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73

A Person having in one Hand a Piece of Gold, and in

the other a Piece of Silver, to tell, &c....

78

The Game of the Ring.....

79

To guess the number of spots on any card which a

person has drawn from a whole pack..... 80

.....

Page.

A person having a certain number of counters in each

hand, to tell how inany he has altogether... 81

Several cards being given, to tell which of them a per-

son has thought of

82

Another problem of the same kind

ib.

To make all the cards of the same kind be found toge-

ther, however often the pack may have been

cut

83

The four indivisible kings

ib.

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 .. ib.

Three cards being presented to three persons, to guess

that which each has chosen

84

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.

ib.

To make a person believe you can distinguish the

cards by their smell..

88

A pack of cards being divided into two parts, to disco-

ver whetehr the number in each be odd or

ib.

To tell rhe number of spots on several cards which any

person has chosen....

ib.

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.......

ib.

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 toge-

ther till one of them has reached a certain

sum, by what means one of them can reach
that sum before the other

ib.

Sixteen counters being disposed in two rows, to find

that which a person has thought of

92

A certain number of cards being showu to a person, to

guess that which he has thought of ...

93

To arrange 30 criminals in such a manner as to save

15 of them, &c...

94

The game of the nosegays

ib.

A man has a wolf, a goat, and a cabbage, to carry over

a river, &c.

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

ib

Page.

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...

ib.

To tell the figure which has been privately cut off from

a certain product

98

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...... ib.

POLITICAL ARITHMETIC.....

101

Of the proportion between the males and females · ib.

Of the mortality of the human race, according to the

different ages.

102

Of the number of men of different ages in a given

number

105

Of the proportion of the births and deaths to the whole

number of the inhabitants of a country...... 106

Of some other proportions in regard to the inhabitants

of a country ...

107

The

age of a man being given, to tell the probability of

his reaching a certain age

108

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.

ib.

MAGIC SQUARES ..

111

Method of constructing an Odd Square

112

Method of constructing an Even Square

ib.

A Geometrical Square..

113

To make the knight pass over all the squares of the

chess board, without passing twice over the

114

APPLICATION OF ANALYSIS to the Solution of

Various Problems..

116

A lady lamenting that her age was triple that of her

daughter, &c.

ibi

A father on his his death-bed, gaveorders in his will,&c. 117

A caplain being asked how many soldiers he had in his

company, &c.

118

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.

ib.

To divide the number 50 into two such parts, &c. 120

It is proposed to dividc 100 into two such panis, &c... ib.

Two prisons sat down to play, &c.

121

Page.
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

ib.

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 pro-

blem of divining arithmetic

ib.

What number is that the off of which, &c.

124

What number is that the of of which, &c.

ib.

What number is that of of which, &c.

125

What number is that of which of \, &c.

ib.

What number is that of which } + are equal to 1?. 126

What number is that the }, }, and of which make 12 ib.

The triple, the half, and the fourth, &c.

ib.

If 4 and 5 of the hull of a ship, &c.

127

A banker at his death being desirous of rewarding ten
of bis clerks, &c.

ib.

TABLES OF CHANCES on games of play.

130

ACO STICS AND MUSIC

143

Definition of sound, &c

ib.

Of the velocity of sound-method of measuring dis-

tances by it

145

How sounds may be propagated in every direction
without confusion..

146

Of echoes-how produced-account of the most re-

markable, and of some phenomena respecting
_them

ib.

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.....

149

Experiments respecting the vibration of Musical

Strings

...... 151

Scale of Sounds in the Diatonic Progression

152

To determine the vibrations made by a string of a

given length and size

154

Method of adding, subtracting, multiplying, and divid-

ing Concords.

156

To add one concord to another

ib.

To subtract one concord from another......

158

To double a concord, or multiply it any number of

times, at pleasure..

To divide one concord by any number at pleasure...

..: 159

Of the resonance of sonorous bodies, the fundamental

principles of harmony and melody, with some

other harmonical phenomena

159

On the harmonical sounds heard with the principal

sound .

162

Of the modern music

ib.

• 163

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