CONTENTS

OF THE SECOND VOLUME.

PART III.

Containing various problems in Mechanics.

PROB. I. To cause a ball to proceed in a retrograde direc-
tion, though it meets with no apparent obftacle

PROB. 11. To make a false ball for playing at nine pins

PROB. III. How to conftruct a balance, which shall appear

just when not haded as well as when baded with un-

equal weights

PROB. IV. To find the centre of gravity of feveral weights
Solution of a geometrical problem, which feems to be
deducible only from the property of the centre of gravity

PROB. V. When two perfons carry a burthen by means of

a lever or pole, which they support at the extremities;

to find how much of the weight is borne by each

PROB. VI. How 4, 8, 16, or 32 men may be dijiributed
in fuch a manner as to carry a confiderable burthen.
with ease

PROB. VII. A rope ACB of a determinate length being

made faft by both ends but not fretched, to two points

of unequal height A and B, what position will be

affumed by the weight P, fufpended from a pulley, which

rolls freely on that rope?

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PROB. VIII. To caufe a pail full of water to be fupported

by a flick, one half of which only, or lefs, refis on the

edge of a table

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PROB. IX. To hold a stick upright on the tip of the finger,

without its being able to fall

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14

PROB. X. To conftruct a figure which without any coun-

terpoife fhall always raife itself upright, and keep in

that pofition, or regain it, however it may be diflurbed 15

PROB. XI. If a rope ACB, to the extremities of which

are affixed the given weights P and Q, be made to pass

over two pullies A and B; and if a weight R be fuf-

pended from the point C, by the cord RC; what pofition

will be affumed by the three weights and the rope

ACB?

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PROB. XII. Calculation of the time which Archimedes

would have required to move the earth, with the md-

chine of which he spoke to Hiero -

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PROB. XIII. With a very small quantity of water, fuch
as a few pounds, to produce the effect of feveral thou-
Lands

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Two other methods of performing the fame thing -

PROB. XIV. To find the weight of a cubic foot of water

PROB. XV. Two liquors being given; to determine

which of them is the lightest -

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Rules for calculating the abfolute gravity, in English

Troy weight, of a cubic foot and inch, English mea-

fure, of any fubftance whofe fpecific gravity is known

PROB. XVI. To determine whether a mass of gold or silver,

fufpected to be mixed, is pure or not

PROB. XVII. The fame fuppofition made, to determine the

quantity of mixture in the gold-

PROB. XVIII. Suppofe there are two boxes exactly of the

fame fize, fimilar and of equal weight, the one con-

taining gold and the other filver: is it poffible by any

mathematical means to determine which contains the

gold and which the filver? or, if we fuppofe two balls

the one made of gold and hollow, the other of folid filver

gilt, is it poffible to diftinguish the gold from the filver? 33

PROB. XIX. Two inclined planes, AB and AD, being

given, and two unequal fpheres, P and p; to bring

them to an equilibrium in the angle, as feen in the figure 34

PROB. XX. Two bodies P and Q depart, at the fame time,

from two points A and B of two lines given in pofition,

and move towards a and b, with given velocities: re-

quired their pofition when they are the nearest to each

ther poffible?

36

PROB. XXI. To caufe a cylinder to fupport itself on a plane

inclined to the horizon, without rolling down; and even

to afcend a little along that plane.

PROB. XXII. To conftruct a clock, which shall point out

the hours by rolling down an inclined plane -

FROB. XXIII. To conftruct a dress by means of which

it will be impoffible to fink in the water, and which

fhall leave the perfon who wears it, at full freedom to

make every kind of movement

PROB. XXIV. To conftruct a boat which cannot be funk,

even if the water fhould enter it on all fides

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39

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42

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44

PROB. XXV. How to raise from the bottom of the fea a
veffel which has funk

Defcription of the camel, a machine employed by the Dutch

for carrying veffels heavily laden over the fand banks in

the Zuyder Zee

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PROB. XXVI. To make a body afcend, as if of itself, along
an inclined plane, in confequence of its own gravity
PROB. XXVII. To conftruct a clock with water
PROB. XXVIII. A point being given and a line not bori-
zontal, to find the pofition of the inclined plane along
which if a body defcend, fetting out from the given
point, it fhall reach that line in the leaft time

PROB. XXIX. Two points A and B being given in the fame

horizontal line: required the pofition of two planes AC

and CB of fuch an inclination, that two bodies defcend

ing with accelerated velocity from A to C, and then

afcending along CB with the acquired velocity, fhall do
fo in the leaft time poffible

PROB. XXX. If a chain and two buckets be employed

to draw up water from a well of very great depth; it

is required to arrange the apparatus in fuch a manner,
that in every pofition of the buckets, the weight of the
chain fhall be deftroyed; fo that the weight to be raised
fhall be that only of the water contained in the afcend-
Another method of accomplishing the fame thing-555

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FRTE, XXXHE How comes it that a flick loaded with a

wright at the upper extremity, can be kept in equilibrio

an the paint of the finger, much easier than when the

weight is near the Lower extremity; or that a fword,

for example, can be balanced on the finger much better
when the bilt is uppermof?

1

FLOB. XXXIV. What is the muff advantageaus position of
the feet for fanding with firmness, in an erect pofture?
Geometrical problem on this fubject

ROB. XXXV. Of the game of billiards

I. The position of the pocket and that of the two balls,

M and N, being given, to firike your adverfary's

ball M in fuch a manner, that it fall fall into the

pocket-

I. To frike the ball by reflection

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III. If a ball strikes again another in any direction

whatever, what is the direction of the impinging

ball after the frack ?

PROB. XXXVI. To confirud a water-clock

PROB. XXXVH. Mechanical paradox: Howequal weights.

placed at any distance from the point of support of

balance shall be in equilibria

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PROB. XXXVIII. What webcity muß be given to a ma-

chine moved by water, in order that it may produce the

greateft effect?

PROB. XXXIX. What is the greatest number of float-

baards that ought to be applied to a wheel, moved by a

current of water, in order to make it produce the

greatest effect?

PROB, XL. If there be two cylinders, containing exaðly

the fame quantity of matter, the one falid and the other

hallow, and both of the fame length; which of them

will fuflain, without breaking, the greatest weight

fufpended from one of its extremities, the other being

fixedt?

PROB. XLI. To confiruct a lautern, which shall give light

at the bottom of the water

PROB. XLII. To conftruct a lamp, which shall preferve
its oil in every fituation, however moved or inclined
PROB. XLIII. Method of conftructing an anemofcope and

-anemometer

PROB XLIV. Conftruction of a feel-yard, by means of

which the weight of any body may be afcertained, with-

out weigh