 Medea 
 
 Adonis 
 
 Latona 
 
 Hilas 
 
 Thifbe 
 
 Diana 
 
 Icarus 
 
 Clitandcr 
 
 Alcinous 
 
 Endimioa 
 
 Ganymede 
 
 Ariftca 
 
 Hyacinthus 
 
 Circe 
 
 Leander 
 
 Peleus 
 
 Califta 
 
 Cadmus 
 
 Hypolitus 
 
 Corilas 
 
 Procris 
 
 CaparilTa 
 
 Dryope 
 
 NelTus 
 
 Philodetes 
 
 Marfias 
 
 Fifth 
 
 Sixth 
 
 Seventh 
 
 Eighth 
 
 Eglea 
 
 Sirincus 
 
 Thyrfis 
 
 Polyphemus 
 
 Flora 
 
 Danae 
 
 Alcander 
 
 Tirefias 
 
 Atys 
 
 PalameJes 
 
 Melibaeus 
 
 Orion 
 
 Ceres 
 
 CaiTandra 
 
 Pales 
 
 Menelaus 
 
 Palasmon 
 
 Hebe 
 
 Sappho 
 
 Adeon 
 
 Alcidon 
 
 I phis 
 
 Archelous 
 
 Philomela 
 
 Mopfa 
 
 Pi ramus 
 
 Philemon 
 
 Aftrea 
 
 Pfyche 
 
 Semele 
 
 Iphigenia 
 
 Silvia 
 
 Arethufus 
 
 Efon 
 
 Califtus 
 
 Arachne 
 
 Licas 
 
 Ifander 
 
 I (idora 
 
 Melicerte 
 
 Ninth 
 
 "tenth 
 
 Proieus 
 
 Cephalus 
 
 Jafon 
 
 Myrtilus 
 
 IlToria 
 
 Pelias 
 
 Narciluis 
 
 Adrianus 
 
 Nifus 
 
 Alpheus 
 
 Daphnis 
 
 Corydon 
 
 Glaucus 
 
 Pirus 
 
 Rophelina 
 
 Vertumnus 
 
 Medufa 
 
 Ribiis 
 
 Orpheus 
 
 Silvander 
 
 Jiiflead
 
 7^ RATIONAL 
 
 Inftead of ten cards, there may be 
 twenty to each parcel, by adding dupli- 
 cates to each card, which Vvill make the 
 Recreation appear the more myfterious, 
 and will not at all embarrafs it, as you 
 have nothing to remember but the laft 
 name on each card. Or inftead of nam.es, 
 you may write queftions on one of the 
 parcels, and anfwers on the other. 
 
 Of the combinations of the cards. 
 
 THE tables we here give are the bafis 
 of many recreations, as well on num- 
 bers, letters, and other fubjects, as on the 
 cards ; and the efFeft here produced by them 
 is the more fiirpriiing, as that which fhould 
 leem to prevent any coUulion, that is, the 
 fhuffling of the cards, is, on the contrary, 
 the caufe fi'om whence it proceeds. 
 
 It is a matter of indifference what num- 
 bers are made ufe of in forming thefe ta- 
 bles. We ihall here confine ourfelves to 
 fuch as are applicable to the fubfequent 
 
 Recre-
 
 RECREATIONS. 79 
 
 Recreations. Any one may conflrudt them 
 in fuch manner as is agreeable to the pur- 
 pofes he intends they ihall anfwer. 
 
 To make them, for example, correfpond 
 to the nine digits and a cypher, there muft 
 be ten cards, and at the top of nine of them 
 muft be wrote one of the digits, and on 
 the tenth a cypher. Thefe cards muft be 
 placed upon each other in the regular or- 
 der, the number i being on the firft, and 
 the cypher at bottom. You then take the 
 cards in your left hand, as is commonly 
 done in ftiuffling, and taking off the two 
 top cards, i and 2, you place the two fol- 
 lowing, 3 and 4, upon them ; and under 
 thofe four cards the three following 5, 6, 
 and 7 : at the top you put the cards 8 and 
 9, and at the bottom the card marked o. 
 Conftantly placing in fucceflion 2 at top 
 and 3 at bottom, and they will then be ifi 
 the following order : 
 
 8.9..3.4..1.2...5.6.7..0 
 
 If
 
 8o RATIONAL 
 
 If you ihuffie them a fecond time, in the 
 fame manner, they will then ftand in this 
 order : 
 
 6.7..3.4..8.9..i.2.5.^o 
 
 Thus, at every new fliulne, they will 
 have a different order, as is expreffed in 
 the following lines : 
 
 1 ihuffle 8.9.3.4.1.2.5.6.7.0 
 
 2 6.7.3.4.8.9.1.2.5.0 
 
 3 2.5.3.4.6.7.8.9.1.0 
 
 4 9.1.3.4.2.5.6.7,8.0 
 
 5 7.8.3.4.9.1.2.5.6.0 
 
 6 5.6.3.4.7.8.9.1.2.0 
 
 7 1.2.3.4.5.6.7.8.9.0 
 
 It is a remarkable property of this num- 
 ber, that - the cards return to the order in 
 which they were firft placed, after a num- 
 ber of fhuffles, which added to the num- 
 ber of columns that never change the or- 
 der, is equal to the number of cards. Thus 
 the number of lliuffles is 7, and the num- 
 ber of columns in which the cards marked 
 3, 4, &c. never change their places is 3, 
 which are equal to 10, the number of the 
 
 cards.
 
 Recreations. zi 
 
 card-s. This property is not common to 
 all numbers : the cards fometimes return- 
 ing to the firfl order in lefs number, and 
 fometimes in a greater number of fliuffles 
 than that of the cards. 
 
 Though the cards are here diretfted to 
 be Ihuffled by twos or threes only, yet ta- 
 bles may be con{lru€led with equal facility 
 for Muffling them by 2 and i , 3 and 4, or 
 any other number whatever ;• obferving 
 that the fewer cards are taken to sf ether the 
 lefs liable you will be to err. 
 
 Note, before yx>u venture to perform 
 thefe Recreations, you ihould accuftom 
 yourfelf to Ihuffle the cards exactly and 
 readily ; which will be eafily attained by 
 |)ra(£tice» 
 
 Vol, I. o Tables
 
 82 RATIONAL 
 
 TABLES OF COMBINATIONS 
 
 Conftrufted on the foregoing principles. 
 
 TABLE I * 
 
 FOR TEN NUMBERS. 
 
 Order before fhufRing. After ift Ihuffle. After the 2d. After the 3d. 
 
 I 
 
 8 
 
 6 
 
 2 
 
 2 
 
 9 
 
 7 
 
 5 
 
 3 
 
 3 
 
 3 
 
 3 
 
 4 
 
 4 
 
 4 
 
 4 
 
 5 
 
 I 
 
 8 
 
 6 
 
 6 
 
 2 
 
 9 
 
 7 
 
 7 
 8 
 
 5 
 6 
 
 I 
 
 2 
 
 8 
 9 
 
 9 
 
 7 
 
 5 
 
 I 
 
 
 
 
 
 
 
 
 
 * Thefe tables and the following Recreations af 
 piquet, except the 36th, appear to have been com- 
 
 pofed by Mr. Guyot. 
 
 TABLE
 
 recreations: 83 
 
 TABLE II. 
 FOR TWENTY FOUR NUMBERS. 
 
 Oiiti before fliufBing. 
 
 Z 
 2 
 
 3 
 
 4 
 
 I 
 
 7 
 8 
 
 9 
 
 10 
 
 ii 
 i2 
 
 13 
 
 14 
 15 
 26 
 
 '7 
 18 
 
 J9 
 
 20 
 21 
 
 12 
 
 23 
 
 24 
 
 After I ft flu 
 
 iffis. After the ^d 
 
 After fhs ^i, 
 
 23 
 
 21 
 
 ^7 
 
 24 
 
 22 
 
 20 
 
 18 
 
 12 
 
 2 
 
 19 
 
 15 
 
 7 
 
 13 
 
 5 
 
 13 
 
 14 
 
 6 
 
 14 
 
 8 
 
 9 
 
 3 
 
 , 9 
 
 3 
 
 18 
 
 3 
 
 18 
 
 12 
 
 4 
 
 19 
 
 IS 
 
 I 
 
 23 
 
 21 
 
 2 
 
 24 
 
 22 
 
 5 
 
 13 
 
 5 
 
 6 
 
 14 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 4 
 
 19 
 
 u 
 
 I 
 
 23 
 
 12 
 
 2 
 
 24 
 
 ^5 
 
 7 
 
 ^ 
 
 16 
 
 10 
 
 4 
 
 17 
 
 II 
 
 r 
 
 20 
 
 16 
 
 ro 
 
 21 
 
 17 
 
 ir 
 
 22 
 
 20 
 
 16 
 
 G z , TABLE
 
 U RATIONAL 
 
 TABLE III. J 
 
 . FOR TWENTY SEVEN NUMBERS. 
 
 efore : 
 
 fliuffling. After ift niuffle. 
 
 After the 2d. 
 
 Afttr the ji 
 
 I 
 
 23 
 
 21 
 
 17 
 
 2 
 
 24 
 
 22 
 
 20 
 
 3 
 
 18 
 
 12 
 
 2 
 
 4 
 
 19 
 
 '5 
 
 7 
 
 5 
 
 13 
 
 5 
 
 13 
 
 6 
 
 14 
 
 6 
 
 14 
 
 7 
 8 
 
 8 
 9 
 
 9 
 3 
 
 3 
 
 18 
 
 9 
 
 3 
 
 18 
 
 12 
 
 lo 
 
 4 
 
 19 
 
 16 
 
 II 
 
 I 
 
 23 
 
 21 
 
 12 
 
 2 
 
 24 
 
 22 
 
 13 
 
 14 
 
 5 
 6 
 
 13 
 
 14 
 
 5 
 6 
 
 15 
 
 7 
 
 8 
 
 9 
 
 16 
 
 10 
 
 4 
 
 19 
 
 17 
 
 II 
 
 I 
 
 23 
 
 18 
 
 12 
 
 2 
 
 24 
 
 19 
 
 15 
 
 7 
 
 8 
 
 20 
 
 16 
 
 10 
 
 4 
 
 21 
 
 17 
 
 II 
 
 I 
 
 22 
 
 20 
 
 16 
 
 10 
 
 23 
 
 21 
 
 17 
 
 II 
 
 24 
 
 22 
 
 20 
 
 16 
 
 26 
 
 25 
 26 
 
 25 
 26 
 
 25 
 26 
 
 27 
 
 27 
 
 27 
 
 27 
 
 < 
 
 4 
 
 TABLE
 
 RECREATIONS. 
 
 85 
 
 TABLE IV. 
 
 FOR THIRTY TWO NUMBERS. 
 
 Or^er before rtiuffling. After the ift fliuffle. After the 2d. After the i<i. 
 
 I 
 
 28 
 
 26 
 
 22 
 
 2 
 
 29 
 
 27 
 
 25 
 
 3 
 
 23 
 
 17 
 
 7 
 
 4 
 
 24 
 
 20 
 
 12 
 
 5 
 
 18 
 
 10 
 
 2 
 
 6 
 
 19 
 
 II 
 
 9 
 
 7 
 
 13 
 
 I 
 
 23 
 
 8 
 
 14 
 
 2 
 
 28 
 
 9 
 
 8 
 
 14 
 
 9 
 
 IP 
 
 9 
 
 8 
 
 12 
 
 n 
 
 3 
 
 23 
 
 14 
 
 13 
 
 4 
 
 24 
 
 27 
 
 13 
 
 I 
 
 28 
 
 20 
 
 14 
 
 2 
 
 29 
 
 26 
 
 15 
 
 5 
 
 18 
 
 17 
 
 16 
 
 6 
 
 19 
 
 
 
 17 
 
 7 
 
 13 
 
 8 
 
 18 
 
 10 
 
 9 
 
 I 
 
 19 
 
 II 
 
 3 
 
 28 
 
 20 
 
 12 
 
 4 
 
 23 
 
 21 
 
 15 
 
 5 
 
 14 
 
 22 
 
 16 
 
 6 
 
 18 
 
 ^3 
 
 17 
 
 7 
 
 19 
 
 24 
 
 20 
 
 12 
 
 3 
 
 25 
 
 21 
 
 15 
 
 4 
 
 26 
 
 22 
 
 16 
 
 5 
 
 27 
 
 25 
 
 21 
 
 16 
 
 28 
 
 26 
 
 22 
 
 15 
 
 29 
 
 27 
 
 25 
 
 26 
 
 30 
 
 30 
 
 30 
 
 31 
 
 31 
 
 31 
 
 31 
 
 30 
 
 32 
 
 32 
 
 32 
 
 3f 
 
 G 
 
 RE-
 
 8^ RATIONAL 
 
 RECREATION XXX. 
 
 Several letter's that contain 7io meanings 
 being ivrote upon cards, to make the?n, 
 after they have been twice Jhuffled, give 
 mi anfwer to a quejiion that Jhall be pro- 
 pofed; as for example. What is Love ? 
 
 T ET 24 letters be wrote on as many 
 cards, which, after they have been 
 twice Ihuffled, fhall give the following an- 
 fwer : 
 
 A dream of joy that foon is over ■. 
 
 Firfl, write one of the letters in that line 
 on each of the cards*. Then write the 
 anfvver on a paper, and afiign one of the 
 24 firfl numbers to each card, in the fol- 
 lowino" order. 
 
 A DREAM OFJOYTHAT 
 
 I 23456 789101112131415 
 
 SOON I S O ' E R. 
 
 16 17 18 19 202I 22 23 24 
 
 * Thefe letters fhould be wrote in capitals on 
 one of the corners of each card, that the words may 
 be eafily legible when the cards are fpread open : 
 
 Next
 
 RECREATIONS. 87 
 
 Next, write on another paper a line of 
 numbers, from i to 24, and looking in 
 the table for 24 combinations you will fee 
 that the fir ft number after the fecondfhuf- 
 fle is 21, therefore the card that has the 
 ^rft letter of the anfwer, which is A, muft 
 be placed againft that number in the line 
 of numbers you have juft made * in like 
 manner the number 22 being the fecond 
 of the fecond column, indicates that the card 
 which anfwers to the lecond letter, D, of 
 the anfwer, muft be placed againft that 
 number : and fo of the reft. The cards 
 will then ft and in the following order : 
 
 I 23456 7 8 9101112 1314151617 
 OOFSAMNTO I S R H AEO'E 
 
 18 19 20 21 22 23 24 
 J O R A D Y T 
 
 From whence it follows that after theie 
 cards ha^'e been twice fhuffled they muft 
 
 * For the fame reafon if you would have the au- 
 fwer after one fhuffle, the cards muft be placed ac- 
 cording to the firft column of the table : or if after 
 three fhuffles, according to the third columr.. 
 
 G 4 infal-
 
 88 RATIONAL 
 
 infallibly {land in the order of the letter 
 in the aniwer, 
 
 Obferve i. You fhould have feyeral 
 queftions with their anfwers, confining 
 of 24 letters, wrote on cards : thefe cards 
 fhould be put in cafes, and numbered, tha,t 
 you may know to which queflion each an- 
 fwer belongs. You then prefent the quef- 
 tions ; and when any one of them is clofe, 
 you pull out the cafe that contains the an- 
 fwer, and fhewing that; the letters wrote 
 on them make no fenfe, you then fliuf- 
 fie them, and the anfwer becomes ob- 
 vious. 
 
 2. To make this Recreation the mor« 
 extraordinary, you may have three cards 
 on each of which an anfwer is wrote ; one 
 of which cards muft be a little wider, and 
 another a little longer, than the others. 
 You give thefe three cards to any one, and 
 ^ hea he has privately chofe one of them 
 he gives vou the other two, which you 
 put into yonr pocket without looking at 
 
 them,
 
 RECREATIONS, 89 
 
 them, having difcovered by feeling which 
 he has chofe. You then pull out the cafe 
 that contains the cards that anfwer to his 
 quelHon, and perform as before, 
 
 3. You may alfb contrive to have a 
 long card at the botton, after the fecond 
 ihuffle. The cards may be then cut fe- 
 veral times, till you perceive by the touch 
 that the long card is at bottom, and then 
 give the anfwer ; for the repeated cut- 
 tings, however often, will make no alte- 
 ration in the order of the cards. 
 
 The fecond of thefe obfervations is ap- 
 plicable to fome of the fubfequent Recre- 
 ations, and the third may be pra£liled in 
 almoft all experiments with the cards. You 
 fhould take care to put up the cards as 
 foon as the anlwer has been fhewn : fo 
 that if any one fhould defire the Recrea- 
 tion to be repeated, you may offer another 
 queftion, and pull out thofe cards that 
 contain the anfwer. 
 
 Though.
 
 ^o RATIONAL 
 
 Though this Recreation cannot fail of 
 exciting at all times pleafure and furprize, 
 yet it mufl be owned that a great part of 
 the applaufe it receives arifes from the 
 addrefs with which it is performed. 
 
 RECREATION XXXI. 
 
 '^he twenty-four letters of the alphabet be- 
 ing wrote upon fo many cards, to fhuffle 
 them, and pronounce the letters Jhall then 
 he in their natural order \ but that not 
 fucceed'ing, to fhuffe them a fecond time, 
 and thenjhew them hi proper order. 
 
 "TXT RITE the 24 letters on the cards 
 in the following order : 
 
 ^234 ^ (y ^ 8 9 10 II 12 
 
 R S H Qj: F T P G U X C 
 
 13 14 15 16 17 18 19 2021 22 22 24 
 NODYZIK&ABLM 
 
 The cards being difpofed in this man- 
 ner, Ihew them upon the table, that it 
 piay appear they are promifcuoufly mark- 
 ed.
 
 RECREATIONS. 91 
 
 ed. Then fhuffle and lay them again on 
 the table, pronouncing that they will be 
 then in alphabetical order. Appear to be 
 furprifed that you have failed ; take them 
 up again and give them a fecond fhuffle, 
 and then counting them down on the 
 table they will all be in their natural 
 order. 
 
 RECREATION XXXII. 
 
 Several letters heing wrote fromifciioujiy up" 
 on 2fZ cards, after they have been once 
 
 JJmjjied, to find in a part of them a quef- 
 iion ; and then Jhtifflmg the rema'mder a 
 
 fecond time, to fie-w the anfwer, 
 
 C UPPOSE the queflion to be What is 
 each Britoji s boafi ? and the anfwer. 
 His Liberty ; w^hich taken together contain 
 32 letters. 
 
 After you have wrote thofe letters on 
 32 cards, write on a paper the words his 
 
 liberty y
 
 92 RATIONAL 
 
 liberty^ and annexed to the letters the firfl 
 ten numbers thus : 
 
 HIS LIBERTY 
 
 123 456789 10 
 
 Then have recourfe to the table of com- 
 binations for ten numbers, and apply the 
 refpe6tive numbers to them in the fame 
 manaer as in the 30th Recreation, taking 
 the firfl column, as theie are to be fhuf^ 
 fled only once, according to that order. 
 123 456789 10 
 IBS LERTHIY 
 
 This is the order in which thefe cards 
 mufl ftand after the whole number 32 has 
 been once fhuffled, fo that after a fecond 
 fhuffle they may {land in their proper or- 
 der. Next difpofe the whole number of 
 letters according to the firft column for 32 
 letters : the laft ten are to be here placed 
 in tlie order above ; as follows, 
 
 WHAT IS EACHB R I TO N'S 
 
 I 234 ^ d 7891011121314151617 
 
 BOAST? 
 18 19 20 21 22 
 IBSLERTHIY 
 
 23 24 25 26 27 28 29 30 31 32 
 
 Therefore
 
 RECREATIONS. 93 
 
 Therefore, by the iirfl column of the 
 
 table, they will next ftand thus : 
 
 123 4 5 678 giciii2i':!T4i<ji6 
 ITBRONSCHBO A E ASTlongcard 
 17 18 19 20 21 22 33 24 25 26 27 28 29 30 31 32 
 I I S B S L 1 B E R T W H H I Y 
 
 You mufi: obferve that the card here 
 placed the i6th in order, being the lafl of 
 the queftion, is a long card ; that you may 
 cut them, or have them cut, after the firil 
 Ihuffle, at that part, and by that means fe- 
 parate them from the other ten cards that 
 contain the anfvver. 
 
 Your cards being thus difpofed, you 
 fhow that they make no meaning ; then 
 ihuffle them once, and cutting them at the 
 long card, you give the firfl part to any 
 one, who re-ds the queftion, but can find 
 no anfwer in the others, which you open 
 before him ; you then ihuffle them a fe- 
 cond time, and ihew the anfwer as above. 
 
 RECRE-
 
 $4 RATIONAL 
 
 RECREATION XXXIIL 
 
 To wrifo 32 letters on fo many cards ^ then 
 Jhuffle and deal them by twos to two per- 
 Jons, infuch manner, that the cards of one 
 Jhall contain a quejiion, and thofe of the 
 Ather, an atifwer, 
 
 C UPPOSE the queftion to be, Is nothing 
 certain f and the anfwer, Tes, dif- 
 appointmenf. 
 
 Over the letters of this qiieftion and 
 anfwer write the following numbers, 
 which correfpond to the order in which 
 the cards are to be dealt by two and two. 
 
 IS NOTHING CERTAIN 
 
 31 32 27 28 23 24 19 20 15 16 II 12 7 '8 3 4 
 
 YES DISAPOIN TMENT 
 
 29 3025 26 21 22 17 18 13 14 9 10 5 6 I 2 
 
 Then have recourfe to the firfl column 
 
 of the table for 32 numbers, and dif- 
 
 3 po^
 
 RECREATIONS. 
 
 95 
 
 pofe thefe 32 cards ia the following or« 
 der, by that column, 
 
 12345 6 7 8 9 10 II 12 13 14 15 16 
 OIERGCANTPI NTA I S 
 
 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 
 TMEH S D INNO YNT E I S 
 
 The cards being thUs dilpofed, fhuffle 
 them once, and deal them 2 and 2 ; when 
 one of the parties will neceifariiy have the 
 queflion and the other the anfwer, 
 
 Inftcad of letters you may write \^^ords 
 tipon the 32 cards, 16 of which may cQn-^ 
 tain a queftion, and the rem>ainder the an- 
 fwer ; or what other matter you pleafe. 
 If there be found difficulty in accommo- 
 dating the words to the number of cards, 
 there may be two or more letters or iyl- 
 iables wrote upon one card, 
 
 RECRE^
 
 96 RATIONAL 
 
 RECREATION XXXIV. 
 
 I'he Fhe Beatitudes, 
 
 'T^HE five bleffings we will fuppofe to 
 bC) I. Science, 2. Courage, 3. Healthy 
 4. Riches, and 5. Virtue. Thefe are to be 
 found upon cards that you deal, one by- 
 one, to five perfons. Firft write the let- 
 ters of thefe words fucceliively, in the or- 
 der they fland, and then add the numbers 
 htere annexed to them. 
 
 SCIENCE COU RAGE 
 
 31 26 21 16 II 6 I 322722 17 12 72 
 
 HEALTH RICHES 
 
 28 23 18 13 8 3 29 24 19 14 9 4 
 
 VIRTUE 
 
 30 2520 15 10 5 
 
 Then ranfre them in order ao;reeable to the 
 
 firfk column of the table for 32 numbers, 
 
 as in the lafl Recreation, Thus. 
 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 
 
 i 
 
 LHNATEREUA c rgti u 
 
 17 18 19 20 21 22 23 2425 26 27 28 29 30 31 32 
 
 EECI ICHSQHREEV SC 
 
 Next,
 
 RECREATIONS. 97 
 
 Next, take a pack of cards, and write 
 on the four firfl the word Science ; on the 
 four next the word Courage; and fo of 
 the reft. 
 
 Matters being thus prepared, you fhew 
 that the cards on which the letters are 
 wrote convey no meaning. Then take the 
 pack on which the words are wrote, and 
 Spreading open the firft four cards, with 
 their backs upward, you defire the firft per- 
 fon to choofe one. Then clofe thofe cards 
 and Ipread the next four to the fecond 
 perfon ; and fo to all the five ; telling them 
 to hold up their cards left you ftiould 
 have a confederate in the room. 
 
 You then ftiuffle the cards and deal them 
 one by one, in the common order, begin- 
 ning with the perfon who chofe the firft 
 Card, and each one will find in his hind 
 the fame word as is wrote on his card. 
 You Will obferve, that after the fixth 
 round of dealing, there will be two cards 
 
 Vol. I, H left
 
 98 RATIONAL 
 
 left, which you give to the firil and fecond 
 perfons, as their words contain a letter 
 more than the others. 
 
 RECREATION XXXV. 
 
 'The cards of the game of piquet being mixed 
 together^ after Jhuffilng them^ to brings 
 by cutthig them, all the cards of each 
 ' fult together. 
 
 *" I "'HE order in which the cards mufl be 
 placed to produce the efFe£t deiired, 
 being eftablilhed on the fame principle 
 as that explained in the 31 ft Recre- 
 ation, except that the fhuffling is here 
 to be repeated three times, we think it 
 will be fufficient to give the order in 
 which they are to be placed before the 
 firft fhuffle. 
 
 Ordt 
 
 cr
 
 RECREATIONS. 
 
 99 
 
 Order of the Cards, 
 
 -clubs 
 
 \ 
 
 1 Ace \ 
 
 2 Knave 5 
 
 3 Eight 
 
 4 Seven 
 v^ide card 
 
 5 Ten clubs 
 
 6 Eight 1 r 1 
 
 7 Seven J 
 wide card 
 
 8 Ten 1 
 
 Nine ^ 
 
 dimonds 
 
 es 
 
 diamonds. 
 
 I o Queen f 
 
 I I Knave J 
 
 1 2 Queen clubs 
 
 ^ o ^^ Miearts 
 
 14 beven 3 
 
 wide card 
 
 15 Ten 
 
 1 6 Nine 
 
 Hpad( 
 
 1 7 King clubs 
 
 18 Ten 7u 
 
 T^T- the arts 
 
 19 Nuie3 
 
 20 Seven clubs 
 
 2 1 Ace diamonds 
 
 22 Knave fpades 
 
 23 Queen hearts 
 
 24 Knave hearts 
 
 25 Ace fpades 
 
 26 King diamonds 
 
 27 Nine clubs 
 
 29 King) 
 
 qo Eisrht clubs 
 
 ^'"S ?fpade3 
 32 Queen 3 ^ 
 
 31 iving 
 
 You then ihuffle the cards, and cutting 
 at the wide card, which will be the {^y&w 
 of hearts, you lay the eight cards that are 
 cut which will be the fuit of hearts, down 
 on the table. Then fhuffling the remain- 
 ing cards a fecond time, you cut at the 
 H 2 fecond
 
 100 RATIONAL 
 
 fecond wide card, which will be the ieven 
 of fpades, and lay, in like manner, the 
 eight fpades down on the table. You 
 fhuffle the cards a third time, and offer- 
 ing them to any one to cut, he will natu- 
 rally cut them at the wide card*, which is 
 the feven of diamonds, and confequently 
 divide the remaining cards into two equal 
 parts, one of which will be diamonds and 
 the other clubs. 
 
 RECREATION XXXVI. 
 
 Uhe cards at piquet being all mixed together^ 
 to divide the pack into two unequal parts ^ 
 and name the number of points contained in 
 each part, 
 
 "\70U are frit to agree that each king 
 
 queen and knave fhall count, as ufual, 
 
 10, the ace i, and the other cards ac- 
 
 * You muft take particular notice whether they 
 be cut at the wide card, and if they are not, you muft 
 have them cut, or cut them again yourfelf. 
 
 cording
 
 RECREATIONS. 
 
 lOI 
 
 cording to the number of the points. 
 Then dilpofe the cards, by the table for 
 32 numbers, in the following order, and 
 obferve that the laft card of the firft di- 
 vifion muft be a wide card. 
 
 Order of the cards before Jhuffling. 
 
 1 Seven hearts 
 
 17 Nine diamonds 
 
 2 Nine clubs 
 
 1 8 Ace Ipades 
 
 3 Eight hearts 
 
 19 Ten clubs 
 
 4 Eight 1 
 
 20 Knave' 
 
 5 Knave J'fpades 
 
 21 Eight diamonds 
 
 6 Ten 
 
 22 King J 
 
 8 S-r"}='»'^^ 
 
 23 Seven ipades 
 
 ^+ Seven ^^^^^^^^ 
 25 Qiieen 3 
 
 9 Ace hearts 
 
 wide card 
 
 ^^^— 
 
 1 Nine hearts 
 
 26 Knave hearts 
 
 1 1 Queen fpades 
 
 27 King clubs 
 
 12 Knave clubs 
 
 28 Nine ?r j 
 T^ . \ ipades 
 
 29 King 3 ^ 
 
 13 Ten diamonds 
 
 14 Ten 
 
 30 Ace diamoiKls 
 
 15 King 'hearts 
 
 16 Queen J 
 
 21 Seven / , , 
 32 Eight 3 
 
 .You then fhufHe them carefully, ac- 
 cording to the method before defcribed, 
 and they will ftand in the following order. 
 H 3 Cards
 
 I02 
 
 RATIONAL 
 
 Cards. 
 
 Numbers. Cards. 
 
 Numbers. 
 
 I Nine 1 
 
 1 King ?• Spades 
 
 3 Seven J 
 
 4 Seven diamonds 
 
 5 Ace fpades 
 
 9 
 lo 
 
 7 
 
 7 
 I 
 
 Brought up 
 
 6 Ten clubs 
 
 7 Ten diamonds 
 
 8 Ten hearts 
 
 9 Ace clubs 
 I o Ace hearts (wide card) i 
 
 34 
 lo 
 
 lO 
 
 lO 
 
 I 
 
 Carried up 34 
 
 Total 66 
 
 11 Eight Hearts 
 
 12 Eight fpad-s 
 
 13 Seven hearts 
 14. Nine clubs 
 
 17 Queen clubs 
 
 18 Nine hearts 
 
 19 Queen fpades 
 
 20 Knave clubs 
 
 21 King hearts 
 
 es 
 
 Brought up 1 01 
 
 8 22 Qiieen hearts 10 
 
 8 23 Nine -^ 9 
 7 24 Knave | 10 
 
 9 25 Eight J- Diamonds 8 
 10 26 King I 
 10 27 Qiieen J 
 ^° 28 Knave hearts 
 
 9 29 King clubs 
 
 1° 30 Ace diamonds 
 
 ^'I'Tl Clubs 
 32 Eight J 
 
 10 
 10 
 
 Carried up loi 
 
 Total 
 
 10 
 10 
 10 
 10 
 
 I 
 
 7 
 8 
 
 194 
 
 When the cards are by fhuffling dif- 
 pofed in this order, you cut them at the 
 wide card, and pronounce that the cards 
 you have cut off contain 66 points, and 
 confequently the remaining part 194. 
 This recreation excites a good degree 
 of admiration, but the applying of thefe 
 cards to the next Recreation produces 2, 
 much greateio 
 
 RECRE^
 
 RECREATIONS. 105 
 
 RECREATION XXXVIL 
 
 'i'he inconceivable repique.^ 
 
 "VXTHEN you would perform this Re- 
 creation with the cards ukd in the 
 laft, you muft obierve not to diforder the 
 firft ten cards in laving them down on the 
 table. Putting thole cards together, in their 
 proper order, therefore you Ihuffle them a 
 fecond time in the fame manner, and offer 
 them to any one to cut, obferving carefal- 
 ly if he cut them at the wide card, which 
 will be the ace of hearts, and will then be 
 at top ; if not you muft make hirn, under 
 fome pretence or other, cut them till it 
 is ; and the cards will then be ranged in 
 fuch order that you will repique the per- 
 fon againft whom you play, though you let 
 him choofe (even after he has cut) in 
 what lliit you fliall make the repique. 
 
 * This manoeuvre of piquet was invented by the 
 Countefs of L — (a French lady], and communicated 
 by her to M. Guyot. 
 
 H 4 Order
 
 104 
 
 RATIONAL 
 
 Order of the cards after they have beenfhuf 
 fed and cut. 
 
 Eight hearts 
 Eight 
 
 f 
 
 Knave {-fpades 
 Ten 
 
 Knave 3 
 
 f hearts 
 
 King 
 
 3 
 
 4 
 
 5 
 6 
 
 7 
 
 8 Queen 
 
 9 Eight 1 
 
 10 King 1 
 
 11 Queen [diamonds 
 
 12 Ace j 
 
 13 Seven 
 
 1 4 Eight 
 
 1 5 Knave hearts 
 
 1 6 King clubs 
 
 clubs 
 
 diamonds 
 
 17 Nine 
 
 18 Knave 
 
 19 Nine hearts 
 
 20 Queen fpades 
 
 2 1 Seven hearts 
 
 22 Nine clubs 
 
 23 Ten hearts 
 
 24 Ace clubs 
 
 25 Seven ipades 
 
 26 Seven diamonds 
 
 27 Nine "] 
 
 28 King ^ ipades 
 
 29 Ace J 
 
 30 Ten clubs 
 
 3 1 Ten diamonds 
 
 32 Ace hearts 
 (wide card) 
 
 The cards being thus difpofed, you afk 
 your adverfary in v^^hat fuit you fhall re- 
 pique him. If he fay in clubs or diamonds 
 you muil: deal the cards by threes, and 
 the hands v/ill be as follows ; 
 
 E14er
 
 RECREATIONS. 
 
 105 
 
 Elder. 
 
 Hearts, king 
 
 queen 
 
 knave 
 
 ■ nnie 
 eight 
 {even 
 
 Spades, queen 
 • knave 
 
 eight 
 
 Diamonds, eight 
 Clubs, eight 
 feven 
 
 Younger. 
 
 Clubs, ace 
 king 
 
 queen 
 • knave 
 nine 
 
 Diamonds, ace 
 
 king 
 
 queen 
 
 knave 
 
 nine 
 
 Spades, ten 
 Hearts, ten 
 
 Rentree, or take in, Rentree of the 
 
 of the elder. 
 
 Seven ipades 
 Seven diamonds 
 Nine "1 
 King >lpades 
 Acq J 
 
 younger 
 
 Ten clubs 
 Ten diamonds 
 Ace hearts 
 
 If he againfl whom you play, who is 
 fuppofed to be elder hand, has named 
 clubs for the repique, and has taken in 
 five cards, you muft then lay out the 
 queen, knave, and nine of diamonds, and 
 
 you
 
 io6 RATIONAL 
 
 you will have, with the three cards you 
 take in, a fixiem major in clubs, and 
 quatorze tens. If he leave one or two 
 cards, you muft difcard all the diamonds. 
 
 If he require to be repiqued in dia- 
 monds, then difcard the queen, knave 
 and nine of clubs ; or all the clubs if he 
 leave two cards ; and you will then have 
 a hand of the fame ftrength as before. 
 
 Note, if the adverfary fliould difcard 
 five of his hearts, you will not repique 
 him, as he will then have a feptiem in 
 ipades : or if he only take one card : but 
 neither of thefe any one can do, who has 
 the leafl knowledsie of the game. If the 
 perfon againft whom you play would be 
 repiqued in hearts or Ipades, you mufl 
 deal the cards by twos, and the game 
 will ftand thus : 
 
 Elder
 
 RECREATIONS. 
 
 107 
 
 >. clubs 
 
 Elder hand. 
 King 1 
 
 ^^>^^^ ^diamonds 
 Nine '^ 
 
 Eight 
 
 Queen 
 
 Knave 
 
 Nine 
 
 Eio-ht 
 
 o 
 
 Seven 
 
 Eight ?hearts 
 beven 3 
 
 Eight fpades 
 
 Rentree. 
 Seven fpades 
 Seven diamonds 
 Ninel 
 
 } fpades 
 
 Youncrer hand. 
 
 King 
 
 Ace 
 
 Ace 
 
 King 
 
 Ace 
 
 Queen 
 
 Queen 
 
 Knave 
 
 Ten 
 
 Kins; 
 
 Queen 
 
 Knave 
 
 Ten 
 
 Nine 
 
 f clubs 
 
 diamonds 
 
 1 
 
 fpades 
 
 j^hearts 
 
 Rentree. 
 Ten clubs 
 Ten diamonds 
 Ace hearts 
 
 If he require to be repiqued in hearts, 
 you keep the quint to a king in hearts, 
 and the ten of fpades, and lay out which 
 of the reft you pleafe : then, even if he 
 ihould leave two cards, you will have a 
 fixiem m?jor in hearts, and quatorze tens, 
 which will make a repique. 
 
 But
 
 io8 RATIONAL 
 
 But if he demand to be repiqued in. 
 Ipades ; at the end of the deal you mufl 
 dextroufly pafs the three cards that are 
 at the bottom of the flock (that is, the ten 
 of clubs, ten of diamonds, and ace of 
 hearts) t~b the top*, and by that means you 
 referve the nine, king, and ace of Ipades 
 for yourfelf : fo that by keeping the quint 
 in hearts, though you fhould be obliged 
 to lay out four cards, you will have a 
 fixiem to a king in fpades, with which 
 and the quint of hearts, you muft make a 
 repique. 
 
 Obferve here likewife, that if the ad- 
 verfary lay out only three cards, you will 
 not make the repique : but that he will 
 never do unlefs he be quite ignorant of the 
 game, or has fome knowledge of your 
 intention. 
 
 This lafl flroke of piquet has gained 
 great applaufe, when thofe that have 
 
 * The manner of doing this you will find in the 
 Appendix, among the Recreations of Dexterity. 
 
 publicly
 
 RECREATIONS. 109 
 
 publicly performed it, have known how 
 to conduct it dextroufly. Many perfons 
 who underfland the nature of combining 
 the cards, have gone as far as the paffing 
 the three cards from the bottom of the 
 flock, and have then been forced to con- 
 fefs their ignorance of the manner in 
 which it was performed. 
 
 RECREATION XXXVIII. 
 
 '^he metamorphofed Cards, 
 
 pROVIDE thirty-two cards that are 
 differently coloured ; on which feveral 
 different words are wrote, and different 
 obje<5ls painted. Thefe cards are to be 
 dealt^ two and two, to four perlbns, and 
 at three different times, fhuffling them 
 each time. After the firft deal every one's 
 cards are to be of the fame colour : after 
 the fecond deal, they are all to have ob- 
 jeds that are fimilar ; and after the third, 
 words that convey a featiment. 
 
 J)ilpofe
 
 no 
 
 RATIONAL 
 
 Difpofe of the cards in the following order. 
 
 Order of 
 
 
 
 
 the cards. 
 
 Colours. 
 
 Objeas. 
 
 Words. 
 
 I 
 
 Yellow 
 
 Bird 
 
 I find 
 
 2 
 
 Yellow 
 
 Bird 
 
 In you 
 
 3 
 
 Green 
 
 Flower 
 
 Charming 
 
 4 
 
 Green 
 
 Flower 
 
 Flowers 
 
 5 
 
 White 
 
 Bird 
 
 To hear 
 
 6 
 
 White 
 
 Orange 
 
 Beauty 
 
 7 
 
 Red 
 
 Butterfly 
 
 My 
 
 8 
 
 Red 
 
 Flower 
 
 Notes 
 
 9 
 
 Red 
 
 Flower 
 
 In 
 
 lO 
 
 Red 
 
 Butterfly Shepherdefs 
 
 II 
 
 Green 
 
 Butterfly 
 
 Lover 
 
 12 
 
 Green 
 
 Butterfly 
 
 Your 
 
 ^3 
 
 White 
 
 Flower 
 
 Of 
 
 14 
 
 White 
 
 Flower 
 
 an inconftant 
 
 15 
 
 Yellow 
 
 Orange 
 
 Image 
 
 16 
 
 Yellow 
 
 Flower 
 
 Inchanting 
 
 17 
 
 White 
 
 Orange 
 
 Ardor 
 
 18 
 
 Yellow 
 
 Butterfly My 
 
 19 
 
 Yellow 
 
 Butterfly Phyllis 
 
 20 
 
 White 
 
 Bird 
 
 Birds 
 
 21 
 
 Red 
 
 Orange 
 
 Sing 
 
 -22 
 
 Red 
 
 Orange 
 
 Dear 
 
 23 
 
 Green 
 
 Orange 
 
 and Sweetnefs 
 
 24 
 
 Green 
 
 Orange 
 
 The 
 
 25 
 
 - Green 
 
 Bird 
 
 Of 
 
 26 Green
 
 RECREATIONS. iix 
 
 Order of 
 
 
 
 
 the cards. 
 
 Colours. 
 
 Objeas. 
 
 Words. 
 
 26 
 
 Green 
 
 Bird 
 
 Prefent 
 
 27 
 
 Yellow 
 
 Flower 
 
 As 
 
 28 
 
 Red 
 
 Bird 
 
 Changes 
 
 29 
 
 Red 
 
 Bird 
 
 Bofoni 
 
 3° 
 
 Yellow 
 
 Orange 
 
 Me 
 
 31 
 
 White 
 
 Butterfly 
 
 Your 
 
 32 
 
 White 
 
 Butterfly 
 
 I Ions: 
 
 
 The cards thus coloured, figured, and 
 tranfcribed, are to be put in a cafe, in 
 the order they here fland. 
 
 When you would perform this Recrea- 
 tion you take the cards out of the cafe, 
 and fhow, without changing the 'order in 
 which they were put, that the colours, 
 obje6ls, and words are all placed promif- 
 cuoufly. You then fhuffle them in the 
 fame manner as before, and deal them, 
 two and two, to four perfons, obferving 
 that they do not take up their cards till 
 all are dealt, nor mix them together ; and 
 the eight cards dealt to each perfon will 
 be found all of one colour. You then take- 
 5 each
 
 112 RATIONAL 
 
 each perfon's cards, and put thofe of the 
 lecond perfon under thole of the firfl, and 
 thofe of the fourth perfon under thofe of 
 the third. After which you fhuffle them 
 a fecond time, and having dealt them in 
 the lame manner, on the firfl perfon's 
 cards will be painted all the birds ; on the 
 fecond perfon's cards, all the butterflies ; 
 on thofe of the third, the oranges ; and on 
 thofe of the fourth, the flowers. You take 
 the cards a fecond time, and obferving 
 the fame precautions, ihuffle and deal 
 them as before, and then the firfl: perfon, 
 who had the lafl time the birds in his 
 hand, will have the words in his hand 
 that compofe this fentence, 
 
 Sing, dear birds ; / long to hear your en- 
 chanting notes. 
 The fecond perfon, who had the lafl deal 
 the butterflies, will now have thefe words,. 
 Of an inconftant lover your changes frefent 
 me the image. 
 The third, who had the oranges, will 
 have this fentence. 
 
 As
 
 RECREATIONS. 113 
 
 As in mjy Phylis, I find in you^ beauty 
 andfweetnefi. 
 
 The fourth, who had the flowers, will 
 have thefe words, 
 
 Cb.irmingfiowe?-s, adorn the hofom of my 
 Jh perdefs. 
 
 It Teems qiiite unnecefTary to give any far- 
 ther detail, as they who underftand the 
 foregoing Recreations will ealily perform 
 this. 
 
 RECREATION XXXIX. 
 
 I'he repique with carte blanch, 
 
 T N the following Recreations relating to 
 piquet, we fhall confine ourfelves to 
 the order in which the cards mufl: fland 
 after they are cut, and ready to be dealt. 
 They who chufe to fhuffle them iirfl (in 
 order to make the performance appear 
 the more extraordinary) may eafily diipofe 
 them in a proper order for that purpofe, 
 by having recourfe to the table of combi- 
 nations for 32 numbers. 
 
 Vol. I. I Order
 
 114 RATIONAL 
 
 Order of the cards^ 
 
 Elder I Ace 7 c j 
 
 2 beven 3 ^ 
 
 Y 3 Ten clubs 
 
 ° 4 Ten hearts 
 
 P 5 Ace hearts 
 6 Knave Ipades 
 
 Y 7 Nine hearts 
 ^' 8 Eight clubs 
 
 P 9 Queen fpades 
 ' 10 Ace diamonds 
 
 ■y 1 1 Eight hearts 
 '12 Eight fpades 
 
 •p ^3 Qi^s^i^ diamonds 
 ' 1 4 Ace clubs 
 
 Y 1 5 Nine diamonds 
 ' 1 6 Nine clubs 
 
 E. A rp ^ J- diamonds 
 
 Y 19 Seven hearts 
 
 * 20 Seven diamonds 
 
 P 21 Nine fpades 
 '22 Knave diamonds 
 
 * 2^4 Ten di-dinondi 
 
 25 King
 
 RECREATIONS. 
 
 115 
 
 25 King hearts 
 
 26 King clubs 
 
 27 Queen hearts > Elder's rentree 
 
 28 Kino; fpades 
 
 29 Ten fpades J 
 
 30 Queen clubs ~l 
 
 31 Knave clubs >Younger's rentrec 
 
 32 Knave hearts J 
 
 The cards being thus diipofed, the 
 hands of the players, after they have been 
 dealt two and two, will be as follows. 
 Elder. 
 
 ^ Ten -) 
 
 Nine 
 
 Younger. 
 
 Ace 
 
 Queen 
 Knave V fpades 
 
 Nine 
 Seven 
 
 Ace ^ 
 
 King 
 
 Queen > diamonds 
 
 Knave 
 
 Ten 
 
 Ace hearts 
 Ace clubs 
 
 Eight j 
 
 > clubs 
 
 Seven 
 Ten ■} 
 
 -n- u^ J" hearts 
 
 Eight r 
 
 Seven J 
 
 Nine ] 
 
 Eight [diamonds 
 Seven J 
 Eight fpades 
 
 The Rentree. 
 
 ^ '^ f hearts 
 Queen ) 
 
 King clubs 
 
 ^«"^ ? clubs 
 Knave ) 
 
 Knave hearts 
 
 I 2 
 
 The
 
 it6' RATIONAL 
 
 The cards being thus dealt, you defire 
 the other player to caft his eye over the 
 two hands, and take which he pleafe, on 
 condition, that if he keep the hand dealt 
 him he fhall be eldefl ; but if he take the 
 other he fhall be youngeft. 
 
 If he keep the hand dealt him, which 
 in appearance is much preferable to the 
 other, he will naturally lay out the four 
 loweft fpades, and leave a card, by carry- 
 ing the quint in diamonds and four aces. 
 You then tell down your carte blanch, 
 and keeping the two quarts and clubs and 
 hearts, lay out the others, and with your 
 rentree you will have a fixiem in clubs 
 and a quint in hearts, with which you will 
 make a repique, counting 107 points, 
 though if the cards were played you 
 would be capoted. 
 
 If the oppoflte player choofe the 
 youngeft hand, you then difcard the quart 
 to a king in diamonds with the feven of 
 
 ipades,
 
 RECREx^TIONS. it; 
 
 fpades, and with your rentree you will 
 J^ave a fixiem^ major in fpades, and qua- 
 torze of aces : by which you make re- 
 pique and capot. 
 
 Here alio you may mifs the repique, 
 if the other player keep the hand dealt 
 him, and difcard his diamonds ; but this 
 as in the other cafes, no one will do, who 
 has any knowledge of the game. 
 
 RECREATION XL. 
 
 Cafe at piquet, where you repique the elder 
 hand, though he have the choice of the cards 
 after they are dealt. 
 
 T^HE cards mufl here fland, after 
 they have been cut, in the following 
 order. 
 
 El<^" • 2 Ei At S 'P"'^'' 
 
 Younger ^ ,p > clubs 
 
 ■p 5 Ace clubs 
 ' 6 Nine hearts 
 
 I 3 ^'- 7
 
 u8 RATIONAL 
 
 y 7 Eight clubs 
 8 Nine diamonds 
 
 V 9 Qii^^^ clubs 
 
 ' 10 Eight diamonds 
 
 ^11 Seven clubs 
 ' 1 2 Ten diamonds 
 
 p 13 Ten fpades 
 
 * 14 Eight hearts 
 
 Y 15 Nine 7 j^ 
 ^•16 King 5''^''^^ 
 
 1 8 Quee 1 3 ^ 
 
 -^19 Knave diamonds 
 
 * 20 Seven Ipades 
 
 P 21 Seven diamonds 
 
 * 22 Knave fpades 
 
 w^ 23 Ace diamonds 
 
 * 24 Nine fpades 
 
 25 King 
 
 26 Knave 
 RentreeE. 27 Queen > hearts 
 
 28 Seven 
 
 29 Ten 
 
 30 Ace hearts 
 
 RentreeY.3iQueen7^.^^^^^5 
 32 King 3 
 
 The
 
 RECREATIONS. 
 
 119 
 
 The cards being thus difpofed* when 
 they are dealt, the hands of the two play- 
 ers will be as follows. 
 
 Elder. 
 
 Spades, ace 
 
 king 
 
 queen 
 
 • knave 
 
 ■ ten 
 
 eight 
 
 Clubs, ace 
 
 Younger, 
 
 Diamonds, ace 
 
 •- knave 
 
 ten 
 
 nine 
 
 Clubs, king 
 
 knave 
 
 ten 
 
 queen 
 
 Hearts, nine 
 ; eight 
 
 diamonds, eight 
 ' feven 
 
 Rentree. 
 
 King 
 
 Queen 
 
 Knave ^hearts 
 Ten 
 Seven 
 
 ' nnie 
 
 eight 
 
 feven 
 
 Spades, nine 
 {qycii 
 
 Rentree, 
 Ace, hearts 
 
 Q^ f diamonds 
 ueen } 
 
 You then give the other player the li- 
 J>erty of chuling either hand, but without 
 
 * In all 
 
 thefe 
 
 Recreations 
 
 with 
 
 piquet, there 
 
 fliould be a 
 
 wide card laft, that 
 
 they may be properly 
 
 CUtf 
 
 
 I 4 
 
 
 feeing
 
 ijic^ II ATI ON AL 
 
 feeing them. If he choofe the elder hand, 
 you dilcard the king of clubs, with the 
 nine and feven of fpades, and by your 
 rentree you will have a fixiem in dia- 
 monds and the point which will make 22, 
 and that added to the quint in clubs will 
 make 97, and you will neceffarily win, 
 as the adverfary will not fail to lay out 
 his two fmall hearts. 
 
 If, on the contrary, he choofe the 
 younger hand, you difcard the knave, ten 
 and eight of fpades, with the feven 
 and eight of diamonds : then by taking 
 in the quint to a king in hearts, you will 
 have a feptiem in hearts, a tierce major 
 in fpades, and three queens, which will 
 tell 90, though the adverfary fhould dif- 
 card to the mofl: advantage poffible. 
 
 RECRE.
 
 RECREATIONS. 121 
 
 RECREATION XLI. 
 
 Cafe at piquet, where you give the othe?- play- 
 er not only the choice of the fuite in which 
 he will be repiqued, but that of dealing the 
 cards by twos or by threes, a7id of taking 
 either hand after they are dealt, you b&ing 
 to tell and play firfl. 
 
 THE cards mufl be dilpofed as fol- 
 lows : 
 
 1 Queen^ 
 
 2 Nine , , 
 T-x. 1 ^ > clubs 
 
 3 Eight I 
 
 4 Seven J 
 wide card 
 
 5 Ace 
 
 6 King 
 
 7 Knave 
 
 8 Ten 
 
 9 Queen 
 
 10 Nine 
 
 1 1 Eight 
 
 12 Seven - 
 
 wide card 
 
 13 Ace -^ 
 
 14 King 
 
 15 Knave 
 
 16 Ten 
 
 ^hearts 
 
 > fpades 
 
 17 Queen"^ 
 
 1 8 Nine . , 
 
 19 Eight f*^^^^ 
 
 20 Seven J 
 
 wide card 
 
 21 Ace 1 
 
 22 King 
 
 23 Knave 
 
 24 Ten 
 
 25 Queen 
 
 26 Nine 
 
 27 Eight 
 
 28 Seven J 
 
 wide card 
 
 29 Ace n 
 
 o t> V clubs 
 
 31 Knave 1 
 
 32 Ten J 
 
 > diamonds
 
 122 
 
 RATIONAL 
 
 It is evident by this difpofition of the 
 cards, that if they are cut at any one of the 
 wide cards, which are the laft of each fuite, 
 there will be always a flock of eight cards 
 of the fame fuite, Confequently, if he with 
 whom you play require to be repiqued in 
 clubs, by cutting at the firil wide card, 
 which is the feven of clubs, the eight 
 clubs will neceffarily be at the bottom of 
 the pack, and you will have for your ren- 
 tree a quint major in clubs. The fame will 
 happen in all the other fuites, by cutting 
 at the 7 of each. If he deal the cards by 
 twos, the hands will be as follows *. 
 
 Elder 
 Ace -| 
 
 ^ ^ i-hearts 
 l^een f 
 
 Nine J 
 
 Ace -) 
 
 King 
 
 Queen 
 Nine J 
 
 Ace 1 
 
 iving 
 Queen 
 Nine J 
 
 Vfpades 
 n ( ^ 
 
 !> diamonds 
 
 Younger 
 Knave "^ 
 
 T?- u^ V hearts 
 
 Eight r 
 
 Seven J 
 Knave -} 
 
 Seven J 
 
 Knave 
 Ten 
 
 Eight 
 
 diamonds 
 
 Seven J 
 
 * The hands will be always the fame, though in djj^; 
 feient fuilps. 6
 
 RECREATIONS. 
 
 23 
 
 Rentree 
 
 Ace 
 King 
 Knave 
 Ten 
 
 ;^clubs 
 
 Que 
 
 iieen 
 
 But if he deal the 
 hands will fland thus 
 
 Elder 
 Ace -^ 
 
 ir ^ > hearts 
 Knave [ 
 
 Seven J 
 Ace 1 
 
 Nine 1 , , 
 Eight ['^"^^ 
 Seven J 
 
 cards bj threes, the 
 
 Younger 
 
 Ten 
 
 Queen 
 
 N" 
 
 hearts 
 
 ine 
 
 Queen I /- , 
 Nihe f^P^^^^ 
 Eight J 
 Knave 1 
 
 Ten > diamonds 
 Queen J 
 
 King 
 Knave 
 Ten 
 Seven 
 
 Ace 
 
 King 
 Nine 
 Eight 
 Seven 
 
 > ipades 
 
 i 
 J 
 
 > diamonds 
 
 Ace 
 
 King 
 Knave 
 Ten 
 Queen 
 
 Rentree, 
 
 > clubs 
 
 Nine 
 
 Ei^t 
 
 -Seven 
 
 clubs 
 
 If
 
 124 RATIONAL 
 
 If the other player require to be re- 
 piqued ill fpades, you cut them at the 
 1 of that fuite, and tell him he is at liber- 
 ty to deal them by twos or threes *. If he 
 deal them by twos, he is to choofe which 
 hand he will have, without feeing them ; 
 you being ftiil eldefl:. 
 
 If he keep his own hand, youdilcard the 
 nine of hearts, fpades and diamonds, and 
 either of the two queens \ and by your 
 rentree you will have a quint major 
 VOL clubs, quatorze aces, and quatorze 
 kings, with which you make a repique. 
 But if he choofe the cards dealt for the 
 elder, you difcard the feven of hearts, 
 ipades, and diamonds, and any two of 
 the eights ; and you will have by your 
 rentree the fame quint in clubs, qua- 
 torze queens and quatorze knaves ; which 
 will alfo make a repiq-ue. 
 
 * Ycu are to take care he does not fhuffle the cards ; 
 and the better to preven!^ it, you mayfo difpofe them 
 as to fhufRe thcin before him, after the manner ex- 
 plnined in feme of the foregoing Recreations. 
 
 If
 
 RECREATIONS. 125 
 
 If the adverfary deal the cards by 
 threes, and keep his hand, you difcard 
 the king, eight and feven of hearts, with 
 the nine and eight of fpades ; and by your 
 rentree you will liave the quint major in 
 clubs, a tierce to a queen in diamonds, 
 three aces, three queens, and three knaves, 
 with which you make a repique. But if 
 he choofe the cards dealt for the elder, 
 you difcard the queen and nine of hearts, 
 the knave and feven of fpades, and the 
 ace of diamonds, and you will then have 
 the fame quint in clubs, a tierce to a 
 nine in diamonds, three kings and thres 
 tens, with which you will tell 29 points, 
 therefore by playing one, jou can ill this 
 cafe make a pique only. 
 
 RECRE-
 
 126 RATIONAL 
 
 RECREATION XLII, 
 
 An exemplary cafe at piquet^ where yon re- 
 pique your advcrfary^ after giving him the 
 choice rf having the cards dealt either by 
 twos or threes, 
 
 ' I 'O difpofe the cards in the order ne- 
 cefTary to produce the efFedl here re- 
 quired, and in all others where you give 
 the choice of having the cards dealt either 
 by twos or threes, you mufl have re-i 
 courfe to the following table. 
 
 Cards
 
 RECREATIONS. 
 
 127 
 
 Cards that will 
 go to the eldeft. 
 
 13 
 
 21 
 
 Numb, 
 of the 
 Cards. 
 
 Cards that will 
 come to the 
 youngeft. 
 
 Variable 
 cards. 
 
 ro 
 
 IS 
 
 17 
 18 
 
 19 
 
 20 
 
 22 
 
 This
 
 118 RATIONAL 
 
 This table fhews the different hands 
 that refult from the two different me- 
 thods of deahng the cards ; that the el- 
 deft hand has always, in fome order or 
 other, the fix cards placed againft the 
 numbers, i, 2, 9, 13, 14, and 21 ; and 
 the younger, the fix cards placed againft 
 4, II, 12, 16, 23, and 24, It fhows like- 
 wife, that the 12 cards marked 3, 5, 6, 7, 
 8, 10, 15, 17, 18, 19, 20, and 22, may 
 be in either hand, fo far as concerns the 
 manner of dealing the cards. 
 
 Being therefore certain, when you deal, 
 that the cards marked i, 2, 9, 13, 14, and 
 21 will always be in the adverfary's hand, 
 and thole marked 4, 11, 12, 16, 23, and 
 24, will be in your own hand, you muft 
 apply your fix numbers to iuch cards, as 
 with the three of the rentree, (which you 
 may choofe as you pleale) will always 
 make a great hand, and fuperior to the 
 adverfary. The great cards which you are 
 forced to leave, you muft diftribute among 
 
 the
 
 RECREATIONS. 129 
 
 the variable cards, in fuch manner that 
 they can have no remarkable efFeft, whea 
 dealt either way. 
 
 This method we have obferved in the 
 Following example, which we here give 
 for the fatisfa(Slion of thofe who would 
 compofe thefe forts of games themfelves. 
 To the numbers 4, 11, 12, 16, 23, and 
 24, annex a fixiem major in hearts, 
 which joined to the three tens of the ren- 
 tree are fufficient to make a repique, 
 youngefl hand. But as you mufl pre- 
 vent the elder hand from defeating your 
 point, by having feven cards in any of the 
 other fuits, you are fo to diipofe fome part 
 of each fuit, by the column of variable 
 cards, that he may never have, whe- 
 ther the cards are dealt by twos or 
 threes, any large fequence* : as you will 
 
 * If you cannot efFeft this by the cards that are 
 to be dealt the adverfary, you muft fo difpofe his 
 rentree, that he may lay out his gt;ine, as in the 
 thirty-eighth Recreation. 
 
 Vol. I. K fee
 
 130 
 
 RATIONAL 
 
 fee by the following difpofitiou of the 
 cards. 
 
 I K:.ig 1 
 
 z Ace > diamonds 
 
 3 Nine J 
 
 4 Ace hearts 
 
 5 Queen ijpades 
 
 6 Eignt diarnoiids 
 
 7 Queen clubs 
 
 8 Eight fpades 
 
 9 King clubs 
 10 Seven 1 
 
 \ hearts 
 
 1 1 King 
 
 12 Nine 
 
 D 
 
 9^ 
 
 ueen 
 
 diamonds 
 
 14 Seven 
 
 1 5 Seven clubs 
 
 1 6 Knave hearts 
 
 17 Ace clubs 
 
 18 Seven 1 
 
 19 King j' fpades. 
 
 20 Ace J 
 
 21 Knave diamonds 
 
 22 Eight clubs 
 
 ^^ r\ {►hearts 
 
 24 Queen J 
 
 25 Knave 
 
 26 Nine 
 
 27 Knave clul:* 
 
 28 Eight hearts 
 
 29 Nine clubs 
 
 30 Ten diamonds 
 
 3 1 Ten fpades 
 
 32 Ten clubs 
 
 f fpades 
 
 By this arrangement of the cards ^'Oll 
 will be flire to fucceed, whether you 
 deal the cards by twos or threes : even 
 though the adverfary, thinking to fruf- 
 trate your intention, fhould leave three 
 cards. 
 
 Remark :
 
 RECREATIONS. 131 
 
 Remark: there is no danger that any 
 of thefe recreations at piquet fliould be ap- 
 plied to a bad purpofe, for after the cards 
 have been once fhuffled by both players, 
 it will be impollible to fucceed in any one 
 of them. There are, however, tricks to 
 be played at this, as at all other games, with 
 the cards ; filch as chansrino; the whole 
 
 ' DO 
 
 pack, or fome particular cards, or taking 
 in part, or all the difcard, or making the 
 pafs, that is, bringing part of the cards at 
 bottom to the top, as will be more fully 
 explained in the fourth vol. all of which 
 many perfbns can perform fo dextroufly, 
 that it is impoffible for the eye to difcover 
 them. We fay nothing of the pradrice of 
 marking the cards, for of that almofl every 
 one*s experience will afford fufficicnt 
 proof. To aggravate the misfortune, it 
 is indubitably certain, that many perfons 
 who are flridlly honeft in all other reipeds j 
 are difhoneft at cards ; and that no rank 
 or condition of men, no, nor woman nei- 
 tiler, is entirely free from this vice. 
 
 K 2 They
 
 132 RATIONAL 
 
 They who make a trade of dexterity 
 frequently exhibit other recreations with 
 the cards; but as thofe have no rela- 
 tion to numbers, they will be found among 
 the mifcellaneous articles in the Appendix 
 to the lall volume, 
 
 RECREATION XLIIL 
 
 Several different cards being fjjown to dif- 
 ferent perfons, that each of them may fx 
 071 one of thofe cards, to name that on 
 which each perfon fixed. 
 
 y I iKERE mufl be as many different 
 JL cards {hown to each perlbn, as there 
 are perfons to chooie ; therefore, fuppoie 
 there are three perfons, then to each of 
 them you muft ihow three cards, and tell- 
 ing the firft perfon to retain one in his 
 memory, you lay thofe three cards down, 
 and fliow three others to the fecond per- 
 fon, and fo to the third. You then take 
 up the iirft perfon's cards, and lay them 
 down one by one, feparately, with their 
 
 faces
 
 RECREATIONS. 133 
 
 faces upwards. You next place the fe- 
 cond perfon's card over the firil:, and in 
 like manner the third perfon's card over 
 the fecond's ; fo that in each parcel there 
 will be one card belonging to each per- 
 fon. You then afk each of them in which 
 parcel his card is, and when you know 
 that, you immediately know which card 
 it is ; for the firft perfon's card will al- 
 ways be the firft, the fecond perfon's the 
 fecond, and the third perfon's the third, in 
 that parcel where they each fay his card is. 
 
 This Recreation may be performed with 
 a fingle perfon, by letting him fix on 
 three, four, or more cards. In this caie 
 you mull: fhow him as many parcels as 
 he is to choofe cards, and every parcel 
 muil: confift of that number, out of which 
 he muft fix on one ; and you then pro- 
 ceed as before, he telling you the parcel 
 that contains each of his cards. 
 
 K 3 RE-
 
 134 R x\ T I O N A L 
 
 RECREATION XLIV. 
 
 5o name the rank of the card that a per/on 
 has drawn from a piquet pack, 
 
 Y the rank of the card we mean whe- 
 ther it be ace, king, queen, &c. You 
 are therefore firfl to fix a certain number 
 to each card, thus, you call the king 4, 
 the queen 3, the knave 2, the ace i, and 
 the others according to the number of 
 their pips. 
 
 You then fhuffle the cards, and let the 
 perfon draw any one of them : then turn- 
 ing up the remaining cards, you add the 
 number of the firfl to that of the fecond, 
 that to the third, and fo on, till it amount 
 to ten, which you then rejedl and begin 
 again ; or if it be more, you reje6l the ten, 
 and carry the remainder to the next card ; 
 and fo continue till you come to the laft 
 card ; and to the laft amount you muft add 
 4, and fubtrad that fum from 10 if it be 
 
 lefs,
 
 RECREATIONS. 135 
 
 lefs, or from 20 if it be more than 10, and 
 the remainder will be the number of the 
 card that was drawn : as for example, if 
 the remainder be 2, the card drawn was a 
 knave; if 3, a queen, &c. 
 
 RECREATION XLV. 
 
 To tell the amount of the numbers of two 
 cards that a perfon has drawyi from a 
 common pack of cards *. 
 
 nPHE fmall cards here tell, as before, 
 according to the number of their 
 pips, but each pictured card tells for 10. 
 Let the perfon add as many more cards to 
 each of thofe he has drawn, as will make 
 each of their numbers 25. Then take 
 the remaining cards in your hand, and 
 feeming to fearch for fome card amons 
 them, tell them over to yourfelf, and their 
 
 * This Recreation may be made with two perfons, 
 by letting each of them draw, and adding their 
 numbers together. 
 
 K 
 
 num-
 
 136 RATIONAL 
 
 number will be the amount of the two 
 cards drawn. An example will make this 
 plain. Suppofe the perfon has drawn a 
 10 and a 7, then he muft add 15 cards to 
 the firff:, to make the number 25, and 18 
 cards to the lafl:, for the fame reafon : 
 now 15 and 18 make ^^-f and the two cards 
 themfeives make 35, which deducted from 
 52 leaves 17, which muft be the number 
 of the remaining cards, and alfo of the 
 two cards drawn. 
 
 This Recreation may be performed 
 without your touching the cards thus : 
 let the perfon who has dr^wn the tVi'o 
 cards deducl the numbers of each of them 
 from 26, which is half the number of the 
 pack, and after adding the remainders to- 
 gether, let him tell you the amount, which 
 you privately deduct from 52, the num- 
 ber of all the cards, and the rem.ainder 
 will be the amount of the two cards. For 
 example, fu^ poie the two cards to be, as 
 before, i o and 7 ; then the perfon deduc- 
 ing 4
 
 RECREATIONS. 137 
 
 ing 10 fi-om 26 there remnins 16 ; and de- 
 ducing 7 from 26 there remains 19 ; thofe 
 two remainders added together will make 
 ^^, which you fubtrad from 52, and there 
 mail; remain 17, for the amount of the 
 two cards, as before. 
 
 As the number 26 may be thought to 
 lead to a diicovery of the principle on 
 which the Recreation is founded, it beins: 
 manifeftly the half of the pack, to render it 
 more myfterious you may take any other 
 number lefs than 26, but greater than 10, 
 as for example 24, and let the party ilib- 
 tracl the number of each of his cards from 
 that ; therefore, fuppoling the numbers to 
 be as before 10 and 7, the remainders will 
 be 1 4 and 17, which make 31, to which 
 you mud add 4, for the double of the 2 
 you took from 26, and the amount will 
 be ^§, which is to be deducted from 52, 
 as before. By this alteration the perform- 
 ance will not only be rendered more ab- 
 
 foufe.
 
 138 RATIONAL 
 
 ftrufe, but alfo more diverfified, as you 
 may change the number, from which thole 
 of the two cards are to be deducted, every 
 time you repeat the experiment. 
 
 This Recreation may be performed, 
 equally well, with a pack of piquet cards, 
 and then the numbers of the two cards 
 muft be deducted from 16, which is the 
 half of the pack ; or if you chufe to make 
 it more myfterious, from any other num- 
 ber lefs than 1 6 and more than i o ; after- 
 wards adding, as in the laft cafe, the double 
 of what that number wants to make it 
 
 16. 
 
 RECRE-
 
 RECREATIONS. 139 
 
 RECREATION XLVl. 
 
 5o tell the amount of the numbers of any 
 three cards that a perfon fhall draw from 
 the pack^. 
 
 A FTER the party has drawn his three 
 cards, you are to draw one yourfelf, 
 and lay it afide ; for it is neceflary that 
 the number of the remaining cards be di- 
 vifible by 3, which they will not be, in a 
 pack of 52 cards, if only 3 be drawn. 
 The card you draw you may call the con- 
 federate, and pretend it is by the aid of 
 that card you difcover the amount of the 
 others. Then tell the party to add as 
 many more to each of his cards, as will 
 make its number 16, which is the third 
 part of the remaining 48 cards ; therefore, 
 fuppofe he has drawn a 10, a 7, and a 6 : 
 
 * This Recreation may alfo be performed with 
 three perfons, but much more readily with one, as 
 the feparate additions and fubtradions will be very 
 like to occafion confufion. 
 
 then
 
 I40 RATIONAL 
 
 then to the firft he muft add 6 cards, to 
 the fecond 9, and to the third 10, which 
 together make 25, and the 4 cards drawn 
 being added to them make 29. You then 
 take the remaining cards, and telhng 
 them over, as in the lafl Recreation, you 
 find their number to be 23, which muft 
 be the amount of the three cards the 
 perfon drew. 
 
 You may perform this Recreation Hke- 
 wife without touching the cards, as thus : 
 after the party has drawn his three cards, 
 and you have drawn one, let him deduct 
 the number of each of the cards he has 
 drawn from 1 7, which is one- third of the 
 pack, after you have drawn your card : 
 and let him tell you the amount of the fe- 
 veral remainders, to which you privately 
 add one for the card you drew, and de- 
 ducting that amount from 52, the whole 
 number of cards, the remainder will be 
 the amount of the three cards drawn. 
 For example, fuppofe the three cards to 
 
 be
 
 RECREATIONS. 
 
 14.1 
 
 be lo, 7, and 6, as before; then each of 
 thofe numbers being fubtra£led from i^^ 
 the remainders will be refpe6lively 7, 10, 
 and II, which, added together, make 28, 
 to which the lingle card you drew being 
 added makes 29, and that number deduct- 
 ed from 52 leaves 23, which is the amount 
 of the three cards the party drew. 
 
 There is little reafon to imagine any one 
 will difcover why you here make choice 
 of the number 1 7 ; but if you are defirous 
 of rendering the Recreation ftill more ab- 
 ftrufe, and at the fame time fufceptible of 
 greater variety, you may fix on any other 
 number lefs than 17, but more than 10; 
 and afterwards add to the amount of the 
 remainders the double of what that num- 
 ber is lefs than 17; in the fame manner 
 as in the laft Recreation. 
 
 This Recreation alfo may be performed 
 
 with a pack of piquet cards; but then 
 
 •you mufl draw, or, what \n'<A anfvver 
 
 the
 
 142 RATIONAL 
 
 the iame purpofe, dedu£t 2, in your own 
 mind, from the whole number 32, that 
 the remainder may be divifible by 3 ; and 
 let him deduct the number of each of his 
 cards from that fiim, which is 10, and add 
 the remainders together, as before ; thus, 
 if his three cards be 10, 7, and 6, he is to 
 dedu6l each of them from 10, which is 
 the third part of 30 ; therefore the re- 
 mainders will be o, 3, and 4, which, added 
 together, make 7, and that added to the 
 2 you dedu<5led from the whole number, 
 m.akes 9, which taken from 32, leaves 23, 
 and that mufl be the amount of his three 
 cards. 
 
 Among the different purpofes to which 
 the dodrine of combinations may be ap- 
 plied, thofe of writing in cypher, and de- 
 cyphering, hold a principal place, as will 
 appear by the following Recreations, 
 
 DIF-
 
 RECREATIONS. I43 
 
 DIFFERENT METHODS OF 
 WRITING IN CYPHER. 
 
 The Lacedaemonians are faid to be the 
 inventors of cyphers, or at leaft they were 
 not, to our knowledge, uied by any people 
 before them. Their method was by a 
 wooden cylinder or roller, called a Scytala 
 Laconia, round which they rolled a thin 
 parchment, and wrote their difpatches. It 
 was then taken off and fent to the confe- 
 derate, who had another roller, exactly of 
 the fame fize, round which he wrapped 
 the parchment, and read its contents. 
 
 RECREATION XL VII. 
 
 To communicate intelligence by a pack of pi- 
 quet cards, 
 
 nPHE parties mufl previoufly agree in 
 what manner the cards fliall be firit 
 placed, and then how they ihall be fhuffled. 
 Thus, fuppofe the cards are to be liril 
 placed in the order as hereafter follows, 
 
 and 
 
 3
 
 144 RATIONAL 
 
 and then fhuffled by taking off 3 from the 
 top, putting the next 2 over them, and 
 the following 3 under them*, and fo al- 
 ternately. Therefore the party who fends 
 the cypher firft writes the contents of it 
 on a feparate paper, and then copies the 
 firft 32 letters on the cards, by writing 
 one letter on every card ; he then fhuffles 
 them in the manner defcribed, and writes 
 the fecond 32 letters : he ihuffles them a 
 fecond time and writes the third 32 letters, 
 and {o of the reft. An example will make 
 this plain. Suppofe the letter to be as fol- 
 lows : 
 
 I am In full march to relieve you ; withif\ 
 three days Ifhall be with you. If the ene\my 
 In the jnean time fhould make an affadjt^ re- 
 member what you owe to your countr\y, to 
 your family and your felf hive with ho\nour 
 or die with glory. 
 
 * By fiiuffling the cards in lliis manner, there 
 will remain only 2 to put under at laft. 
 
 Order
 
 RECREATIONS. 145 
 
 Order of the cards 
 before the ift fhuffle. 
 
 Ace ipades 
 
 i a d u y i 
 
 Ten diamonds 
 
 a I e u I 
 
 Eight hearts 
 
 m I m i u 
 
 King fpades 
 
 I s u m I 
 
 Nine clubs 
 
 n h I € 
 
 Seven diamonds 
 
 f b m r i 
 
 Nine diamonds 
 
 u e a c t n 
 
 Ace clubs 
 
 I zu k r y i 
 
 Knave hearts 
 
 I s c e a e 
 
 Seven fpades 
 
 in i a r m w 
 
 Ten clubs 
 
 a i t h e r 
 
 Ten hearts 
 
 r r h f 
 
 Queen fpades 
 
 c h e e i 
 
 Eisfht diamonds 
 
 h a b y w 
 
 Eight clubs 
 
 t y 00 I 
 
 Seven hearts 
 
 y a h 
 
 Queen clubs 
 
 r n u y h 
 
 Nine fpades 
 
 e u i y f y 
 
 Kino; hearts 
 
 I e t e u 
 
 Queen diamonds 
 
 e d s e 
 
 Eight Ipades 
 
 i i n "tc; s 
 
 Knave clubs 
 
 v.f a n t g 
 
 ioL, I. 
 
 L 
 
 Seven
 
 146 RATIONAL 
 
 Seven clubs e t s I y 
 
 Ace hearts y r e b r 
 
 Nine hearts I nw t 
 
 Ace diamonds u h s t& a 
 
 Knave fpades w I m a I 
 
 Ten fpades i e y t r r 
 
 King diamonds / / /" b u t^ 
 
 Queen hearts h h m m u 
 
 King clubs t n a t h 
 
 Knave diamonds n e u r 
 
 The perfon that receives thefe cards 
 firft places them in the order agreed on, 
 and tranfcribes the firfl: letter on every 
 card. He then Ihuffles them, according to 
 order, and tranfcribes the fecond letter on 
 each card. He Ihuffles them a fecond 
 time and tranfcribes the third letters ; and 
 fo of the rell. 
 
 If the cards were to be fhuffled the fe- 
 cond time by threes and fours, the third 
 time by twos and fours, &c. it would make 
 
 the
 
 RECREATIONS. 147 
 
 the cypher ftill more difficult to difcover : 
 though as all cyphers depend on the com- 
 bination of letters there are fcarce any 
 that may not be decyphered with time 
 and pains ; as we fhall Ihow farther on. 
 Thofe cyphers are the beft, that are by 
 their nature moft free from fiifpicion of 
 being cyphers ; as for example, if the let- 
 ters were here wrote with one of the 
 fympathetie inks, defcribed in the fourth 
 volume of this work, the cards might then 
 pafs for a common pack. 
 
 RECREATION XLVIIL 
 
 ^he myjlical dial. 
 
 ^r\ N a piece of fquare pafteboard ABCD 
 (Plate II.) draw the circle EFGH 
 land divide it into twenty-fix equal parts, 
 in each of which muft be wrote one of 
 the letters of the alphabet. 
 
 On the irilide of this there mufl be an- 
 other circle of pafteboard, II^N, move- 
 L 2 able
 
 148 RATIONAL 
 
 able round the center O, and the extre- 
 mity of this muft be divided into the fame 
 number of equal parts as the other. On 
 this alfo muft be wrote the letters of the 
 alphabet, which, however, need not be 
 difpofed in the fame order. The perfon . 
 with whom you correfpond muft have a 
 fimikr dial, and at the beginning of your 
 letter you muft put any two letters that 
 anfwer to each other when you have fix- 
 ed the dial. 
 
 Example. 
 
 Suppofe you would write as follows : 
 
 If you will come over to usyoujhall have 
 a pen/ton, and you may Jiill make ajhamop- 
 pojition. 
 
 You begin with the letters Ma, which 
 fhow how the dial is fixed ; then for If 
 you, you write un juc, and io for the reft, 
 as you will fee at the bottom of the plate. 
 
 The fame intention may be anfwered by 
 a ruler, the upper part of which is fixed 
 
 and
 
 RECREATIONS. 149 
 
 and the lower part made to Aide ; but in 
 this cafe the upper part muft contain two 
 alphabets in fucceffion, that fome letter of 
 that part may conflantly correlpond to one 
 in the lower part. The divifions {landing 
 dire6:ly over each other in a ftraisfht line 
 will be much more obvious than in the 
 circumference of a circle. Or two ftraisrht 
 
 o 
 
 pieces of pafteboard regularly divided, the 
 one containing a fingle and the other a 
 double alphabet, would anfwer exa(Slly 
 the fame purpofe. In this cafe a blank Ipace 
 may be left at each end of the lingle alpha- 
 bet, and one or two weights being placed 
 on both the pieces will keep them fteady. 
 
 RECREATION XLIX. 
 
 ^he correfpond'mg fpaces, 
 
 'T^AKE two pieces of pafleboard or flifF 
 paper, through which you muft cut 
 long fquares, at different diftances, as you 
 will fee in the following example. One of 
 thefe pieces you keep yourfelf, and the 
 L 3 other
 
 ^5® 
 
 RATIONAL 
 
 other you give to your correfpondent. 
 When you would fend him any fee ret in- 
 telHgence, you lay the pafteboard upon a 
 paper of the fame fize, and in the fpaces 
 cut out, you write what you would have 
 xmderflood by him only, and then fill up 
 the intermediate fpaces with fomewhat that 
 makes with thofe words a different fenfe« 
 
 I fhall be 
 
 much obliged to you, as read- 
 ing 'alone I engages my attention jat pre- 
 fent, if you will lend me any one of the 
 
 leight volumes of the Spedator. I hope 
 
 you will excufe this freedom, , but for 
 a winter's evening I don't know a bet- 
 
 ter entertainment. If I fail 
 
 to return it 
 
 foon, never trufl me for the time 
 
 to come. 
 
 A paper of this fort may be placed four 
 different ways, either by putting the bot- 
 tom at top, or by turning it over, and by 
 thofe means the fuperfluous words may be 
 
 the
 
 RECREATIONS. 151 
 
 the more eafily adapted to the fenfe of 
 the others. 
 
 This is a very ehgible cypher, as it is 
 free from fufpicion, but it will do only for 
 ihort meflages : for if the fpaces be fre- 
 quent it will be very difficult to make the 
 concealed and obvious meanings agree to- 
 gether ; and if the fenfe be not clear, the 
 writing will be liable to fufpicion. 
 
 RECREATION L. 
 
 T^he jnuftcal cypher. 
 
 nPHE conftrudlion of this cypher, is fi- 
 milar to that of the forty-eighth Re- 
 creation. The circle EFGH (PL III.) is 
 to be divided into twcnty-fix equal parts, 
 in each part there muft be wrote one of 
 the letters of the alphabet : and on the in- 
 terior circle ILMN, moveable round the 
 center O, there is to be the fame number 
 of divifions ; the circumference of the in- 
 ner circle rnufl be ruled in the manner of 
 L 4 ^ rnufiQ
 
 152 RATIONAL 
 
 a mufic paper, and in each divifion there 
 is to be placed a note, different either in 
 figure or pofition. Laftly, within the 
 mufical hnes place the three keys, and on 
 the outer circle, the figures that are com- 
 monly ufed to denote the time. 
 
 Then provide yourfelf with a ruled pa- 
 per, and place one of the keys, as fup- 
 poie that of ^^ refold againfl the time two- 
 fourths at the beginning of the paper, which 
 will inform your correfpondent how to fix 
 his circle. You then copy the notes that 
 anfwer to the feveral letters of the words 
 you intend to write, in the manner ex- 
 prelTed at the bottom of the plate. 
 
 A cypher of this fort may be made more 
 difficult to difcover by frequently chang- 
 ing the key, and that will not in the lead 
 embarrafs the reader. You may likewife 
 add the mark « or b to the note that be- 
 gins a word, v/hich will make it more 
 ealy to read, and at the fame time giv-e 
 
 the
 
 >n ( A- J I o w 1/ a 
 
 r t f( )• (' a Av ( n d 
 
 JM-d.-
 
 A ^;^ 
 
 ^-^ 
 
 j^ 
 
 n> 
 
 ,-^^^ 
 
 »*¥/X 
 
 
 i 
 
 s 
 
 p« 
 
 ^ 
 
 
 M 
 
 9 
 
 |l 
 
 l^^isS 
 
 
 m 
 
 B 
 
 ^m 
 
 is^-Vt ' 
 
 MJdAi 
 
 1 
 
 ■ 
 
 H 
 
 ^P¥K# 
 
 : \ VV^s;^ 
 
 ^H 
 
 ^B 
 
 ^^H 
 
 ^^mJ/tirrJ. b— 
 
 fc^ 
 
 i 
 
 1 
 
 
 ^ 
 
 
 
 ' /" // ^ f r t It > , il />! / // (f 
 
 c
 
 RECREATIONS. 153 
 
 the mufic a more natural afpedt. This 
 cypher is preferable to that of the 48th 
 Recreation, as it may be enclofed in a let- 
 ter about common affairs, and pafs unflif- 
 pe6led : unlefs it fhould fall into the hands 
 of any one who underflands compofition, 
 for he would very likely furmife, from the 
 odd difpolition of the notes, " that more is 
 meant than meets the ear." 
 
 OF DECYPHERING. 
 
 The rules of decyphering are different 
 in different languages : by obferving the 
 following, you will foon make out any 
 common cypher wrote in Englifh. 
 
 1. Obferve the letters or characters that 
 mofl frequently occur, and iet them down 
 for the fix vowels, including j)/ ; and of 
 thefe the moft frequent will generally be 
 e, and the leaft frequent u. 
 
 2. The vowels that moft frequently 
 come together are e a and o //. 
 
 ^. The
 
 ,54 RATIONAL 
 
 3. The conlbnant moft common at the 
 ends of words is s, and the next frequent 
 r and /. 
 
 4. When two {irallar characters come to-r 
 gether, they are mofl Hkely to be the confo- 
 nantsy, /, or j, or the vowels e or 0. 
 
 5. The letter that precedes or folio w§ 
 two fimilar characters is either a vowel, or 
 /, m, n, or r. 
 
 6. In decyphering, begin with the words 
 that confift of a lingle letter, which will be 
 either a, /, 0, or ^. 
 
 7. Then take the words of two letters, 
 one of which will be a vowel. Of thefc 
 words the moil frequent are, an, to, be, 
 "by, of, on, or, no,fo, as, at, if. In, is, it, he^ 
 nie, 7ny, us, we, am.' 
 
 8. In words of three letters there are 
 mofl commonly two confonants. Of thefe 
 words the mofl: frequent are, the, and, iiot, 
 but, yet, for, thQ\ how, why, all,you,Jhe, his, 
 her, our, who, may, can, did, was, are, has, 
 had, let, one, two, fix, ten, &c*. 
 
 * Some of thcfe, or thofe of two letters, will be 
 found in every fentcnce. 
 
 q. The
 
 RECREATIONS. 155 
 
 9. The moft common words of four 
 letters are, this^ that, then, thus, *with, when, 
 
 from, here,fome, mojf^none, they, them, whom, 
 mine, your, felf, muji, will, have, been, were^ 
 
 four. Jive, nine, &c. 
 
 1 o. The moft ufual words of five letters 
 are, there, thefe, thofe, which, where, whikj 
 ftnce, their, Jhall, might, could, would, ought ^ 
 three, feven, eight, &c. 
 
 1 1 , Words of two or more fyllables fre- 
 quently begin with double conlbnants, or 
 with a prepofition ; that is a vowel join- 
 ed with one or two confonants. The mofl: 
 common double conlbnants are, bl, br, dr, 
 
 /» /"» ^A gr, ph, pi, pr, Jh, fp,Jf, th, tr, 
 wh, wr, &c. and the mofl common prepo- 
 fitions are, com, con, de, dif, ex, im, in, inty 
 mif, par, pre, pro, re, fub, fup, un, &c. 
 
 12. The double confonants mofl fre- 
 quent at the end of long words are, ck, id^ 
 If, mn, nd, ng, rl, rm, rn, rp, rt,fm, y?, 
 xt, &c. and . the mofl common termina- 
 tions are, ed, en, et, es, er, ing, ly, fin, 
 
 fton.
 
 156 RATIONAL 
 
 fion^ tion, able, ence, ent, ment, full, lefs^ 
 nefs, Szc. 
 
 We fhall here give an example of a 
 cypher wrote in arbitrary charadlers, as is 
 commonly pradlifed. 
 
 cXxoo ex+io X+rc/A 
 srD. r-f-c 4-ro icro + 
 Lxeoi sro. eoxuc3c+eA 
 v+e ecu. csin +u 
 exeoorLo <>. Lsecc+r 
 r-i- cxscc+x cc CA 
 crocuuoxorLo o 
 roTiOLC ocrAox ucro. 
 A+Xo XosrA r-\- Aoro. 
 
 xo S lOCCOX AX-fXCIV 
 IOC XO AOO cXsccc 
 L-hXOA ux+X cXo Xosxc 
 
 +x roNoxosxo r+ AOO 
 
 XV USLO X+XO.
 
 RECREATIONS. i^l 
 
 The foregoing will be eafily decyphered 
 by obferving the rules ; but when the cha- 
 ra<aers are all placed clofe together, as in 
 the following example, and as they always 
 fhould be, the decyphering is much more 
 difficult. 
 
 UGNooNceuruuexesT 
 
 OSAUCX VXXrVVSTOAD 
 
 Nx^ noc N vvroox E+vx 
 +XASO X u ex cruxsA u G 
 xeNurDXV.+xiToeuTr 
 vusuexesTor^oesEX 
 cxvvioxirox D usox c 
 rNOnsTovN+xo u n so n 
 NX+orXXvnueNONoue 
 xoNceuueruxNuexoE 
 
 reXOTOSOTODSXOTOL 
 TNUX.
 
 158 RATIONAL 
 
 To decypher a writing of this fort, yotl 
 muft firft look for thofe chara(£ters that 
 moft frequently occur, and {et them 
 down for the vowels, as before. Then 
 obierve the fimilar characters that come 
 together ; but you mufl remember that 
 two fuch characters may here belong to 
 two words. You are next to remark the 
 combinations of two or three chara6lers 
 that are mofl frequent, which will be fome 
 of the words in the feventh and eighth of 
 the foregoing rules ; and by obferving the 
 other rules, you will infallibly diicover^ 
 with time and attention, any cypher wrote 
 on thele principles*. 
 
 * When the words are wrote all clofe togetherj 
 if the key to the cypher, were to be changed every 
 word, according to a regular method agreed oi> 
 between the parties, as might be done by either of 
 the methods mentioned in the 48th Recreation,- 
 Ivith very little additional trouble, the writing would 
 be then extremely difficult to decypher. The longer 
 any letter wrote in cypher is, the more eafy it is to' 
 decypher, as then the repetitions of the ehara6lers 
 sind combinations are the more frequent. 
 
 The
 
 RECREATIONS. 159 
 
 The following are the contents of the 
 two foregoing cyphers ; in which we have 
 inverted the order of the words and let- 
 ters, that they who are defirous of trying 
 their talent at decyphcring, may not, in- 
 advertently, read the explanation before 
 the cypher. 
 
 enil eno ton dna shtnom elohw eerht, 
 suoidifrep dna leurc o. noituac & ecnedurp 
 fo klat lliw uoy : on, rotiart, tcelgeii 
 & ecnereffidni si ti. yltrohs rettel a em 
 dnes ot snaem emos dnif rehtie, traeh eht 
 morf semoc ti taht ees em tel &, erom 
 ecaf ym ees ot erad reven ro. 
 
 evlewt fo ruoh eht ta thgin siht, ledatic 
 eht fo etag eht erofeb elbmella lliw sdneirf 
 ruo 11a. ruoh eht ot lautcnup eb : deraperp 
 Hew emoc dna, ytrebil ruoy niager ot, 
 ylevarb eid ro. thgin eht si siht, su sekam 
 rehtie taht, etiup su seodnu ro. 
 
 The
 
 p 
 
 i6o RATIONAL 
 
 The method of correfponding by fig- 
 nals being nearly related to that of cyphers, 
 we ihall here give two inflances of the 
 manner in which it may be performed. 
 
 RECREATION LI. 
 
 Vifucil Correfpondence. 
 
 ROVIDE a circle of wood ABCD 
 (Plate IV. Fig. i.) of about four feet 
 in diameter, and divide its circumference, 
 which will be about 12 feet, into 25 equal 
 parts. In one of thefe fpaces cut an open 
 fquare, and through each of the others cut 
 one of the 25 letters of the alphabet. (I 
 fervincT for J.) Over the fpaces that are 
 cut out, pafte a thin oiled paper. 
 
 On the top of a pole P (Fig. 2.) fixed to 
 the ground or floor, place a frame of wood 
 EF, in which there is to be an opening of 
 the fame fize with one of the divifions on 
 the wheel. On the outfide of this open- 
 
 ing
 
 RECREATIONS. i6i 
 
 ing let there be a door, by which it may 
 be occafionally clofed. To the pole let the 
 wheel be fixed, at its center G, round 
 which it muft turn, and be placed at fuch 
 a height that the letters on its circumfe- 
 rence may anfwer to the hole in the frame. 
 Behind' that part of the wheel which is 
 oppofite the board, let there be fixed, on 
 a ftand, a flrong light. 
 
 When you would communicate your 
 intelligence, open the door on the outfide 
 of the frame ; then put that divifion of the 
 wheel in which the fquare is cut, againfl 
 the opening, and place the light behind 
 it ; that ferves for a fignal to your cor- 
 refpondent, which he anfwers by putting 
 his wheel in the fame pofition*. What 
 you intend to communicate being wrote 
 on a paper and placed before you in a 
 
 * Where there is a frequent correfpondence re- 
 quired, certain hours of the day fhould be fixed 
 /or obferving this fignal. 
 
 Vol. I. M pro-
 
 i62 RATIONAL 
 
 proper pofition, you turn the wheel round, 
 till that divifion which contains the firfl 
 letter of the firfl word come before the 
 opening, and keep it there while } ou tell 
 4 ; you then turn the wheel, either back- 
 ward or forward*, to the fecond letter 
 and keep that before the opening the fame 
 time ; and fo of all the letters of that word ; 
 and between every word you place the 
 vacant divifion before the opening, while 
 x^ou, in like manner, tell 4. When you 
 have finifhed the whole of your intelli- 
 gence, you fhut the door of the frame, or 
 withdraw the light. 
 
 If your correfpondent be far off", as 
 fuppofe two or three miles, or farther, 
 you mufl be each provided with a telel- 
 cope, of a fize adapted to the diftance 
 between you. 
 
 * There may be placed handles on different parts 
 ©f the wheel as at ay by r, dy by which it will be the 
 more readily turned about. 
 
 Your
 
 RECREATIONS. 163 
 
 Your apparatus fhould be placed fome 
 way within the room, that it may not be 
 obvious to palTengers. It is evident, from 
 the conftrudion of this inftrument, that it 
 is full as well adapted for a correfpondence 
 by night as by day. 
 
 A machine of this fort may be con- 
 ftruded at a trifling expence, and will 
 be found highly uleful in many inftances, 
 as where two perfons live on the oppofite 
 lides of a large river, or in a country 
 where the roads are for a great part of the 
 year impaiTable, &c. If you are fearful 
 any perfon, befide your correfpondent, 
 fhould know what palTes, inftead of let- 
 ters, you may ufe 24 chara6lers, like thole 
 we have given in the laft example of 
 cyphers. 
 
 This invention may alfo be applied to 
 
 pubhc ufe, as to convey intelligence to 
 
 the garrifon of a town befieged ; or where 
 
 great difpatch is required; and in that 
 
 M 2 caie
 
 i64 RATIONAL 
 
 cafe feveral machines may be placed at 
 different diflances, that may convey the 
 intelligence to each other ; and here the 
 wheel may be of a much larger dimenflon. 
 There is one circumftance, however, that 
 will render this contrivance entirely ufe- 
 lefs, and that is a thick mift or fog ; for in 
 that cafe, let the light be as ftrong, and 
 the letters as large as they may , it will be 
 impoiiibie to difcern them at any con- 
 fiderable difiance. How to maintain a 
 correfpondence in that fituation, will be 
 (hown in the next Recreation. 
 
 RECREATION LII. 
 
 Auricular Correfpondence. 
 
 C\ N the top of a houfe, or any other build- 
 ing, fix two bells A andB, (PI. IV. Fig. 
 3,) by the iron rod CD, that paffesthro* their 
 handles, from which there muft hang two 
 ropes that go to the room beneath. The 
 
 weight
 
 RECREATIONS. 165 
 
 weight of the handles fliould be nearly 
 equal to that of the bells, lb that a fmali 
 additional force applied to the ropes may 
 di'aw them up. One of the bells mull: be 
 much larger than the other, that there 
 may be no difficulty in diftinguifliing their 
 founds. 
 
 The letters of the alphabet are to be 
 cxprefTed by pulling of thefe bells, ac- 
 cording to the followino; order ; in which 
 you are to obferve, that the fmall figures 
 denote the number of pulls of the leiTer, 
 and the numeral letters, thole of the 
 
 greater 
 
 bell. 
 
 
 
 
 A I 
 
 G I I 
 
 N I 
 
 III 
 
 Til I 
 
 B 2 
 
 H 2 I 
 
 2 
 
 III 
 
 VII 2 
 
 C 3 
 
 I 3 I 
 
 P3 
 
 III 
 
 UII 3 
 
 D I 
 
 K J II 
 
 QJ 
 
 I 
 
 Willi 
 
 E II 
 
 L 2II 
 
 R I 
 
 2 
 
 XIII 2 
 
 F III 
 
 M3II 
 
 S I 
 
 3 
 
 YIII 3 
 
 - 
 
 M 3 
 
 
 
 ZIIII 
 
 Afte
 
 i66 RATIONAL, &c. 
 
 After each letter you mufl ftop while 
 you tell 4, and at the end of each word 
 you may, for greater diftindion, pull both 
 bells twice together. 
 
 The above combinations may be conti- 
 nued to what number you pleafe ; fo as to 
 take in the moft common words, fuch as 
 and^ the^you^ he^Jhe^ they^ them^ this, that^ 
 may, can, do, &c. 
 
 MECHA«
 
 PLATE/ TV. 
 
 /? fee 
 
 F(^ . I . ft 
 
 /60.
 
 ^ 
 
 C)
 
 MECHANICS.
 
 RECREATIONS. 169 
 
 MECHANICS, 
 
 DEFINITIONS. 
 
 I. TV/f ECHANICS is that fcienee which 
 explains the properties of moving 
 bodies, and of thofe machines from which 
 they frequently receive their motion. 
 
 2. Gravity is that power by which every 
 body naturally defcends toward the center 
 of the earth. 
 
 3. The center of Gravity, in a fuigle 
 body, is that point round which the feve- 
 ral parts of the body, in every fituation, 
 exa(9:ly balance each other, and conie- 
 quently if that point be fufpended the 
 body will remain at reft. 
 
 4. The center of gravity, in two or 
 more bodies, is that point between them, 
 from which the diftance of each is in pro- 
 portion to the quantity of matter it con- 
 tains. The lefs the matter the greater 
 the diflance. 
 
 5. The
 
 j;o RATIONAL 
 
 ,5. The Vis Inertiae, or Inert Force, is 
 that property in bodies, by which they 
 refift the power that endeavours to put 
 them in motion. 
 
 6. The denfity of bodies is the quantity 
 of matter they contain, compared with 
 their magnitude or dimenfions. 
 
 7. Elaflicity is that property in bodies 
 by which, when their parts are forced out 
 of their natural ftate, they return to it 
 ao-ain ; and by which two moving bodies, 
 after ftriking, recoil from each other. 
 
 8. Power, in mechanics, is the force by 
 which any body is put in motion. 
 
 Q. Weight, is the body to be moved. 
 
 10. Motion, is either fimple or com- 
 pound : fimple motion is that which pro- 
 ceeds from one power only; and com- 
 pound motion is that which proceeds from 
 two or more powers, either at the lame 
 time or in fucceffion. 
 
 1 1 . The center of motion is that point 
 round which one or more bodies move. 
 
 12. Ve-
 
 RECREATIONS. 171 
 
 12. Velocity of motion, is the fpace 
 pafTed over by a body in a given time. 
 
 13. Accelerated motion, is that which 
 continually increafes, and retarded motion, 
 is that which continually decreafes. 
 
 14. The quantity of motion, or mo- 
 mentum of a moving^ body, arifes from its 
 velocity multiplied into the quantity of 
 matter it contains. 
 
 15. There are fix primary mechanic in- 
 ftruments, commonly called mechanic 
 powers, which are (i.) the lever *, (2.) the 
 balance. (3.) the pulley, (4.) the wheel and 
 axis, (5.) the fcrew f, and (6.) the wedge: 
 to which is fometimes added the inclined 
 
 * Levers are faid to be of the firft, fecond, or 
 third fort, according to the fituation of the fulcrum 
 F, as in PI. V. Fig. i, 2, 3; to which is added the 
 bended lever, Fig. 4. 
 
 t There are feveral forts of fcrews ufed in ma- 
 chines, of which thofe of Fig. 8, and 9, PI. V. are 
 moft common. In Fig. 8, the part A B is called 
 the male fcrew, and C D the nut, or female fcrew. 
 The part A B (Fig. 9.) which is turned by the wheel 
 C D, is called an endlefs fcrew, becaufe, while the 
 wheel goes, it turns inceflantly. 
 
 plane :
 
 172 RATIONAL 
 
 plane : and of fome or all of thefe, every 
 compound machine is compofed. See 
 Plate V. 
 
 1 6. A pendulum is any body fufpended 
 from a point, from which it ofcillates, or 
 vibrates, as from a center ; but is gene- 
 rally underftood to be a ball fulpended at 
 the end of a firing or wii-e. 
 
 1 7, That refinance which arifes from the 
 rubbing of the parts of a machine againfl 
 each other, is called their frldion. 
 
 APHORISMS. 
 
 1. Every body, whether at reft or in 
 motion, will conftantly continue in its 
 prefent flate, unlels compelled to alter 
 it by fome external power. 
 
 2. All motion, whether changed or ge- 
 nerated, is in proportion to the force im- 
 prefTed, and is made in the diredlion that 
 force a6ls. 
 
 3. A£lion and re-a£lion, that is, the im- 
 pulfes of two bodies on each other, are 
 
 ^Iways
 
 RECREATIONS, 173 
 
 always equal, and in contrary direc- 
 tions. 
 
 4. In bodies not elaflic, if one in motion 
 ftrike againft another at reft, they will both 
 move in the diredlion of the firft movinsf 
 body ; and the quantity of motion in both 
 bodies will be the fame as it was in the 
 firft before the ftroke. 
 
 5. If one flich body in motion, ftrike 
 acrainft another moving in the fame direc- 
 tion, but with lefs velocity, they will both 
 continue in that diredlion, and the quan- 
 tity of motion in both bodies will con- 
 tinue the fame. 
 
 6. When two fuch bodies, with equal 
 (quantities of motion, and moving in op- 
 pofite diredions, ftrike againft each other, 
 their whole motion will be deftroyed, and 
 they will remain at reft. 
 
 7. If two fuch bodies, with different 
 quantities of motion, and moving in op- 
 pofite diredions, ftrike againft each other, 
 they will continue to move in the direc- 
 tion of that body which had the greatef^ 
 
 momeu-
 
 174 RATIONAL 
 
 momentum, and the quantity of motion 
 in both bodies, after the ftroke, will be 
 equal to the difference of their motions 
 before it. 
 
 8. The force of a^Elion in elaftic bodies 
 is twice as great as that of non-elaflic bo- 
 dies ; for the former flrike each other not 
 only by impulfe, but by repulfe ; recoiling 
 from each other after the ftroke *. 
 
 9. The inert force of every body is in 
 proportion to its denfity. 
 
 10. All bodies near the furface of the 
 earth defcend equal fpaces in equal times f . 
 
 1 1 . The velocity of falling bodies, in 
 unrefifling mediums, is 16 feet the firfl 
 
 * In thefe aphorifms bodies are fuppofed to be 
 perfeftly elaftic or non-elaltic : in all other bodies 
 they will hold true only in proportion to the degrees 
 of their clafticity. 
 
 t This muit be underftocd of fuch as are called 
 heavy bodies ] for in thofe that are light the refift- 
 ance of the air makes a confiderable difference. A 
 bullet and a feather fall with very different veloci- 
 ties in the air, though in the exlaufled receiver they 
 defcend together* 
 
 fecond,
 
 RECREATIONS. 175 
 
 fecond, nearly, and becomes continually 
 accelerated in a regular pro greffion. 
 
 12. In every pendulum all its vibrations 
 in fmall arches, or parts of circles, are 
 made in the fame time. 
 
 13. The times of vibrations in different 
 pendulums, are as the fquare roots of their 
 length * : therefore a pendulum of four 
 feet will vibrate twice while one of 16 
 feet vibrates once. 
 
 1 4. The length of a pendulum that vi- 
 brates every fecond, will be 39 inches, 
 nearly f , and one that vibrates twice in a 
 fecond will be 91 inches. 
 
 15. Any body, in the form of a rod or 
 ftafF, that is every where of equal denfity, 
 as an iron rod, and that is one third loneer 
 than a pendulum, will vibrate in the fame 
 time as that pendulum. 
 
 16. In the lever, w^here the power P 
 
 * See page 2. definition 2. 
 
 t A pendulum of this fort is therefore a regular 
 meafure of time, and may be of ufe on many oc- 
 cafions, 
 
 5 (PI-
 
 176 RATIONAL 
 
 (PL V. Fig. I.) and weight W are to each 
 other reciprocally as their diflances from 
 the fulcrum f\ they will be in equi- 
 libno*- 
 
 1 7. The balance being a lever of the iirft 
 kind, where the fulcrum is placed exaftly 
 between its two extremities, if two weights 
 E, F, (PL V. Fig. 5.) be placed anywhere, 
 at equal diflances from the fulcrum, and 
 the balance remain in equilibrio, thofe 
 weights muft be equal. 
 
 18. When a power fuftains a weight, 
 by a rope going over a fixed pulley, the 
 v/eight and power will be equal : but if 
 one end of the rope be fixed, and the pul- 
 ley be moveable v/ith the weight, then the 
 power will be but half the weight. 
 
 10. In a combination of pullies, as 
 A, B, C, D, (PL V. Fig, 6.) called a tackle 
 of pullies, the power will be to the weight, 
 
 * The lever is to be regarded as the origin of 
 the other powers, feeing they all a6l in a fimibr 
 manner, though in different diredions. 
 
 as
 
 RECREATIONS. 177 
 
 as I to the number of ropes applied to the 
 moveable pullies C D, that is, in this cafe, 
 as I to 4. 
 
 20. In the wheel and axis, the power 
 will be to the weight, as the diameter of 
 the axis is to the diameter of the wheel. 
 
 21. When there is a combination of 
 wheels and axles, the power will be to the 
 weight, as the diameters of the axles mul- 
 tiplied into each other, is to the diameters 
 of the wheels multiplied into each other. 
 
 22. In the fcrew, the power is to the 
 weight, as the perpendicular diftance be- 
 tween any two threads of the fcrew A B, 
 (PL V. Fig. 8.) is to the circumference of 
 the circle defcribed by the power at C 
 orD*. 
 
 23. In the wedge, the power is to the 
 weight or refiftance, as half the length of 
 the bafe C E (Fig. 10.) to its heighth EF. 
 
 24. In the inclined plane, the power is 
 
 * The fcrew has the peculiar advantage of fuf- 
 taining a confiderable weight, when once raifed, 
 though the power be taken away. 
 
 Vol. I. N to
 
 178 RATIONAL 
 
 to the weight, as the height of the plane 
 C D (Fig. 1 1.) is to its length A B. 
 
 25. A body acquires the fame velocity 
 by rolling down an inclined plane A B 
 (Fig. II.) as it would by falling through 
 its perpendicular height C D. 
 
 26. It is evident from the foregoing 
 aphoriirns, that whatever is gained in 
 time is loft in power ; and that no ma- 
 chine can of itfelf give any frefh power, 
 but by diminifhing the velocity of the 
 weight, and increaling that of the power, 
 bring them to an equality. 
 
 27. When a fly is added to any machine, 
 as to a common jack, it does not increafe, 
 but diminifh, the ftrength of the power; 
 its only ufe being to regulate the motion 
 of the machine, and keep it coiiftantly 
 equal *. 
 
 * Though the fly does not in reality add any 
 frcfh power, yet by regulating the motion, it will 
 in fome cafes, as when a man is employed to turn a 
 large wheel, render the operation of the power more 
 eafy and effxacious. 
 
 28. In
 
 t78. 
 
 FLATJi .V; 
 
 J Mfc Sru^>
 
 n
 
 RECREATIONS. 179 
 
 28. In every machine, when the weight 
 and power are in equilibrio, the leaft ad- 
 ditional power fhould put it and keep it 
 in motion; but from the fridion of the 
 feveral parts of the machine, it is found 
 that, on a medium, near one-third of the 
 firfl power muft be added to keep the ma- 
 chine in motion. 
 
 29. The fridiion of a machine does not 
 arife merely from the number of the rub- 
 bing parts, but from the weight with which 
 they are charged, multiplied into the velo- 
 city of the motion. 
 
 30. In all machines, (implicity is their 
 primary excellence, as they are thereby 
 lefs liable to fridion and impediment ; the 
 diforder of any one piirt of a machine 
 frequently obflruding the operation of 
 the whole. 
 
 N 2 RE-
 
 i8o RATIONAL 
 
 RECREATION LIII. 
 
 ^0 conJiru6l a mechanical dial w'lthQiit ivheels^ 
 fpring, or weight. 
 
 nPHIS dial confifts of a tm or copper 
 barrel or cylinder C D, (Plate VL 
 Fig. I.) which is fupported by two firings 
 of catgut that are faftened to the points 
 A and B. This cylinder, for common 
 life, may be about a foot long, and nine 
 inches diameter. 
 
 The principal mechanifrn of this dial 
 is in the internal ftrudure of the cyhnder 
 which is reprefented by Fig. 2. and con- 
 fifts of five divifions*, that are formed 
 by the five pieces af^hg^ c h, di, and e /, 
 placed perpendicular to the ends of the 
 cylinder : all theie divifions mufl be pre- 
 cifeiy equal ; and in each of the partitions 
 
 * There are fometimes fix or more divifions, and 
 the machine is commonly efteemed the more accu- 
 
 rate for having a greater number. 
 
 almoft
 
 RECREATIONS. i8i 
 
 almoft clofe to the circumference of the 
 cylinder, there is to be a fmall hole, fuch 
 as is made with a large needle. 
 
 In the divifions muft be placed a quan- 
 tity of water, equal to about one-fourth 
 of the content of the cylinder ; but the 
 exa£l proportion can be determined by 
 trial only. This water fliould be diftilled, 
 or at leaft well filtered, that it may not, 
 by growing foul, impede the motion of the 
 machine ; and if there be a due quantity 
 of fpirits mixed with the water, it will be 
 thereby prevented from freezing. At one 
 end of the cylinder is a fmall hole, by 
 which it may at any time be emptied ; 
 this hole is to be flopped with wax. 
 
 The barrel being brought up to the 
 points A and B, by winding the ftri^ig 
 round its axis, it would there reft, but 
 the water oozino^ through the fmall holes 
 in the upper partitions deftroys its equi- 
 librium ; and as it flowly and gradually de- 
 N 3 fcends.
 
 i82 RATIONAL 
 
 fcends, the finall points at the end of its 
 axis fhow the hours, and parts of an hour, 
 according to the number of divifions on 
 the fcales E or F. 
 
 If this dial go too fafl or flow, it may 
 be eafily regulated, either by diminifhing 
 or increafing the lize of the catgut, or the 
 quantity of water in the cylinder. 
 
 Machines of this kind are moil: common 
 m monafleries, and are frequently made 
 by the monks themfelves, for their own 
 private ule ; the purchafe of a watch re- 
 quiring a film of money which is very 
 rarely pofTefTed by any of that clafs of 
 men ; if they can be called men who dif- 
 claim the principal charadleriftic of man- 
 hood. 
 
 RECRE-
 
 PJ.A.TE . VI.
 
 RECREATIONS. 183 
 
 RECREATION LIV. 
 
 A dial tojhoiv the hour by gradually defcend- 
 ing an inclmed plane, 
 
 'T'HE external ftrudure of this dial 
 confifls of two parrallel plates, con- 
 neaed by a hoop AB (PI. VI. Fig. 3.) 
 which is placed about one-eighth of an 
 inch beneath the circumference of the 
 plates. Theie plates are indented, to pre- 
 vent their Aiding down the plane. On the 
 front plate are infcribed the 24 hours; and 
 at its center is a fmall hollow hemiiphere g^ 
 moving freely on a pin : the lower part 
 of this hemiiphere is filled with lead, that 
 keeps the little gentleman who fits upon 
 it, and points with his finger to the hour, 
 conflantly in an ere6t pofition. The deep 
 iliades in the plate reprefent its concavity, 
 which is about half an inch. 
 
 Fig. 4. in the fame plate, reprefents the 
 internal flruoiure of this dial. LETQ^ 
 N 4 is
 
 i84 RATIONAL 
 
 h the circumference of the hoop ; f a 
 frame-plate, on which is placed the train 
 of wheels, i, 2, 3, 4, which are nearly fi- 
 milar to thofe in another dial, and are, in 
 like manner, governed by a balance and 
 regulator. There is here no fpring:, nor 
 fufee, their effe£ls being otherwife fup- 
 plied, as will appear hereafter. The great 
 wheel of the train is placed upon the axis 
 of the movement, at the center, and the 
 other wheels on one fide, which would 
 eive the machine a movement, for a ihort 
 time, on a horizontal plane : it is therefore 
 neceifary to fix a thin plate of lead, C, on 
 the oppofite fide, to preferve the equili- 
 brium. The machine^ will then refl in 
 any pofition on the horizontal plane H H ; 
 but if it be placed on the inclined plane 
 DGD, it will touch it in the point G, but 
 cannot reft there ; for the center of gra- 
 vity at M, a6ling in the dire^ion MT, 
 and having nothing to fupport it, muft 
 neceffarily defcend, and carry the body 
 down the plane. 
 
 But
 
 RECREATIONS. 185 
 
 But if on the other fide fuch a weight 
 P. be fixed, as fhall remove the center of 
 gravity from M to V, in the Hne LG, 
 which paffes through the point G, then 
 it will naturally reft on the inclined 
 plane. 
 
 Now if the weight P be not fixed, but 
 fuipended at the end of an arm or lever, 
 which is faftened to the center- wheel i, 
 moving on the axis of the machine at M, 
 and which communicates, by its teeth, 
 with the other wheels ; in that cafe, if the 
 weight P be jufl equal to the refiflance 
 arifuig from the friction of the train, the 
 dial will remain at reft, as on a horizontal 
 plane. 
 
 But if the weight P be fuperior to the 
 refiftance of the train, it will necefTarily 
 put it in motion, and the dial will then 
 gradually defcend the inclined plane ; 
 while the weight P, its arm PM, and 
 the wheel i, conftantly preferve the fame 
 
 pofition
 
 i86 RATIONAL 
 
 pofition they were in when tlie dial began 
 to move. 
 
 From what has been faid it is eafy to 
 conceive that the weight P may have fuch 
 a determinate gravity as fhall zS: upon 
 the train with any required force, and 
 confeqiiently produce a motion in the 
 machine of any required velocity, flich, 
 for example, as ihall carry it round once 
 in 24 hours. Therefore, if the diameter 
 of the dial plate be four inches, it will 
 defcribe the length of its circumference, 
 that is, 12 inches five-tenths, nearly, in 
 the 24 hours. From whence it follows, 
 that this movement may be made to con- 
 tinue any number of days by a propor- 
 tional increafe of the length of the plane ; 
 and if that were infinite, the motion of the 
 dial would be perpetual. 
 
 The motion of this dial is eafily accele- 
 rated or retarded by raifing or deprefling 
 the inclined plane, by means of the fcrew 
 
 S (Fig. 
 
 J
 
 RECREATIONS. 187 
 
 S (Fig. 3.) The angle to which the plane 
 is firft railed is about 10 degrees, that is, 
 the ninth part of a quadrant, or quarter 
 of a circle. 
 
 RECREATION LV. 
 
 A clock to go perpetually by the influence of 
 the celejiial bodies. 
 
 npHE conftru£lion of the movements 
 in this clock is the fame with thole 
 in common ufe : it differs from thofe only 
 in its (ituation, and the manner in which 
 it is wound up. 
 
 This clock is to be placed near a wall, 
 by, or againft which the tide conflantly 
 flows. To each of the barrels, round which 
 the firing that carries the weight is wound, 
 there muft hang a bucket, and into that, 
 when the tide rifes to a certain height, 
 the water runs, by means of a pipe fixed 
 in the wall. The bucket then overbalan- 
 cing the weight, defcends, and winds up the 
 2 clock ;
 
 i88 RATIONAL 
 
 clock ; but when it comes to a certain 
 depth, it is taken by a catch fixed in the 
 wall, which, by turning it over, difcharges 
 the water. The weights of the clock then 
 defcend in the ufual manner, and the 
 buckets are drawn up. 
 
 Now as this clock is kept in motion by 
 the tide, and as the tide proceeds frorh 
 the influence of the fun and moon, it ne- 
 cefTarily follows, that the motion of the 
 clock proceeds from the fame caufe ; and 
 that as long as the parts of the machine 
 remain, motion will be perpetual. 
 
 This, according to the common accep- 
 tation of the term, is certainly a perpetual 
 motion ; and fo is every mill that is driven 
 by a conflant ilream ; but that is not the 
 fenfe in which the term was ufed by the 
 advocates for a perpetual motion in the 
 laft century. They meant a machine, 
 which, being once put in motion, (liould, 
 by its peculiar conflrudion, move perpe- 
 tually.
 
 RECREATIONS. 189 
 
 tually, without any frefli force imprefled. 
 This they attempted by various means; 
 as the attradlion of a loadftone, the defcent 
 of heavy bodies, the difference of the mo- 
 mentum, in revolving weights, &c. all of 
 which, though ingenious enough, difcover 
 a want of due attention to the principles 
 of mechanics. Befides, if a perpetual 
 movement could be effeded by either of 
 thofe means it would be of very little, or 
 no ule : for the unavoidable wear of the 
 feveral parts of the machine, ariiing from 
 the inceflant fridlion, muft necefTarily 
 deftroy that equality of motion, which 
 alone could render its perpetuity of any 
 confequence. 
 
 RECRE-
 
 I90 RATIONAL 
 
 RECREATION LVL 
 
 T^he Infcrutable Lock, 
 
 T^HE difficulty a ftranger would find in 
 opening this lock, when in pofleffion 
 of the key, arifes partly from the fcutcheon 
 that is placed before it, and partly from 
 the peculiar form of the key. 
 
 The fcutcheon A B (PI. VII. Fig. i.) 
 confiils of a circular plate of brafs or iron, 
 onwhofe rim are 24 teeth, that take the 
 leaves of the pinion C : this fcutcheon may 
 therefore be placed in 24 different pofi- 
 tions ; in feveral, or all of which, the key 
 may be inferted, but the lock opened in 
 one of them only ; D, is the aperture for 
 the key, and ^, ^, r, d, are four knobs by 
 which it is turned about. 
 
 The key ABC D (Fig. 2.) confifls of 
 two fets of wards, which are divided into 
 
 twelve
 
 RECREATIONS. 191 
 
 twelve parts, as is exprefled by the paral- 
 lel lines ill the figure, and which fhould 
 be made to join fo exactly, that when 
 they are prefTed together, their divifions 
 may not be vilible. At the middle of the 
 key is a fcrev»^ E, which, when turned in, 
 faftens all the parts together, and when 
 fcrewed out, fets them at liberty, that they 
 may be turned round the barrel of the key, 
 at the center of each part. When you 
 have locked the door, you turn the 
 fcutcheon about by one of the knobs ; then 
 unfcrewing the wards of the key, you 
 turn part of them half round, that is, you 
 bring fbme of thofe parts that were next 
 AB to CD, and then make them faft again, 
 by the fcrew at the end. 
 
 Now if the perfbn, into whofe hands 
 this key fhall fall, be ignorant of the 
 fcrew, it will be abfolutely impofTible for 
 him to open the lock ; and if he Ihould 
 know the ufe of it, the trials he muft make 
 before he can have any profped of fuc- 
 
 cels,
 
 192 RATIONAL 
 
 cefs, will render the attempt highly ab- 
 fiird ; for there being 1 2 divilions in the 
 key, it appears by the i8th Recreation 
 of this volume, they may be placed in 
 479,001,600 different pofitions, and as 
 each of thefe portions may be applied to 
 the ieveral ways in which the fcutcheon 
 may be placed, it follows, that if the 
 foregoing number be multiplied by 24, 
 the produd, which is 11,496,038,400, 
 will be the number of all the trials that 
 can be made : therefore, it is eleven 
 thoufand four hundred and ninety-fix 
 millions, thirty-eight thoufand, three 
 hundred and ninety-nine, to one, at each 
 trial, that he does not open the lock. 
 
 For common purpofes a much lefs num- 
 ber may luffice : fuppofe, for example, 
 there are only feven divifions in the key, 
 the number of trials will be then 120,960. 
 Now fuppofing 60 trials to be made in an 
 hour, it would require 20 16 hours to make 
 all thofe trials that is, to be fure of fuc- 
 
 cceding ;
 
 RECREATIONS. £f)3 
 
 ceeding ; that is, fuppofing again, a regu- 
 lar account to be kept of each trial as it is 
 made, for otherwife the fame trial might, 
 and naturally would, be made feveral 
 times. 
 
 RECREATION LVIL 
 
 So to dlfpofe a hand-mill^ to grind corn^ &c, 
 that being once put in motion, it fhai/ zuork 
 incejfantly, from morning to nighty with-- 
 out the ajftjiance of any animal power. 
 
 nPHE form of this mill may be iimilar 
 to thofe in common ufe : its motion 
 is to be maintained by means of a fmoke- 
 jack : the ufe of this fort of jack is com- 
 mon enough ; but its conftru£tion and 
 manner of aQing being clearly under- 
 flood by few, we fhall here defcribe 
 them. 
 
 The horizontal wheel AB (Plate VIL 
 Fig. 3.) is placed in the narrowed part 
 of the chimney that is next the fire : its 
 wings, which are made of tin, are mclin- 
 
 VoL, L O ed
 
 194 RATIONAL 
 
 ed to the horizon, that is, placed in ^ 
 floping diredion. To the fame axis on 
 which AB turns, is iikewife placed the 
 cog-wheel C, that takes the teeth of the 
 perpendicular wheel D. On the fame axis 
 with D, is placed the wooden wheel E, 
 round which runs the rope F, on whofe 
 lower part is placed the wheel of the {pit. 
 
 Now, the air, being rarefied by the fire, 
 forces up the chimney, and roeeting with 
 the wings of the horizontal wheel in the 
 narroweft part, necefl^rily turns it round, 
 and at the fame time turns the cog-wheel 
 C, which turns D and E, together with 
 the rope, which by its fridion againft the 
 wheel of the fpit, keeps that Iikewife con- 
 ftantly turning ; and its velocity will be 
 always in proportion to its weight, and 
 the ftrength of the fire. 
 
 Therefore, if Inftead of the iron ipit, 
 the handle of the mill be fixed in the cen- 
 ter of the lower wooden wheel, it mufl, 
 in like manner, turn that round ; and the 
 
 mption
 
 PLATE/.\1I. 
 
 / Lod^c S-<f'/i
 
 c
 
 RECREATIONS. 195 
 
 motion will continue not only while the 
 fire lafts, but a confiderable time after; 
 for there will be a continual circulation 
 of the air up the chimney, till that in 
 the room becomes equally cold with the 
 external air. 
 
 This machine may in like manner be 
 applied to the reeling of yarn ; to the 
 making a hammer flrike perpetually on 
 an anvil ; and many other domeftic pur- 
 pofes. 
 
 RECREATION LVIII. 
 
 A carriage to go without any other force than 
 what it receives from the pafengers, 
 
 ^ I ^HIS machine is reprefented by AB 
 CD, (PI. VIII. Fig. I.) It is moved 
 by the footman behind it ; and the fore 
 wheels, which a£t as a rudder, are guided 
 by the perfon who {its in the carriage *. 
 
 * This machine was invented by M. Richard, a 
 phyfician of Rochelle, and was exhibited at Paris in 
 the laft century. It is defcribed by M. Ozanam in 
 his Recreations Mathem&tiques. 
 
 O 2 Between
 
 196 RATIONAL 
 
 Between the hind wheels is placed a 
 box, in which is concealed the machinery 
 that moves the Carriage. A A, Fig. 2. is 
 a fmall axis, fixed into the box. B is a 
 pulley, over which runs a rope, whoie 
 two ends are faftened to the ends of 
 two levers or treddles CD, whofe other 
 ends are fixed in fuch manner in the piece 
 E, which is joined to the box, that they can 
 ealily move up and down. FF are two flat 
 pieces of iron, that are joined to the tred- 
 dles, and take the teeth of the two wheels 
 HH, which are fixed on the lame axis 
 with the hind wheels of the carriage, I, I, 
 
 It is evident that when the footman 
 behind prefles down one of the treddles, 
 fuppofe C, with his foot, he mufh bring 
 down one of the pieces of iron F, and con- 
 fequently turn the wheel H that is next 
 to it, and at the fame time, by means of 
 the rope that goes over the pulley, he muft 
 raife the other treddle D, together with 
 its piece F, which being thrufi: down, will 
 turn the other wheel H ; and fo alternate- 
 
 ly:
 
 Plate ATI! . 
 
 c/ - It oJjfC Scu/fh
 
 RECREATIONS. 197 
 
 ly ; and as the great wheels are fixed on 
 the fame axis, they muft neceffarily move 
 at the fame time. 
 
 It is eafy to conceive that if the ends 
 of the treddles next E, inftead of being 
 placed behind the carriage were turned the 
 oppoiite way, fo as to come under the feet 
 of the perfon who fits in it, he might 
 move it with equal, or even greater faci- 
 lity, than the footman, as it would then 
 be charged with the weight of one perfon 
 only. 
 
 A machine of this kind will afford a 
 falutary recreation in a garden, or park, 
 or on any plain ground, but in a rough or 
 deep road mull: be attended with more 
 pain than pleaflire. 
 
 O n RE-
 
 198 RATIONAL 
 
 RECREATION LIX. 
 
 l!he catapulta. 
 
 'T^HIS engine was in great repute among 
 the ancients, and ufed by them in 
 throwing darts or fpears againfl their ene- 
 mies, from whence it had its name. Some 
 of the fpears or darts thrown by thefe en- 
 gines are faid to have been eighteen feet 
 long, and to have been thrown with fuch 
 velocity as to take fire in their courfe *. 
 
 * It will not be improper to infert here, what is 
 related by writers of the laft century concerning 
 the force of darts or arrows. Greaves, in his Pyro- 
 modographia, fays, " Some Turkifh bows are of 
 *< that ftrength as to pierce a plank fix inches thick." 
 He adds, ** I fpeak what I have feen." And Bar- 
 clay, a writer of fufficient credit, in his Icon Ani- 
 morum, fpeaking of the Turkifli bow, which dif- 
 fered very little in form from the long low bow, 
 anciently in ufe among us, being drawn by the 
 hand, without the help of the rack that is ufed to 
 fome other bows — He fays, *' I was an eye witnefs, 
 " how one of thefe bows, with a little arrow, did 
 " pierce through a pie^c of fteel three fingers 
 
 *' thick."
 
 RECREATIONS. 199-^ 
 
 ABCD, (PI. IX. Fig. I. ) is the frame 
 
 that holds the darts or arrows, which may 
 
 be of different numbers, and placed in 
 
 different dire£tions. EF, is a large and 
 
 ftrong iron Ipring, which is bent by a 
 
 rope that goes over the three pullies I, K, L, 
 
 and is drawn by one or ieveral men ; this 
 
 rope may be faftened to a pin at M. The 
 
 rope therefore being fet at liberty, the 
 
 Ipring muft ftrike the darts with great 
 
 violence, and fend them with iiirpriling 
 
 velocity to a great diflance. This inflru- 
 
 ment differs in fome particulars from the 
 
 defcription we have of that of the ancients ; 
 
 principally of throwing of feveral darts at 
 
 the lame time, one only being thrown by 
 
 their's. A machine of this fort would be 
 
 of ufe in thofe countries where there are 
 
 frequently large flights of birds, for a great 
 
 ** thick." Of fads like thefe a man may be very 
 well ^allowed tp doubt, or to fuppofe they were at- 
 tended with fonie deception : yet totally to difbelieve 
 them, when related by fuch witnefles, merely be- 
 caufe they are to us impradlicable, favours rather of 
 ignorance and temerity than a rational caution. 
 
 O 4 number
 
 zoo RATIONAL 
 
 number of arrows being thus difcarged 
 at the fame iiiftant, could not fail of doing 
 remarkable execution. 
 
 RECREATION LX. 
 
 ^fo fail as faji^ with a fair wind, by land at 
 by water, 
 
 'T^HIS is to be effedted by means of a 
 failing chariot, or boat fixed on four 
 wheels ; as A B (Plate IX. Fig. 2.) which 
 is driven before the wind by the fails CD, 
 and guided by the rudder E. In a chariot 
 of this kind the wheels would be farther 
 afunder, and the axle-trees longer, than in 
 other carriages, to prevent overturning. 
 
 A machine of this fort was confl:ru6led 
 ifx the laft century by Stephinus, at Sche- 
 veling in Holland, and is celebrated by 
 many writers. Its velocity with a flrong 
 wind is faid to be fo great, that it would 
 carry eight or ten perfons from Scheveling 
 to Putten, which are forty- two Englifh 
 miles diflant, in two hours. 
 
 2 Carriages
 
 PL ATE. IX
 
 c
 
 RECREATIONS. 201 
 
 Carriages of this kind are faid to be fre- 
 quent in China ; and in any wide, level 
 country, muft be fometimes both pleafant 
 and profitable. The great inconvenience 
 attending this machine is, that it can only 
 go in the diredion the wind blows : and 
 even not then unlefs it blows flrong ; fo 
 that after you have got fome way on 
 your journey, if the wind fhould fail, or 
 change, you muft either proceed on foot, 
 or go back. Some remedy for this in- 
 convenience will be found in the next 
 recreation. The Hollanders have, or 
 had, fmall vefTels, fomething of this kind, 
 that carry one or two perfons on the ice, 
 having a fledge at bottom inftead of 
 wheels ; and being made in the form of 
 a boat, if the ice break the pafTengers are 
 fecured from drowning. 
 
 RECRE-
 
 1P2 RATIONAL 
 
 RECREATION LXI. 
 
 'To fail by land agatnjl the wind. 
 
 T ET ABCD (Plate X. Fig. i.) be the 
 body of a failing chariot : M the 
 mail:, to which are fixed the wings or fails 
 E F G H ; the two firft of which E F, are 
 here fuppofed to be expanded by the 
 wind. R is the rudder by which it is 
 guided. Therefore the wind drivinoj the 
 fails round, with the maft M, and the cog 
 wheel K, take the teeth, placed perpen- 
 dicular to the fides of the two fore wheels 
 of the carriage, and confequently keep it 
 in continual motion. 
 
 The body of this machine fhould not 
 be large, nor placed very high, not only 
 to prevent overturning, but that its mo- 
 tion may not be thereby impeded ; for the 
 velocity will be in proportion to the force 
 of the wind on the fails to that on the 
 body of the machine. Therefore if they 
 
 be
 
 RECREATIONS. 203 
 
 be both equal it will ftand ftill ; or if the 
 force Oil the body be the greateft, it will 
 go backwards ; vinlefs there be a contri- 
 vance to lock the wheels. The upper 
 part of the machine next A, may be made 
 to take off, when the wind is contrary, and 
 there may be another fet of fails placed be-!- 
 tween the two hind wheels, which will con- 
 fiderably increafe its velocity. But after 
 all, for general ufe, a common carriage 
 mufl be preferable ; for this cannot be ex- 
 pelled to go up a moderate afcent without 
 great difficult, nor down a declivity, when 
 there is a ftrong wind, without danger ; 
 and even on level ground, if the road be 
 in any degree rough, its progrefs mufl be 
 very flow, attended both with difficulty 
 and danger. In an open country, how- 
 ever, where there is a large tra£l of level 
 and fmooth ground, and frequent flrong 
 winds, a machine of this fort will cer- 
 tainly be very convenient ; and in moil 
 countries, when made of a fmall fize, may 
 be ufeful to young people, by affording 
 them a pleafant and healthful exercife. 
 
 RECRE-
 
 T 
 
 204 RATIONAL 
 
 RECREATION LXII. 
 
 I'he unmvertlhle carriage, 
 
 HE body of this carriage miift confiil: 
 of a regular hollow globe, as A B 
 (Plate X. Fig. 2.) at the bottom of which 
 is to be an immoveable weight, and which 
 mufl be proportioned to the number of 
 perfons, or the load the machine is intend- 
 ed to carry. Round the globe mufl: go 
 two horizontal iron circles D, E, and two 
 others F, G, that are perpendicular to the 
 former. All thefe circles mufl be made 
 exadly to fit the globe, that it may move 
 freely in every diredion. The two hori- 
 zontal circles are to be joined on each fide 
 by a perpendicular bar, one of which is ex- 
 preffed in the figure by H I. All thefe 
 irons fhould be lined with leather, to pre- 
 vent unnecefiary friclion. The body of 
 the carriage may be either of leather or 
 hard wood, but the latter will be mofl ele- 
 gjbie, as leafl liable to wear. The wheel 
 
 on
 
 RECREATIONS. 205 
 
 on each fide is to be fafleiied to the per- 
 pendicular bar by means of a handle K, 
 that keeps it Iteady. 
 
 Now the body of this machine move- 
 ing freely in the iron circles, every way, 
 the center of gravity will always lie at C ; 
 therefore iji whatever pofition the wheels 
 are, or even if they overturn, the body of 
 the carriage will conftantly remain in the 
 fame perpendicular dire6lion. 
 
 At L is placed a pin, round which 
 is a hollow moveable cylinder : this pin 
 moves up and down in the groove M N, 
 that it may not impede the perpendicular 
 motion of the circles, at the fame time 
 that it prevents the body of the machine 
 from turning round in a horizontal direc- 
 tion. O, is one of the windows, P the 
 door, and QR the fhafts to this ma- 
 chine. 
 
 When a carriao;e of this fort is intend- 
 cd for a fingle perlbn, or a light weight, 
 
 it
 
 20^ RATIONAL 
 
 it may be hung on fwivels, in the fame 
 manner as the rolling lamp or the fea 
 compafs, which will make its horizontal 
 motion flill more regular : and when it is 
 defigned to carry feveral perfons, by add- 
 ing another perpendicular bar, on each 
 lide, between the two horizontal circles, 
 it may be placed on four wheels. The 
 body of this machine fhould be frequent- 
 ly oiled or greafed, not only to prevent 
 any difagreeable noife that may arife from 
 its rubbing againft the circles, but to pre- 
 vent unneceflary wear in the feveral parts. 
 
 This carriage is not intended for frnooth 
 roads, or a regular pavement ; there, cer- 
 tainly, thofe of the common conflrudion 
 are much preferable ; nor Ihould a car- 
 riage totally free from irregular motion be 
 fought after by thofe who are in perfect 
 health : but there are many perfons, fub- 
 je£l to different diforders, who, by being 
 obliged to travel over rough roads in the 
 common caiTiages, fuffer tortures of which 
 
 the
 
 . ■-' / /.■ ::,'o. 
 
 
 
 Pj.atkx. 
 
 [f 
 
 G 
 
 
 fl 
 
 //<? . /./i ?r>2. 
 
 1 
 
 
 1 
 
 K^^^ 
 
 1 
 
 
 1" 
 
 
 ^ 
 
 Kj^M 
 
 Lk 
 
 D^^Hf^HB 
 
 k 
 
 
 
 R M^v^tff* 
 
 ■ 
 
 
 
 
 
 //.A.-'.,-'; /^ 
 
 g 
 
 
 t' 
 
 r Miff 
 
 
 f\§if 
 
 \k 
 
 
 
 ^^ 
 
 B 1 1 
 
 !! 
 
 S 
 
 J^ 
 
 c
 
 RECREATIONS. ztu; 
 
 the healthful have no idea, to all thefe, 
 therefore, aiid to every one who is forced 
 to travel through dangerous roads, a car- 
 riage of this fort mufl doubtlefs be high- 
 ly defirable. 
 
 As this defign may appear to fbme per- 
 fbns, on a fuperficial view, impracticable, 
 wc fhall here infert an account of a fimi* 
 lar carriage, which we have taken from 
 the firfl volume of the Abridgement of the 
 Philofophical Tranfa£lions, by Lowthorp, 
 p. 592. There is not, however, any de- 
 fcription of the manner in which that ma- 
 chine was conftrudled. The account is as 
 follows : " A new fort of calefh defcribed 
 " by Sir R. B. This calefh goes on two 
 " wheels ; carries one perfon : is light 
 " enouo;h. Thougjh it hangs not on braces 
 *' yet it is eafier than the common coach. 
 " A common coach will overturn if one 
 *' wheel go on a fiiperficies a foot and a 
 " half higher than the other, but this 
 " will admit of the difference of three 
 
 *« foot
 
 2o8 RATIONAL 
 
 " foot and one third in height of the fu- 
 " perficies, without danger of overturn - 
 *' ing. We choofe all the irregular banks, 
 *' and fides of ditches, to run over, and I 
 " have this day feen it, at five feveral 
 *' times, turn over and over, and the horfe 
 ** not at all difordered. If the horfe 
 *' fhould be in the leail: unruly, with the 
 *' help of one pin, you difengage him 
 *' from the calefh without any incon- 
 *' venience (a contrivance of this fort may 
 *' be eaftly added to the foregoing defgn.) 
 " I myfelf have been once overturned, 
 ** and knew it not till I looked up, and 
 *' faw the wheel flat over my head : and 
 ** if a man went with his e}es fhut, he 
 '' would imaeine himfelf in the moil 
 *' fmooth way, though at the fame time 
 "' there be three foot difference in the 
 ** heig-ht of the 2:round of each wheel." 
 
 RECRE-
 
 RECREATIONS. 209 
 
 RECREATION LXIIL 
 
 ne columnar dial, 
 
 T>LATE XL Fig. i. reprefents a column 
 or obeliik A B, whofe fliaft GH is 
 fluted, and divided by horizontal lines, 
 that appear as joints, and ferve to mark 
 the hours : the infide of this column is hol- 
 low, and is reprefented by Fig. 2 . in the 
 bafe is placed the hollow cylinder A, con- 
 flrudled exactly in the fame manner with 
 that of the 53d Recreation of this volume, 
 but here it is kept in motion by the weight 
 B, faftened to a firing that goes over the 
 pulley C, and to this ftring is hkewife 
 faflened the index H, that, as the weight 
 defcends, points to the hours marked on 
 the outfide of the column, as is exprefTed 
 in Fig. I , at H. The axis of the cylinder 
 comes through the front of the column, 
 and to the end of it is fixed an index that 
 points to the minutes of each hour, mark- 
 VoL. I. P ed
 
 2 LO RATIONAL 
 
 ed on a circle in the front of the bafe, as 
 in Fig. I . at B. 
 
 The flriking part of this dial is con- 
 tained in the capital of the column, (fee 
 Fig. 2.) where DE is an axis, on which 
 are placed the two brafs wheels F and G, 
 that are of an equal diameter. On the 
 circumference of the wheel G are fix 
 teeth placed at equal diftances from each 
 other ; thefe teeth are taken by the detent 
 or lever IKL. The wheel F is likewife 
 divided into fix equal parts, in each of 
 which is placed a different number of 
 teeth from one to fix. The Ihort end of 
 the detent or lever MNO takes the teeth 
 of this wheel, and to the other end of it is 
 fixed the hammer P, that ftrikes the bell Q. 
 
 The wheel A making a complete re- 
 volution every hour, when it comes to X, 
 its tooth raifes the end a of the lever 
 /2, b^ r, confequently deprelTes the opposite 
 end r, which by means of the firing cd^ raife^ 
 
 the
 
 RECREATIONS. 211 
 
 the end I of the lever IKL, and the wheel 
 G is turned by the weight W from G to 
 Z, but can go no farther ; for the end I, 
 of that lever, being heavier than the other 
 end, defcends again immediately after it 
 has quitted the tooth. Now the wheel F 
 being of the fame dimenfion as G, and 
 fixed on the fame axis, muft necefTarily 
 move the fame fpace, in order to which it 
 mufl pufh up the end of the lever MNO, 
 that prefTes againfl one of its teeth, and 
 that end defcending again immediately, 
 being heavier than the other, the hammer 
 O will ftrike the bell ; it will, in like man- 
 ner, be forced over and fall between each 
 tooth, till it come to the end of the divi- 
 iion, and confequently give as many flrokes 
 on the bell as there are teeth in that divi- 
 fion. As the end NO of the lever 
 MNO is three times as long as MN, 
 while the fhort end is pufhed over one of 
 the teeth, the other will be pufhed three 
 times as far from the bell. 
 
 P 2 Due
 
 Ill RATIONAL 
 
 Due care muft be had in adjufting the 
 weight to the efte6l it is to produce: foi" 
 if it be too hght, it will not overcome the 
 fridlion of the lever with the teeth ; and 
 if it be too heavy,- the wheel will move 
 with too great velocity, and not give the 
 lever fufficient time to fall in between 
 the teeth. To the axis of each of the \^ heels 
 A and F is fixed a racket-wheel and a 
 ketch, by which they were wound up. The 
 time of this dial's going may be conii- 
 derably increafed by adding one or more 
 puUies to thofe at C and W. 
 
 It is evident from the conflrUL^ion of 
 this dial that it flrikes from one to fix 
 only : it may, hov/ever, be made to ftrike 
 all the twelve hours, but then the num- 
 ber of teeth on the wheel F mufl be in- 
 crealtd from 21 to 78, and confequently 
 the wheels muft be larger or the teeth 
 fmaller, eitiier of which would be incon- 
 venient ; and as we have obferved elfe- 
 where, iimplicity is a capital excellence in 
 
 the
 
 rLATKXI
 
 r 
 
 !'(•/. /n-m 
 
 o
 
 RECREATI.ONS. Z13 
 
 the conftrutftion of every machine. It 
 would certainly be more eligible for 
 clocks in general to found no more hours 
 than 6, as they would be lefs complex in 
 their conflrucSlion, the hours would be more 
 readily told and lefs liable to be miftook ; 
 nor could it be attended with any incon- 
 venience, as it is impoffible for any one, 
 to whom time is of the leafl: importance, 
 not to diftinguifli morning, noon, and 
 night from each other. 
 
 A clock of this fort may be conftrucled 
 at a fmall expence, and will make an ele- 
 gant piece of furniture ; or if elegance 
 be not regarded, the machinery may be 
 placed in the corner of a room, with a 
 plain board before, and it will anfwer the 
 intention equally well. It is ealy to con- 
 ceive, that with a fmall alteration this 
 machine may ferve as a reveilleur or 
 alarum. 
 
 P 3 RECRE-
 
 214 RATIONAL 
 
 RECREATION LXIV. 
 
 An air chronometer, 
 
 pROVIDE a gkfs tube (Plate XII. Fig. 
 I.) of about an inch diameter, and 
 three or four feet long : the diameter of 
 the infide of this tube muft be precifely 
 equal in every part : at the bottom is to 
 be a fmall hole, that is clofely covered 
 with a valve. In the tube place a piflon 
 E, (Fig. 2.) which is made to fit it exa(5lly, 
 and muft be oiled, that it may move in 
 the tube with the greatefl freedom : in 
 this pifton there is a cock, that fhuts quite 
 clofe, and from the top of it there goes 
 a cord F, that pafTes through the han- 
 dle G. 
 
 Now the cock of the piflon being 
 
 clofed, it is to be let down to the bottom 
 
 of the tube, and being then drawn up to 
 
 the top, the air will rufh in by the valve 
 
 5 at
 
 RECREATIONS. 215 
 
 at the bottom of the tube, and fupport the 
 pifton. You are then to turn the cock, 
 fo as to make a very fmall vent, and the 
 air pafling flowly through that vent, the 
 pifton will gradually defcend and fhow 
 the hour, either by lines cut in the tube 
 with a diamond, or marked with paint, or 
 by fmall flips of paper pafted on the 
 glafs. If this chronometer Ihould go too 
 faft or flow, it may be eafily regulated 
 by altering the pofition of the cock 
 in the piflon, as it is on that the whole 
 depends. 
 
 If, inftead of marking the tube, you 
 would have the time fhown by a dial, it 
 may be eafily efFe6led by placing an axis, 
 to which the hand of the dial is fixed, 
 diredly over the tube, and winding the 
 firing, to which the piflon is joined, round 
 that axis : for then as the piflon de- 
 fcends the axis will gradually turn the 
 hand, and fhow the hour : but you are 
 P 4 to
 
 2i6 RATIONAL 
 
 to obferve, that as the defcent of the 
 pifton is not conftantly regular, occa- 
 fioned by the decreafe of refiflance from 
 the quantity of fubjacent air as the pifton 
 defcends, the axis, therefore, mufl not be 
 a regular cylinder, but conical, like the 
 fufee of a watch, as in Fig. 3 ; by which 
 means the motion of the hand of the dial 
 will be conftantly uniform. 
 
 RECRj:-
 
 RECREATIONS, 217 
 
 RECREATION LXV. 
 
 ^he lamp chronometer. 
 
 pL ATE Xil. Fig. 4. reprefents a cham- 
 ber-lamp A, confifting of a cylindri- 
 cal veffel about three inches high and 
 one inch diameter, placed in the ftand B, 
 The infide of this vefTel muft be every- 
 where exactly of the fame diameter. To 
 the ftand B is fixed the handle C, which 
 fupports the frame DEFG, about twelve 
 inches higrh and four inches wide. This 
 frame is to be covered with oiled paper, 
 and divided into twelve equal parts, by 
 horizontal lines ; at the end of which are 
 wrote the numbers for the hours, from i 
 to 12, and between the horizontal lines 
 are diagonals, that are divided into 
 halves, quarters, &c. On the handle B, 
 and clofe to the glafs, is fixed the flyle 
 pr gnornon H,
 
 2i8 RATIONAL 
 
 Now as the diftance of the flyle from 
 the flame of the lamp is only half an inch, 
 if the diftance of the frame from the ftyle 
 be fix inches, then while the float that 
 contains the light defcends, by the de- 
 creaie of the oil, one inch, the ihadow of 
 the ilyle on the frame will afcend twelve 
 inches, that is, its whole length, and 
 ihow by its progrefTion, the regular 
 increafe of the hours, with their feveral 
 divifions. 
 
 It is quite necelTary that the oil ufed in 
 this lamp be always of the fame fort, and 
 quite pure, and that the wick alfo be con- 
 ftantly of the fame fize and fubftance, as it 
 is on thefe circumftances and the uniform 
 figure of the veflel, that the regular pro- 
 grefs of the fliadow depends. 
 
 To make this machine ornamental as 
 well as ufeful, there may be drawn in the 
 middle of the frame, yet fb as to leave the 
 divifions of the hours quite vifible, the 
 
 figures
 
 RECREATIONS. 219 
 
 figures of trees, flowers, animals, or 
 whatever elfe the owner's imaginatiou 
 Ihall fuggeft; and if they be properly 
 painted, in lively colours, they will have 
 a very pleafing effect. 
 
 RECREATION LXVL 
 
 '^he no&urnal dial, 
 
 'y HE two wheels A and B (Plate XIL 
 Fig. 5.) are of the fame diameter, 
 and have each fifty-four teeth : their axis 
 are parallel, but have no connection with 
 each other. The pinion C and the wheel 
 D have each fix teeth, and the wheel ^ 
 eighteen teeth ; the t^^^o laft wheels, D and 
 E, are placed on the fame axis : all thefe 
 wheels mull: be of brafs or copper, and as 
 light as polfible. Near the circumference 
 of the wheel A are the figures for the 
 hours and their divifions, which are cut 
 through the plate, and coyered with oiled 
 
 paper.
 
 220 RATIONAL 
 
 paper. On the wheel B, at F, is {{yted 
 a lamp, the oil of which mufh be of the 
 pnreft fort, and the wick cohftantly of the 
 lame fize and matter ; and round the axis 
 of this wheel is wound a rope, to which 
 hangs the weight G. 
 
 Now the quantity of oil in the lamp is 
 fo adjufted, as to exaflly counterbalance 
 th£ weight G ; but as the oil is continu* 
 ally decreafing, the weight mufl defcend, 
 though very gradually, and confequently 
 turn the wheel B, and that mufl turn the 
 pinion C and wheel D, which being fixed 
 on the fame axis as E, turns that alfo, 
 and confequently the wheel A. But as 
 each of the great wheels A and B have 
 fifty-four teeth, the pinion C and wheel 
 D only fix teeth, and the wheel E eighteen 
 teeth, it neceffarily follows, that while the 
 wheel B moves from F to H, that is, one- 
 third of its circumference, the wheel A 
 mufl make a complete revolution ; and as 
 
 fome
 
 RECREATIONS. 221 
 
 /> 
 
 fome parts of its circumference Ivill be 
 continually oppofite the lamp, the num- 
 ber of the hour will be always vifible. 
 
 A hollow cone or funnel, as Fig. 6, is 
 to be placed to that fide of the lamp oppo- 
 fite the wheel A, the fmall end of this 
 cone ihould be fquare, and which will 
 confine the light of the lamp to a deter- 
 minate part of the wheel A : if a move- 
 able lens be adjufted to this fmall end, 
 the quantity of light may be extended or 
 contracted at pleafure. 
 
 This dial may be made to found the 
 hours, by adding the apparatus defcribed 
 in the 63d Recreation, and fixing a tooth 
 on the rim of the wheel A, againft each 
 hour, which will take the end of the 
 lower lever, in the ftriking part of that 
 machine, and it may, like that, ferve as 
 an alarum. 
 
 To
 
 222 RATIONAL 
 
 To thofe who are troubled with an In- 
 fomny, or iiiabiUty to deep, whether from 
 conllitution or difeale, a dial of this fort 
 will prove an agreeable companion, as it 
 will continually ihow how the tirefome 
 hours wear away ; and to make it more 
 amufing, over each hour fome motto may 
 be cut out ; for if the diameter of the 
 wheel be one foot, its circumference will 
 be fomething more than three feet, and 
 confequently there will be a fpace of three 
 inches to every hour. In the twelve com- 
 partments under the hours there may be 
 likewife figures of hiftory, either religious 
 or profane ; or emblems of devotion, love, 
 morality, or whatever elfe the temper and 
 difpofition of the owner may require ; and 
 if thefe figures be covered with tranfpa- 
 rent paper, properly coloured, this ma- 
 chine, at the fame time that it anfwers 
 the common purpofes of a dial and lamp, 
 will afford a pleafing reprefentation ; and 
 as the wheels are in continual motion, and 
 
 the
 
 ri^TE xir
 
 roL.I.n-ri' 
 
 r
 
 RECREATIONS. 223 
 
 the light confined to a certain ipace, one 
 that is continually varying. 
 
 We might here give a much greater 
 variety of mechanical conftrudions, but 
 we choofe to confine ourfelves to fuch as 
 are mofl remarkable, and which, when 
 duly confidered, will be quite liifficient to 
 exemplify the foregoing aphorifms. They 
 who are defirous of more variety, will 
 readily find a great number of experi- 
 ments that are confliantly repeated by 
 every writer on mechanics. 
 
 THE
 
 THE 
 
 CONTENT S< 
 
 A DVERTISEMENT. 
 INTRODUCTION. 
 
 ARITHMETIC. 
 
 DEFINITIONS. pager 
 
 APHORISMS. 4 
 
 Of the amount and produ£t of even and 
 vineven numbers, aph. r to 6 — Of the 
 divifibility of numbers, aph. 6 and 7. — ■ 
 Properties of the number 9, aph. 8 and 
 9. — Properties of arithmetic progref- 
 fions, aph. i o to 1 4. — of geometric pro- 
 VoL. L Q gref-
 
 226 CONTENTS. 
 
 greffions, aph. 14 and 15. — Of com- 
 binations and permutations, aph. 16 
 and 17. 
 
 THE ROMAN ABACUS. p. 11 
 
 An inftrument by which any fum may be 
 fet down, added to or fubtra6ted from, 
 another, by counters, and without the 
 ufe of figures. 
 
 NEPER'S RODS. p. 13 
 
 A method of multiplying and dividing by 
 a table of figures, engraved on move- 
 able rods (fee Plate I. Fig. i and 2.) 
 
 THE CHINESE SWAN- PAN. p. 17 
 
 An inflrument that performs all the oper- 
 ations of arithmetic, by moveable balls 
 flrung on wires (Plate I. Fig. 3.) and 
 Avithout the aid of figures. A blind 
 perfon, with this inftrument may make 
 any calculation with certainty. 
 
 RECRE-
 
 CONTENTS. 
 
 227 
 
 RECREATION I. p. 22 
 
 .Any number being named by adding a figure to 
 it, to make it divifible by nine. 
 
 By adding as much to the amount of the 
 figures that compofe the number, as 
 will make it divifible by nine. 
 
 RECREATION II. p. 23 
 
 A perfon having an even number of coun- 
 ters in one hand and an odd number in the 
 other ^ to tell in which hand the odd or even 
 number is. 
 
 By dire£ting hirti to multiply the number 
 in one hand by an odd number, and 
 that in the other by an even number, 
 and to tell you whether the amount of 
 the two produ<5ts be even or odd. 
 
 Qj2 RE-
 
 22S CONTENTS. 
 
 RECREATION III. p. 24 
 
 A perfon making choice of fever al numbers^ 
 another is to name him the number by which 
 the fum of thofe numbers is divifble. 
 
 By putting a parcel of tickets, marked 
 with numbers divilible by 3, into one 
 divifion of a bag, and into another di- 
 vifion tickets marked with the number 
 3 only, and letting two perfons draw 
 one from each divifion. 
 
 RECREATION IV. p. 25 
 
 'T'o find the difference between two numbers^ 
 the greateft of which is unknown. 
 
 By fubtrading the leaft number from an 
 equal number of nines, and diredling 
 another perfon to add to, and fubtraft 
 from, the amount, in a determinate 
 manner. 
 
 RECRE-
 
 CONTENTS. 229 
 
 RECREATION V. p. 27 
 
 To tell by the dial of a watch y at what hour 
 any perfon Intends to rife. 
 
 You tell him to place the hand of the dial 
 at what hour he pleafe, and you private- 
 ly add 1 2 to that number ; you then 
 tell him to count fo many hours on the 
 dial as are equal to the amount, and 
 the lafl will be the hour required. 
 
 RECREATION VI. p. 28 
 
 A per/on choofing any tvjo out of fever al given 
 numbers^ and after adding them together ^ 
 ftriking out one of the figures of the amount y 
 to tell what the figure was. 
 
 By offering fuch numbers only as are di- 
 vifible by 9, and the fum of any two of 
 them is either 9 or 18, and contains no 
 cypher. 
 
 0^3 RE-
 
 230 CONTENTS. 
 
 RECREATION VII. p. 29 
 
 ^wo perfons choojing two numbers^ and mul- 
 tiplying them together , by knowing the laji 
 Jigure of the produ£l to tell th^ other f." 
 
 giires. 
 
 By putting into one diviflon of a bag tic- 
 kets marked 73, and into another divi- 
 sion fuch numbers, as when multiphed 
 by 73, will end with the nine digits. 
 
 RECREATION VIIL p. 31 
 
 'The magical century. 
 
 If two perfons flake a number of counters 
 alternately, but never more than ten 
 at once, he that flakes firft mufl make 
 the century, provided he make the 
 others flake each time, equal to one 
 more than the fum of one of the nine 
 digits multiplied by 11— the fame Re- 
 creation with a pack of cards, p. 32. 
 
 RE-
 
 CONTENTS. 
 
 231 
 
 RECREATION IX. p. 34 
 
 'i'he confederate counters, 
 
 A ring, a feal, and a liiuff-box being chofe 
 by three perlbns, to tell, by means of 
 twenty-four counters, and a verfe of 
 fourteen fyllables, which of them each 
 perfon has chofe. 
 
 RECREATION X. p. 36 
 
 A per/on privately fixing on any number, to 
 tell him that number. 
 
 By direfling him to double, add to, and 
 multiply that number, and fubtradt 
 another number from it, in a determi- 
 nate order. 
 
 0^4 RE-
 
 232 CONTENTS. 
 
 RECREATION XL p. 37 
 
 I'hree dice being thrown on a table ^ to tell the 
 number of each die^ and the order in which 
 they Ji and. 
 
 The perfon who threw the dice is to dou- 
 ble and multiply each number, and fub- 
 tra6t another number from the amount, 
 as in the laft Recreation. 
 
 RECREATION XII. p. 39 
 
 To tell the number a perfon has fixed on^ with^ 
 out a/king him atiy quejiion. 
 
 By directing him to halve and triple his 
 number four times, and by obferving 
 when he is obliged to add one to the 
 fum, before he can halve it and apply- 
 ing thofe cafes to the fyllables of eight 
 Latin words. 
 
 RECREATION XIII. p. 42 
 
 'Thirty foldiers having deferted, fifteen of 
 them are to be punijhed; fo to place the 
 
 whole
 
 CONTENTS. 233 
 
 whole number in a r'mg^ that you may fave 
 any fifteen you pie afe^ and it Jhall feem the 
 effed of chance. 
 
 By placing them according to numbers 
 annexed to the vowels of a Latin 
 verfe. 
 
 RECREATION XIV. p. 43 
 
 Some perfon in company putting a 7'ing^ pri- 
 vately^ on one of his fingers^ to name the 
 perfon^ the hand ^ the finger^ and the joint, 
 on which it is placed. 
 
 Another perfon is to double, add to, and 
 multiply the number of the rank in 
 which the firfl perfon ftands, and tell 
 you the amount, from which you de- 
 duct a certain fum, and the remainder 
 will anfwer the queftion. 
 
 OF ARITHMETICAL MAGIC SQUARES, p. 46 
 
 They coniifl: of numbers in arithmetic 
 progreffion, placed in equal rows, and 
 
 in
 
 ^34 CONTENTS. 
 
 in fuch manner that the fum of each 
 row taken either perpendicularly, ho- 
 rizontally, or diagonally, is the fame — 
 method of conftruding thefe fquares. 
 
 RECREATION XV. p. 49 
 
 '^he Jerks of numbers from i to 25, being 
 wrote on that number of cards ^ after they 
 have been /huffed, to deal them to fve 
 perfons, either by twos or threes, at the 
 option of the parties, and the amount of 
 the numbers on each one's cards to be the 
 fame. 
 
 There is to be a wide card — table for dif- 
 pofing the cards, before they are fhiif- 
 fled, according to the magic fquare, 
 p. 50 — manner of dealing them, p. 51. 
 
 RECREATION XVI p. 52 
 
 5o deal the thirty-two cards of the game of 
 piquet to four perfons, after you have 
 floujffled them, and the parties have chofe 
 
 whether
 
 CONTENTS. z^^ 
 
 whether you Jhall deal them by twos or 
 by threes, infuch mamier that all the cards 
 m each perforis hand Jloall be of the fame 
 fu'it. 
 
 Order of difpofing the cards — manner of 
 dealing them, p. ^'^, 
 
 OF GEOMETRIC MAGIC SQUARES. p. 54 
 
 To be filled after the fame manner as the 
 
 arithmetic fquares — ^the product of each 
 
 line, taken in any diredion, is the 
 
 fame. 
 
 RECREATION XVII. p. ^^ 
 
 Several numbers being wrote upon cards, to 
 foufie them, and deal the whole, or part 
 of them, to three perfons, infuch manner, 
 that each one multiplying the numbers on 
 his cards together, the prodiiB of each 
 perforis cards fhall be the fame ; and to 
 repeat the recreation after having Jhujfled 
 the cards afecond time. 
 
 The numbers wrote on the cards are to be 
 thofe of the geometric magic fquare — 
 
 there
 
 236 CONTENTS. 
 
 there muft be three wide cards, p. ^6 — ■ 
 method of repeating the experiment, 
 p. ^y — may be performed with the 
 numbers of the arithmetic magic fquare. 
 
 RECREATION XVIII. p. 58 
 
 1*0 find the number of changes that may be 
 rung on twelve bells. 
 
 By multiplying the numbers from i to 
 1 2 into each other. 
 
 RECREATION XIX. p. 59 
 
 Sufpofing the letters of the alphabet to be 
 wrote fo fmall that no one of them Jhall 
 take up more fpace than the hundredth part 
 of an inch ; to find how many fquare 
 yards It would require to write all the per- 
 mutations of the twenty -four letters in 
 thatfize. 
 
 The permutations of the twenty-four let- 
 ters are found as in the laft Recre* 
 ation — the number of fquare yards re- 
 quired
 
 CONTENTS. 237 
 
 quired to contain thofe permutations is 
 18620 times as large as the furface of 
 the earth p. 60. 
 
 RECREATION XX. p. 60 
 
 To fnd how many different ways the eldeji 
 hand at piquet may take in his Jive cards. 
 
 This number found by the fixteenth apho- 
 rifm. — it is 15503 to i that he does not 
 take in any five certain cards, p. 61 
 
 RECREATION XXL p. 61 
 
 To find the number of deals a per/on may 
 play at agameofwhifi, without ever hold- 
 ing the fame cards twice. 
 
 The number alfo is found by the fix- 
 teenth aphorifm. 
 
 THE ARITHMETIC TRIANGLE, p. 62 
 
 Its conflruaion— its ufe in finding the 
 combination of fmall numbers, p. ^'^^ 
 
 RECRE-
 
 238 C O N T E K T $. 
 
 RECREATION XXII. p. 64 
 
 To find hozv many different founds may be 
 produced by friking on a harpfichord two 
 or more of the f even natural notes at the 
 fame time. 
 
 This number which is 120, found by the 
 foregoing table. 
 
 RECREATION XXIIL p. 64 
 
 '^ake four pieces of pafehoard^ of the fame 
 d'lmenfwn^ and divide them diagonally, 
 as in the figures^ into eight triangles: 
 paint f even of thefe triangles with the pri- 
 mitive colours y redy orange^ yellow^ green, 
 hluCy indigo^ and violet^ and let the eighth 
 be white. 'To find how many chequers or 
 fourfided figures, differing either inform 
 or colour, may be made out of thofe eight 
 triangles. 
 
 This number, which is 196, found in the 
 fame manner as in the laft recreation, p. 66 
 
 RECRE-
 
 CONTENTS. 239 
 
 RECREATION XXIV. p. 66 
 
 A man has 12 different forts of fowers^ 
 and a large number of each fort. He is 
 deftrous of fitting them in beds or flour ifhesy 
 in his parterre. Six flowers in fome^ 7 in 
 others^ and 8 in others -, fo as to have the 
 greateft variety poffible\ the flowers in no 
 two beds to be the fame. 'To find how 
 
 many beds he mufl have. ^^ 
 
 • 
 
 This number which is 221 1, is alfo found 
 by the foregoing table. 
 
 RECREATION XXV. p. 67 
 
 To flnd the number of chances that may be 
 thrown by two dice. 
 
 This number is 2,^ — the whole number of 
 points is 252 — ^it is an equal chance, at 
 every throw, to bring feven points, 
 p. 68 — method of finding the number 
 of chances on any number of dice. 
 
 RECRE-
 
 240 CONTENTS. 
 
 RECREATION XXVI. p. 69 
 
 To dif cover the number of points on 3 cards 
 placed under three different heaps of 
 cards. 
 
 As many cards are to be put over each of 
 them as with the number of its points 
 will make 15, then telling the number 
 of the remaining cards, privately, and 
 addins: 1 6 to 'that number, the amount 
 will be the number of points on the 
 three cards. 
 
 RECREATION XXVII. p. 70 
 
 The ten duplicates. 
 
 Twenty cards being laid in pairs, and in 
 four rows, feveral perfons are to look 
 at different pairs, and tell you in which 
 rows they are, when you tell them, by 
 the aid of four Latin words, which 
 cards they looked at, 
 
 RECRE-
 
 CONTENTS. 241 
 
 RECREATION XXVIII. p. 7^ 
 
 To name the number of cards that a perfon 
 fhall take out of the pack. 
 
 This is done by previoufly dilpoiing the 
 cards in a certain order, and by an 
 English verfe to aid the memory. 
 
 RECREATION XXIX, p. 74 
 
 A century oj different names being wrote on 
 the cards, to tell the particular name that 
 any perfon has thought on^ 
 
 A hundred names are wrote on 10 cards, 
 and the laft name of each card begins 
 with one of the letters of a word that 
 has ten letters ; and on ten other cards, 
 the fame hundred names are wrote, in 
 different difpofitions. A perfon is to 
 draw a card from the firfl ten, and 
 after fixing on a name, give it you 
 
 Vol. I. R again;
 
 242 CONTENTS. 
 
 again ; you then fhow him the other ten 
 cards, and when he tells you the card 
 that has the name, you tell him, by 
 means of the lafl name on the card he 
 drew, which it is. This recreation may 
 be performed \vith twenty cards, in- 
 fiead of ten ; and queftions and anfwers 
 may be ufed inftead of names. y^ 
 
 OF THE COMBINATIONS OF THE 
 CARDS, p. 78. 
 
 The tables formed by thefe combinations 
 
 are applicable to many other fubje£ls 
 
 befide cards — xnanaer of ihuffling the 
 
 cards, fo as to make them correfpond 
 
 to the tables, p. 79. 
 
 Table of combinations for ten numbers, 
 
 and for one, two, and three fhufflcs, p. 82 
 
 Table for twenty-four numbers 83 
 
 Table for twenty-feven numbers 84 
 
 Table for thirty-two numbers 85 
 
 RE-
 
 CONTENTS. 243 
 
 RECREATION XXX. p. 86 
 
 Several letters that contain no meanings being 
 wrote upon cards, to make them, after they 
 have been tvoice flmffed, give an anfwer to 
 a quejlwn that Jhall be propofed\ as for ex- 
 ample, W^hat is love ? 
 
 The twenty-four letters of the anfwer 
 are to be wrote on that number of cards, 
 and the anfwer itfelf to be wrote on a 
 paper; the numbers from i to 24 are 
 to be affixed to the letters, and the 
 cards to be diipofed according to the 
 third column in the table for twenty- 
 four numbers — neceflary obfervations 
 for conducing this and limilar experi- 
 ments, p. 88, 
 
 RECREATION XXXI. p. 90 
 
 'the tzventyfour letters of the alphabet being 
 
 wrote on fo many cards, to Jhuffle them 
 
 and pronounce the letters foall then be iji 
 
 their natural order ; but that not fucceed- 
 
 R 2 ing
 
 144 CONTENTS. 
 
 ing- to JJ^uffle them afecond time^ and then 
 Jhow them in proper order. 
 
 The cards are here to be difpofed after 
 the fame method as in the laft recre- 
 ation — the experiment is to fail at firft, 
 that it may appear the more extraor- 
 dinary after the fecond fhuffle, 
 
 RECREATION XXXII. p. 91 
 
 Se'-jeral letters behig wrote promifcuoujiy up- 
 
 on 2)'^ cards, after they have been once 
 
 fhuffled, to find on apart of them a quef- 
 
 t'lon ; atid then fhuffing the remainder a, 
 
 fecond thne^ tofheiv the anfwer. 
 
 The letters of the queftion and anfwer, 
 which are -32, are to he wrote on the 
 cards ; the letters of the anfwer, which 
 are ten, are to be wrote on a paper, and 
 the numbers from i to 10 affixed to 
 them. They are then to be ranged by 
 the fecond column of the table for ten 
 numbers, and the whole thirty-two cards 
 
 are
 
 CONTENTS. 245 
 
 ar6 next to be difpofed by the fecond 
 column of the table for that number — 
 there is to be a long card, by which 
 they are to be cut and then fhuffled, 
 
 P- 93 
 
 RECREATION XXXIII. p. 94. 
 
 I0 write 32 letters on fo many cards ^ then 
 Jhiiffe aftd deal them by twos to two perfons 
 infuch manner, that the cards of one Jh all 
 contain a quejiion, and thofe of the other y 
 the anfiver. 
 
 The numbers from i to 32 are to be wrote 
 over the letters of the queftion and an- 
 fwer ; they are then to be ranged ac- 
 cording to the firft column of the table 
 for thirty-two numbers, fhufEed and 
 dealt. 
 
 RECREATION XXXIV. p. 96 
 
 l!hefive beatitudes, 
 
 Thefe five bleffings, which are fcience, 
 
 courage, health, riches, virtue, are to 
 
 R 3 be
 
 24-6 CONTENTS. 
 
 be found on thirty-two cards that are 
 dealt to five perfons — the numbers from 
 I to 32 are to be wrote over the letters 
 of thofe words in a determinate order : 
 the cards are then to be ranged accord- 
 ing to the firfl column for thirty-two 
 numbers. The five beatitudes being 
 wrote, each of them on four cards, each 
 perfbn is to draw one from one of the 
 fours, and when the other cards are 
 dealt one by one, each perfon will 
 have the fame word on the cards dealt 
 him as on that he drew. 
 
 RECREx\TION XXXV. p. 98 
 
 The cards of the game at piquet being mixed 
 together^ after fhuffling them, to bring, 
 by cutting them^ all the cards of each fuit 
 together. 
 
 The order in which the cards are to be 
 ranged before the firft fhuffle, p. 99 — 
 they are then to be cut at a wide card, and 
 the part cut off laid afide ; the remaining 
 
 cards
 
 CONTENTS. 247 
 
 cards are to be fhufiled a lecond time, 
 and cut at another wide card ; the fame 
 operation is to be repeated a third time ; 
 and the four fuits will then be all fe- 
 parate. 
 
 RECREATION XXXVI. p. 100 
 
 T'he cards at piquet being all mixed together, 
 to divide the pack into two unequal parts , 
 and name the number of points contained. 
 In each part. 
 
 The cards are to be difpofed bv the table 
 for thirty-two numbers ; they are then 
 to be fhuffled, according to order, and 
 cut a wide card, when each parcel 
 will have a determinate number. 
 
 RECREATION XXXVII. p. 103 
 
 *J!he inconceivable repiqiie. 
 
 This recreation Is to be performed with 
 
 the cards ransred in the order defcribed 
 
 R 4 in 
 
 /
 
 248 CONTENTS, 
 
 in the laft : they are to be fliuffled a fe- 
 cond time, and cut at the wide card, 
 and they will be then ranged in fuch 
 order, that you will repique your ad- 
 verlary, though you let him choofe, af- 
 ter the cards are cut, in what fuit you 
 
 fhall make the repique — in a particular 
 
 * 
 
 circumftance you muft pafs the three 
 bottom cards to the top, p. 108. 
 
 RECREATION XXXVIII. p. 109 
 
 I'he inetamorphofed Cards, 
 
 Thirty-two different words being promif- 
 cuoufly wrote, and four different co- 
 lours and objects painted on thirty-two 
 cards, they are to be Ihuffled as before, 
 and dealt to four perfons, and after 
 the firft deal every one's cards are to be 
 all of the lame colour : after the fecond 
 deal they are all to have the fame ob- 
 ject; and after the third deal each 
 perfon*s cards are to contain a diffe- 
 rent fentimciit. 
 
 RECRE-
 
 CONTENTS. 
 
 249 
 
 RECREATION XXXIX. p. 1 13 
 
 The repique with carte blanch. 
 
 The order in which the cards are to be 
 diipoled before the deal, p. 114 — the 
 hands of the two players, p. 115 — one 
 of them is to have the choice of the two 
 hands, on condition of his beingr eldefl: 
 or youngeft, p. 1 1 6 — method of the 
 other's difcarding accordingly. 
 
 RECREATION XL. p. 117 
 
 Cafe at piquet^ where yau repique the elder 
 hand^ though he have the choke of the cards 
 after they are dealt. 
 
 The order in which the cards muft ftand 
 after they have been cut — ^the hands of 
 the two players, p. 1 1 9 — one of the 
 players is then to choofe either hand, 
 but without feeing them — manner in 
 which the other muft difcard, p. 120. 
 
 RECRE-
 
 250 
 
 CONTENTS. 
 
 RECREATION XLI. p. i2t 
 
 C^ife at piquet^ where you give the other phy^ 
 er not only the choice of the fu'ite in which 
 he will be repiqucdj but that cf dealing the 
 cards by twos or threes^ and rf taking either 
 hand after they are dealt ^ you being to tell 
 mid play firjl. 
 
 Previous difpofition of the cards ; there 
 are to be four wide cards — if they are 
 cut at any one of the wide cards, the 
 flock will be all of one fuit, p. 122 — 
 the hands and rentrees of the two play- 
 ers, when the cards are dealt by twos 
 and when they are dealt by threes, p. 
 123 — method of difcarding according. 
 to the hand the adverfary choofes, and 
 as the deal is by twos or threes, p. 1 24 
 
 RECREATION XLII. p. 126 
 
 An exemplary cafe at piquet^ where you re- 
 pique your advcjfary after giving him 
 
 the
 
 CONTENTS. 251 
 
 the choice of having the cards dealt either 
 by twos or threes. 
 
 Table for difpofing the cards in this and 
 hke cafes, p. 127 — remark on the fore- 
 going manoeuvres at piquet, p. 131, 
 
 RECREATION XLIII. p. 132 
 
 Several different cards being JJo:'wn to different 
 perfonsy that each of them may fx on one 
 of thofe cards y to name that on which each 
 perfon hasfxed. 
 
 As many cards are to be fho\^^n each pcr- 
 {oi\ as there are perfons to choofe ; 
 each one's cards to be laid down fepa- 
 rately, and the firft perfon's card v^dll 
 be the firft in the heap where it is ; the 
 fecond perfon's card the fecond, &c. — 
 The fame recreation may be performed 
 with a fingle perfon, p. 133. 
 
 RE<
 
 252 CONTENTS. 
 
 RECREATION XLIV. p. 134 
 
 'To name the rank of a card a per fin hai 
 drawn from a piquet pack. 
 
 By affigning a certain number to each 
 card, and adding the number of the 
 firft to that of the fecond, &c. rejeding 
 the tens and carrying the remainder, 
 and flibtradling 4 from 10 or 20, for 
 the number of the card dra\'\^n. 
 
 RECREATION XLV. p. 135 
 
 51? tell the amount cf the Jiumbers of tW7 
 cards that a perfn has drawn from a c:m- 
 mon pack of cards. 
 
 He is to add as many cards to each of thole 
 he has drawn as will make its number 
 25. You then tell the remaining cards 
 filently, and their number will be the 
 amount of the cards drawn. This re- 
 creation may be performed without tell- 
 ing
 
 CONTENTS. 253 
 
 ing the cards, p. 136 — or with a pack 
 of piquet cards, p. 138. 
 
 RECREATION XLVI. p. 139 
 
 To tell the amount of the numbers of any 
 three cards that a per f on has drawn from 
 the pack. 
 
 You are to draw a fingle card yourfelf, 
 to make the remaining number divifi- 
 ble by three : the perfon is then to add 
 as many more to each of his cards as 
 will make its number 16, and the num- 
 ber of the remaining cards will be the 
 amount of the cards he drew. This re- 
 creation alfo may be performed with- 
 out telling the remaining cards, p. 140, 
 —and with a pack of piquet cards, p. 
 ?4i» 
 
 DIFFE.
 
 254 CONTENTS. 
 
 DIFFERENT METHODS OF 
 WRITING IN CYPHER. 
 
 RECREATION XLVII. p. 143 
 
 ^0 communicate intelltgence by a pack of fi" 
 quet cards. 
 
 The parties are previoufly to agree how 
 the cards are to be difpofed and fhiif- 
 fled — he who fends the cypher, copies 
 the letters on thirty-two cards, alter- 
 nately, and fhuffles them as agreed, 
 p. 144 — example of a cypher of this 
 kind — methods of making it more dif- 
 ficult to decypher, and lefs liable to fuf- 
 picion, p. 146. 
 
 RECREATION XLVIII. p. 147 
 
 'The myjitcal dial. 
 
 A moveable circle of pafteboard Is placed 
 within another circle, and on each of 
 them are wrote the letters of the alpha- 
 
 8 bet
 
 CONTENTS. 255 
 
 bet (Plate II.) The moveable circle is 
 . placed as agreed on between the parties 
 and the letters of the one wrote for the 
 other — the fame intention may be an- 
 fwered by a ruler, p. 148. 
 
 RECREATION XLIX. p. 149 
 
 ^he correfpond'ing fpaces. 
 
 Similar fpaces to be cut in two pieces of 
 pafteboard, and one of them kept by 
 each party. The fecret intelligence 
 to be wrote in thefe fpaces, when laid 
 on a paper, and the diftances between 
 them to be filled up by words that make 
 a different fenfc. 
 
 RECREATION L. p. 151 
 
 ^hc mufical cypher. 
 
 The conftrudion of this inftrument is 
 iimilar to that of the 48th Recreation. 
 The notes of mufic anfwer to the let- 
 ters of the alphabet (PL III.) The cy- 
 pher
 
 256 CONTENTS. 
 
 pher to be wrote on ruled paper, as a 
 piece of mufic, p. 152 — is liable to very 
 little fufpicion, p. 1 53. 
 
 Rules for decyphering p. 153 
 
 Example of a cypher wrote in arbitrary 
 characters, and the words feparate 
 from each other 156 
 
 A cypher wrote in arbitrary characters, 
 and the words all clofe together 157 
 
 IN'Ianner of decyphering a writing of this 
 fort 158 
 
 Method of rendering a limilar writing ex- 
 tremely difficult to decypher 158 (note) 
 
 The contents of the two foregoing cy- 
 phers 159 
 
 R E C R E A T I O N LI. p. i6q 
 
 Vifual Correfpondence. 
 
 The letters of the alphabet are cut thro* 
 a circle of wood, near its circumference, 
 and the circle beins; made to turn on a 
 pole, the letter wanted is brought be- 
 fore
 
 CONTENTS. 257 
 
 fore aa opening at the top of it, and a 
 light placed behind the letter (Plate IV. 
 Fig. I. and 2.) — method of ufing this 
 machine, p. 161 — a telefcope is necef* 
 iary when the diftance is confiderable, 
 p. 162 — particular purpofes to which 
 this machine may be applied, p. 1 6^^ 
 
 JIECREATION LII. p. 164 
 
 Auricular Correfpondence, 
 
 Two bells are placed at the top of a build- 
 ing, and the letters of the Alphabet 
 are exprelTed by the number of ftrokes 
 on one or both bells — a correfpond- 
 cnce may be carried on by this con- 
 trivance, where that of the lafl recre- 
 ation can have no effed. 
 
 Vol. L S ME-
 
 258 CONTENTS. 
 
 MECHANICS. 
 
 DEFINITIONS - - - p. 169 
 
 APHORISMS ... 172 
 
 Properties of moving bodies, apli. i to 
 1 2 — Properties or pTidulums, aph. 1 2. 
 to 1 6 Of the mechanic powers, aph. 
 16 to 26. — Of compound machines, 
 aph. 26, to the end. 
 
 RECREATION LIII. p. 180 
 
 Uo conjlrucl a mechanical dial^ without 
 wheels, Jp^ing or weight. 
 
 This dial conffls of a hollow cylinder^ 
 (PL VI. Fig. I and 2.) on the ends of 
 whofe axis are wound two ftrings, the 
 other ends of which are faftened to the 
 top of the wainfcot. Within the cy- 
 linder are five partitions, and between 
 them water is placed, which paffing, 
 
 by.
 
 CONTENTS. 259 
 
 by a fmall hole, from one partition to 
 the other, taufes the cyHnder to de- 
 fcend (lowly and fhow the hour, by 
 the ends of the axis pointing to a table 
 of numbers on the wainfcot. 
 
 RECREATION LIV. p. 183 
 
 j^ dial tofhew the hour by gradually defcend- 
 ing an Inclined plane. 
 
 It confifls of two parallel plates conne(5l- 
 ed by a hoop (Plate VI. Fig. 3 and 4.) 
 Between the plates are a train of 
 wheels, and on the outlide is a weisfht, 
 which is faflened to the centre wheel, 
 and therefore caufes the dial to defcend 
 in a regular progreffion— this dial will 
 go for any time, according to .th»> 
 length of the inclined plane, p. 18^. 
 
 RE-
 
 26o C O N T E J^ T 5. 
 
 RECREATION LV. p. 187 
 
 j4 clock to go perpetually by the infuence of 
 the cekjlial bodies. 
 
 This clock is of the common conftruc- 
 tion, but is placed againfl: a wall by 
 which the tide flows, and is moved by 
 that, as that is by the moon, &c* 
 
 RECREATION LVI. p. 19© 
 
 ^he mfcrutable lock. 
 
 The infcrutability of this lock arifes from 
 the combinations of the moveable parts 
 of the ward of the key, with the dif= 
 ferent pofitions in which the fcutcheon 
 before the lock may be placed, (Plate 
 VII. Fig. I and 2.) which make it 
 more than eleven thoufand four hun- 
 dred and ninety-fix millions to one, 
 at every trial, that a flranger does not 
 
 open
 
 CONTENTS. 261 
 
 open the lock : which, however Is open- 
 ed inftantly by the owner. 
 
 HECREATION LVII. p. 193 
 
 So to difpofe a hand-mill, to grind corn, &c, 
 that being once put in motion^ it Jhall work 
 incejfantly 'without the ajftjlance of a7iy 
 animal power » 
 
 This piill is to be moved by a fmoke jack 
 — a defcription of that machine (Plate 
 VII. Fig. 3.)~^s the motion of the 
 jack is incefTant while there is a fmoke 
 in the chimney, the motion of the 
 mill connected with it muft be incefTant 
 alfo — this machine may be applied to 
 other ufcful purpofes. 
 
 S 3 RE*
 
 ^,oJ. C O IM r E Ivj T S. 
 
 R E C R E AT I O N LVIII. p. 195 
 
 ji cm'riage to go without any force hit what 
 it receives from the pajfengers. 
 
 XHi» carriage is moved by machinery 
 (Plate VIIL Fig. i and 2.) contained 
 in a box that is placed behind it, and 
 is worked by the footman — might be 
 nio\'ed, with equal or greater facility, 
 hy the perfon who fits in it, p. 197 — 
 tiie iiie or convenience of this carriage. 
 
 RECREATION LIX. p. 19S 
 
 'The catapulta. 
 
 This macliinc (Plate IX. Fig. i.) ufed by 
 the ancients to tiirow darts a9;ain{l their 
 enemies — amazing force of fome darts 
 (note)— life to which this machine may 
 he aj^plicd, p. \fy.}. 
 
 RECRE-
 
 CONTENTS. 263 
 
 RECREATION LX. p. 200 
 
 f^ fall as f aft J with a fair windy by land 
 as by water. 
 
 By a failing chariot, or boat fixed on fonr 
 wheels, (Plate IX. Fig. 2.)— its fur- 
 prizing velocity — fimilar machine to 
 go on the ice, p. 201. 
 
 RECREATION LXI. p. 202 
 
 'To fail by latid againjl the wind. 
 
 The body of this machine is fimilar to 
 that in the laft recreation, (Plate X. 
 Fig. I .) but on the inlide there are wheels 
 that are worked by the maft, which is 
 turned round by the force of the wind 
 a2;ainll: its wines ; and the wheels within 
 the machine communicating with thofe 
 on which it ruus, drive it forward — the 
 
 advan-
 
 ^^^ CONTENTS. 
 
 advantages and inconveniencics attend- 
 ing this machine, p. 203. 
 
 RECREATION LXII. p. 204 
 
 5rX<? uninverttble carriage. 
 
 This carriage confifts of a hollow globe, 
 furrounded by two perpendicular and 
 two horizontal brafs or iron circles, in 
 which it moves freely every way; its 
 two wheels are fixed to two perpendi- 
 cular pieces ; and at the bottom of 
 the glebe is a weight that keeps it con- 
 ftantly upright— the great utility of 
 this carriage in certain circumftances, 
 p. 206— account of the trial of a funilar 
 machine, p. 207. 
 
 RECRE-
 
 CONTENTS. 265 
 
 RECREATION LXIIL p. 209 
 
 ^he columnar d'taL 
 
 The cafe of this dial is a hollow column^ 
 in the bafe of whith is the wheel that 
 guides the hour and minute hands ; an^ 
 in the capital is the machinery that 
 flrikes the hours. On the fhaft of the 
 column the hours are marked by hori- 
 zontal lines, to which an index points 
 as it defcends from the top of the (haft 
 to the bottom; and on the bafe is a 
 circle of minutes, marked by a hand 
 fixed on the end of the wheel within. 
 
 RECREATION LXIV. p. 2.14 
 An air chronometer. 
 
 This chronometer confifls of a glafs tube, 
 wherein a pifton is placed, that has a 
 cock by which the fubjacent air is fuf- 
 ' fere<l
 
 266 CONTENTS. 
 
 fered to pafs very flowly : as this pifloit 
 defcends, it fhows the hours, by divi- 
 {ions marked on the tube — a dial may 
 be added to this chronometer, the hand 
 of which may be moved by the firing 
 that is joined to the pillon. 
 
 RECREATION LXV. p. 217 
 
 T^he lamp chronometer, 
 
 ^lie (hadow of a ftyle, placed before a 
 lamp is thrown upon a frame covered 
 with oiled paper, on which the hours 
 ' and their divifions are marked. This 
 inftrument may be made ornamental 
 as well as ufeful. 
 
 RECREATION LXVI. p. 219 
 
 I'he noBurnal dial. 
 
 This dial conhfts of two large and three 
 
 fmall wheels, a weight, a lamp, and a 
 
 c hollow 
 
 I
 
 CONTENTS, ^bj 
 
 hollow conCc Through one of the large 
 wheels, which is placed in the froHt dF 
 the machine, the figures for the hours 
 are cut, on each of which the light 
 of the lamp is Jire£lcd to faJl, by the 
 boi-iow cone, in a regular progredion — 
 this dial may be made to louixd the 
 hours, or ferve as an alarm, p. ^21. — 
 method of making this machine exhibit 
 a pleafing reprefeQtatjon, p. 222, 
 
 THE END OF THE FIRST VOLtfME.
 
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