Enfield, William, M.A.: Scientific Amusements in Philosophy and Mathematics ©1821 A.K. Newman and Co., etc. Hardcover, no dj, 276 pages

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Comments: "Together With Amusing Secrets". Mathematics, math puzzles, magic tricks, and lots of science experiments.

Contents (from book):

1 Preface

7 Amusements
7 Introduction
7 Of Fractions
9 Of Powers
12 Of Equations
12 General Rules In Regard To Equations
12 Of Ratios And Proportions
14 Properties Of Arithmetical Proportion And Progression
17 Properties Of Geometrical Proportion And Progression
19 Rule Of Three

20 Arithmetic
20 Of Our Numerical System And Tbe Different Kinds Of Arithmetic
23 Of Some Properties Of Numbers
23 Of Arithmetical And Geometrical Progression With Some Problems Which Depend On Them
32 Of Harmonical Progression
33 Problems In Geometrical Progression
38 Exercises In The Single And Compound Rule Of Three Both Direct And Inverse
38 Single Rule Of Three Direct
39 Single Rule Of Three Inverse
39 Compound Rule Of Three
40 Rule Of Fellowship
42 Rule Of Alligation
45 A Chronological Problem
46 The Rule Of Tare
47 Discount
47 Of Combinations And Permutations
50 Problems In Combinations And Permutations
55 Application Of The Doctrine Of Combinations To Games Of Chance And Probabilities
66 Problems In Probabilities And Games Of Chance
61 A Table Of The Different Ways In Which Any Point Can Be Thrown With One Two Three Or More Dice
72 Arithmetical Amusements In Divination And Combination
72 To Tell the Number Thought of By a Person
74 Another Metod of Telling the Number Any One Has Thought Of
78 A Person Having in One Hand an Even Number of Shillings, and in the Other an Odd, to Tell in Which Hand He Has The Even Number
78 A Person Having In One Hand A Piece Of Gold And In The Other A Piece Of Silver To Tell &c
79 The Game Of The Ring
80 To Guess The Number Of Spots On Any Card Which A Person Has Drawn From A Whole Pack
81 A Person Baring A Certain Number Of Counters In Eaoh Hand To Tell How Many He Has Altogether
82 Several Cards Being Given To Tell Which Of Them A Person Has Thought Of
82 Having Spead Out On the Table 20 Cards, Arranged Two and Two, and Desired One or More Persons to Think of Two, Provided they Lie Close To Each Other, to Tell Which Cards They Have Thought of
83 To Make All The Cards Of The Same Kind Be Found Together However Often The Pack May Have Been Cut
83 The Four Indivisible Kings
84 To Write Down On A Piece Of Paper The Heap Of Cards Which A Person Will Choose
84 Several Cards Being Presented To Several Persons To Guess That Which Each Has Thought Of
85 Three Cards Being Presented To Three Persons To Guess That Which Each Has Chosen
86 To Tell The Number Of Spots On All The Bottom Cards Of Several Heaps Arranged On A Table
86 To Name All The Cards Of A Pack
88 To Make A Person Believe You Can Distinguish The Cards By Their Smell
88 A Pack Of Cards Being Divided Into Two Parts To Discover Whetehr The Number In Each Be Odd Or Even
88 To Tell Rhe Number Of Spots On Several Cards Which Any Person Has Chosen
89 A Person Having Drawn Four Cards From A Pack To Tell The One He Has Thought Of
89 Three Things Privately Distributed To Three Persons To Guess That Which Each Has Got
91 To Tell By Inspecting A Watch At What Hour A Person Has Resolved To Rise Next Morning
91 Two Persons Agree To Take Alternately Numbers Less Than A Given Number And To Add Them Together Till One Of Them Has Reached A Certain Sum By What Means One Of Them Can Reach That Sum Before The Other
92 Sixteen Counters Being Disposed In Two Rows To Find That Which A Person Has Thought Of
93 A Certain Number Of Cards Being Shown To A Person To Guess That Which He Has Thought Of
94 To Arrange 30 Criminals In Such A Mariner As To Save 15 Of Them
94 The Game Of The Nosegays
95 A Man Has A Wolf A Goat And A Cabbage To Carry Over A River
95 To Dispose Counters In The Eight External Cells Of A Square So That There Shall Always Be Nine In Each Row And Yet The Whole Number Shall Vary From 20 To 32
97 To Distribute Among Three Persons 21 Casks Of Wine 7 Of Them Full 7 Of Them Empty And 7 Of Them Half Full So That Each Of Them Shall Have The Same Quantity Of Wine And The Same Number Of Casks
97 A Schoolmaster To Amuse His Scholars &c
98 To Tell The Figure Which Has Been Privately Cut Off From A Certain Product
99 A Person Having Multiplied Two Numbers Together To Tell The Product Provided You Know Only The Last Figure Of It
99 A Person Having Chosen Two Numbers And Divided The Greater By The Less To Tell The Quotient

101 Political Arithmetic
101 Of The Proportion Between The Males And Females
102 Of The Mortality Of The Human Race According To The Different Ages
105 Of The Number Of Men Of Different Ages In A Given Number
106 Of The Proportion Of The Births And Deaths To The Whole Number Of The Inhabitants Of A Country
107 Of Some Other Proportions In Regard To The Inhabitants Of A Country
108 The Age Of A Man Being Given To Tell The Probability Of His Reaching A Certain Age
109 A Young Man Aged 20 Borrows £1000 To Be Paid With Interest When He Attains To The Age Of 25 &c
109 A State Or An Individual Having Occasion To Borrow A Sum Of Money On An Annuity &c

111 Magic Squares
112 Method Of Constructing An Odd Square
112 Method Of Constructing An Even Square
113 A Geometrical Square
114 To Make The Knight Pass Overall The Squares Of The Chess Board Without Passing Twice Over The Same

116 Application Of Analysis To The Solution Of Various Problems
116 A Lady Lamenting That Her Age Was Triple That Of Her Daughter &c
117 A Father On His His Death-Bed Gave Orders In His Will &c
118 A Captain Being Asked How Many Soldiers He Had In His Company &c
119 The Head Of A Fish Nine Inches In Length &c
119 A Person Who Had The Lease Of A House For 99 Years Being Asked &c
120 To Divide The Number 50 Into Two Such Parts &c
120 It Is Proposed To Divide 100 Into Two Such Parts &c
121 Two Persons Sat Down To Play &c
122 The Minute Hand Of A Clock Being At 12 And The Hour Hand At 1 &c
122 If Two Bodies Move Towards Each Other With Unequal Velocities &c
123 To Divide 90 Into Two Parts The Ratio Of Which Shall Be As 2 To 3
123 Application Of Analysis To The Solution Of The 11th Problem Of Divining Arithmetic
124 What Number Is That The 2/3 Of 1/4 Of Which &c
124 What Number Is That The 3/4 Of 2/3 Of Which &c
125 Wbat Number Is That 2/3 Of 4/6 Of Which &c
125 What Number Is That Of Which 2/3 Of 1/4 &c
126 What Number Is That Of Which 1/2 + 3/4 Are Equal To 1?
126 What Number Is That The 1/2 2/3 and 1/4 Of Which Make 12
126 The Triple The Half And The Fourth &c
127 If 3/4 And 1/6 Of The Hull Of A Ship &c
127 A Banker At His Death Being Desirous Of Rewarding Ten Of His Clerks &c

130 Tables Of Chances On Games Of Play

143 Acoustics And Music
143 Definition Of Sound &c
145 Of The Velocity Of Sound—Method Of Measuring Distances By It
146 How Sounds May Be Propagated In Every Direction Without Confusion
146 Of Echoes—How Produced—Account Of The Most Remarkable And Of Some Phenomena Respecting Them
149 To Construct Two Figures To Be Placed At The Two Ends Of A Hall One Of Which Shall Repeat To The Ear Of A Person &c
151 Experiments Respecting The Vibration Of Musical Strings
152 Scale Of Sounds In The Diatonic Progression
154 To Determine The Vibrations Made By A String Of A Given Length And Size
156 Method Of Adding Subtracting Multiplying And Dividing Concords
156 To Add One Concord To Another
158 To Subtract One Concord From Another
158 To Double A Concord Or Multiply It Any Number Of Times At Pleasure
159 To Divide One Concord By Any Number At Pleasure
159 Of The Resonance Of Sonorous Bodies Ibe Fundamental Principles Of Harmony And Melody With Some Other Harmonical Phenomena
162 On The Harmonical Sounds Heard With The Principal Sound
163 Of The Modern Music
163 The Cause Of The Pleasure Arising From Music
169 Of the Properties Of Certain Instruments &c
171 Of Some Musical Instruments Or Machines Remarkable For Their Singularity Or Construction
172 Of A New Instrument Called The Harmonica
173 On What Is Called A False Voice
175 Of The Speaking Trumpet And Ear Trumpet

178 Electricity
178 Definitions
179 Aphorisms
181 Experiments In Electricity
184 The Animated Feather
184 The Artificial Spider
185 The Marvellus Fountain
185 The Magic Picture
186 The Tantalian Cup
186 The Self-Moving Wheel
188 The Magician’s Chace
189 The Planetarium
189 The Incendiaries
190 The Inconceivable Shock
192 Magical Explosions
192 The Prismatic Colours
193 The Artificial Spider
194 The Artificial Earthquake
194 The Electrical Kite
195 Candle Lighted By Electricity
195 Candle Bombs
195 Dancing Balls
196 The Leyden Phial
197 Rosin Ignited By Electricity
197 Spirits Ignited By Electricity
197 Electrified Air
198 To Spin Sealing-Wax Into Threads By Electricity
199 Electrified Camphor
199 Electrical Amusements In The Dark Chamber
199 The Fiery Shower
200 Miraculous Luminaries
201 The Globular Fires
202 The Illuminated Vacuum
203 The Luminous Cylinder
203 The Magical Constellations
204 The Aurora Borealis
205 Circulating Lamps

206 Magnetism
206 Definitions
207 Aphorisms
208 The Magnetic Wand
208 The Mysterious Watch
208 The Magnetic Dial
209 The Magnetic Cards
210 The Communicative Crown
211 The Magnetic Table
212 The Incomprehensible Card

213 Pneumatics
213 Definitions
213 Aphorisms
214 The Bottle Broke By Air
215 The Brass Hemisphere
215 Water Boiled By Air
216 The Aerial Bubbles
216 The Floating Stone
216 The Withered Fruit Restored
216 The Vegetable Air Bubbles
217 The Mercurial Rod
217 The Mystical Bell
218 Feathers Heavier Than Lead
218 The Self-Moving Wheel
219 The Animated Figures
219 The Artificial Halo
220 The Mercurial Shower
220 The Fountain In Vacuo
220 The Cemented Bladder
220 Cork Heavier Than Lead
221 The Animated Bacchus
221 The Artificial Balloon
221 Experiment With A Viper
222 Experiments With Sparrows
  
224 Optics
224 Definitions
228 Three Objects Discernible Only With Both Eyes
229 To Construct The Camera Obscura
230 The Magnifying Reflector
230 Optical Augmentation
231 To Magnify Small Objects By Means Of The Sun’s Rays Let Into A Dark Chamber
231 The Magic Lantern
234 Method Of Painting The Glasses For The Lantern

236 Amusing Secrets
236 To Make A Ring Be Suspended By A Thread After It Has Been Burnt
236 To Make People In A Room Have A Hideous Appearance
236 To Form Figures In Relief On An Egg
236 To Change A Colour From White To Blue
237 To Make A Red Liquor Which When Poured Into Different Glasses Shall Become Yellow Blue Black Or Purple
237 To Make Pomatum With Water And Wax
237 How A Body Of Combustible Matter May Be Penetrated By Fire Without Being Consumed
238 Apparent Transmutation Of Iron Into Copper Or Silver
239 Different Substances Successively Precipitated By Adding Another To The Solution
240 By The Mixture Of Two Transparent Liquors To Produce A Blackish Liquor—Method Of Making Good Ink
241 To Produce Inflammable And Fulminating Vapours
241 The Philosophical Candle
242 To Make An Artificial Volcano
242 To Make Fulminating Powder
243 To Form A Combination Which When Cold Is Liquid And Transparent But When Warm Becomes Thick And Opake
243 To Make A Flash Like That Of Lightning Appear In A Room When Any One Enters It With A Lighted Candle
244 Of Sympathetic Inks And Some Tricks Which May Be Performed By Means Of Them
245 To Make A Drawing Which Shall Alternately Represent Winter And Summer
246 The Magic Oracle
246 Of Metallic Vegetations
247 Arbor Martis Or Tree Of Mars
247 Arbor Dianas Or Tree Of Diana
248 The Lead Tree
248 Non-Metallic Vegetation
249 To Produce Heat And Even Flame By Means Of Two Cold Liqnors
249 To Fuse Iron In A Moment And Make It Ran Into Drops
250 Cement For Making Broken China
250 Process For Whitening Prints
251 Method Of Taking Paintings From The Old Canvass And Transferring Them To New
252 To Fill A Glass With Water In Snob A Manner-That A Person Shall Not Be Able To Remove It Without Spilling It All
252 To Construct Two Figures One Of Which Shall Blow Out A Candle And The Other Light It Again
252 Japan Vases
252 To Construct A Vessel From Which Water Shall Escape Through The Bottom As Soon As Its Mouth Is Unstopped
253 Transparencies
253 Method Of Fixing Crayons
257 A Curious Illusion
257 An Object Being Placed Behind A Convex Glass To Make It Appear Before It
257 The Chinese Shadows Ombres Chinoises
259 To Direct A Swarm Of Bees At Pleasure
260 A Powder Which Inflames When Exposed To The Air
260 Fulminating Gold
261 To Cut Glass By Means Of Heat
261 To Melt A Piece Of Money In A Walnut-Shell Without Injuring The Shell
262 Phosphorus
262 A Liquor Which Shines In The Dark
263 To Make Luminous Characters Appear On A Piece Of Paper Or A Wall &c
263 A Liquor Shut Up In A Bottle Which When The Bottle Is Unstopped Becomes Luminous
263 Method Of Speedily Delineating All Sorts Of Plants And Flowers
264 The Changeable Rose
264 The Magic Picture
265 The Changeable Picture
265 Golden Ink
266 Process Translated From The German
266 Another Process
266 White Ink to Write On Black Paper
267 Red Ink
267 Blue Ink
267 Yellow Ink
267 Green Ink
267 Ink Of Different Colours Made From The Juice Of Violets
268 Tracing Ink
269 China Or Indian Ink
270 Ink Powder
270 To Revive Old Writing
271 To Take Off The Impression Of Any Drawing
272 To Take Off The Impression Of Old Prints
272 Method Of Teaching Drawing To Young Persons
272 To Construct A Lantern Which Will Enable A Person To Read By Night At A Great Distance
273 To Take Off Impressions In Plaster Of Paris Or Sulphur
273 Baits For Catching Fish
275 To Produce Variety In The Colours Of Flowers
275 To Obtain Double Flowers
276 To Obtain Flowers Of Different Colours On The Same Stem