The Elements of Mechanics

Front Cover
Carey & Lea, 1832 - Mechanics - 508 pages
 

Contents

Enunciation and illustration of the principle of DAlem
69
BOOK III
77
Forces that determine the mechanical state of bodies
81
Division of the subject growing out of the different me chanical states of bodies
82
Quantity of motion in bodies CHAP II
83
84 Fall of heavy bodies near the earth
84
Direction of the force of gravity
85
Convergence of these directions PAGE
86
Relation of the attraction of gravitation to the quantity of matter and velocity
87
Question in relation to the mutual attraction of bodies
88
Experiment of Schehallien
89
Principles of the experiment of Cavendish
90
Description of the apparatus of Cavendish
91
Principles on which the mass of the planets is deter mined
92
Consideration of gravity as an accelerating force
93
Experiments of Galileo
94
Experiments and machine of Atwood
95
and 97 Proofs of the mutual action of the earth and moon Law according to which the intensity of gra vity decreases
96
Proofs of the universal influence of gravitation
98
Force of gravity cannot be considered constant even at small distances from the surface of the earth
99
Effect of the earths rotation on the force of gravity at the earths surface
100
Investigation of the relation between the centrifugal force at the equator and the whole force of gravity
101
Effect of the combined action of gravitation and the cen trifugal force on the figure of the earth
102
Recapitulation of the laws of universal gravitation
103
Direction of the force of gravity Definition of Weight
104
Definition of the Centre of Gravity Application of the conditions of equilibrium of parallel forces to the determination of the position of the centre of...
105
Conditions of equilibrium of a body supported by a point 107 Conditions of equilibrium of a body resting on an edge 108 and 109 Conditions of eq...
108
a surface
109
Effect of the figure of bodies on their stability
110
Stability of bodies resting on inclined surfaces
111
CHAP IV
115
Conditions of equilibrium in bodies resting on points
119
Friction of rolling bodies
121
Definition of the Lever
134
Examples of the use of the different kinds of lever
139
Principles on which the properties of the balance depend
140
Error arising from inequality of the arms of a balance Mode of counteracting and correcting that error
141
Properties of a good balance
142
Condition of equilibrium in a compound system of levers
143
Description and theory of the platform balance
144
Description and theory of the steelyard 146 Investigation of the effect of friction upon the lever Of the Wheel and Axle PAGE
145
Combinations of wheels and axles by means of bands
148
Wheels and Pinions
149
Examination of the proper form to be given to the teeth of wheels and pinions
150
Change of intensity of force and of velocity produced in the action of wheels upon pinions and of pinions upon wheels
151
Change in the direction of motion produced by different forms of the wheel and pinion
152
Effect of friction upon the equilibrium of the wheel and axle
153
Allowance for friction in the action of wheels and pin ions Of the Pulley
154
Conditions of equilibrium in the fixed and moveable Pulley
155
Conditions of equilibrium in combinations of pullies
156
Effect of a want of parallelism in the ropes on the equi librium of pullies
157
Friction of pullies and modes of lessening
158
Of the Wedge 159 Definition of the Wedge
159
Condition of equilibrium in the isosceles wedge
160
Practical action of the wedge
161
Valuable applications of the wedge
162
Extension of the principle of the wedge to bodies of other figures
163
and 165 Effect of friction on the action of the wedge Of the Inclined Plane
164
Definition of the Inclined Plane and mode in which the forces act upon
166
Conditions of equilibrium in the inclined plane
167
Applications of the inclined plane
168
Effect of friction on the equilibrium of the inclined plane
169
146
171
155
173
Of the Resistance of Bodies to a Force exerted to crush them
181
Of the Equilibrium of Artificial Structures
184
Expressions for the resistance of a rectangular pillar to
190
Mode in which earth acts on a terrace wall
198
Reasons for the use of Arches Different materials
206
Comparison between domes and cylindric vaults
214
Of Cast Iron Arches
218
100
219
Theory of chain bridges
227
Centre of spontaneous rotation Effects of the varying
237
Description of the Water Level
319
Description of the Spirit Level
320
Mode of using the spirit level
321
Description of the Masons Level
322
Correction of level for the sphericity of the earth
323
Effect of atmospheric refraction on levelling
324
Equilibrium of a homogeneous liquid in a bent tube
325
Equilibrium of heterogeneous liquids PAGE
326
Effects produced on the weight of solids immersed in fluids
327
Equilibrium of a solid floating at the surface of a liquid 329 Comparison of the immersion of the same body floating on different liquids CHAP III
328
Investigation of the expressions for the pressure of a liquid on a surface
330
Inferences from the foregoing investigation
331
Action of a liquid to change the direction and intensity of the forces that act upon
332
Hydrostatic paradox
333
Comparison of the theory with the results of experiment
334
Properties of the centre of fluid pressure 336 Investigation of the amount of pressures exerted by a liquid on a body immersed in it CHAP IV
335
Definition of Specific Gravity standard in which it is estimated
337
Changes produced in the density of water by variations of temperature
338
Principles of the method of specific gravities
339
Modes of determining the specific gravity of solid bodies
340
Modes of determining the specific gravity of liquids
341
Method of ascertaining the weight of given bulks
342
liquids 325
347
Characters of condensable elastic fluids or Vapours
353
Of the Air Pump
359
Experimental investigation of the law of Mariotte
365
Vapour is formed at other temperatures than that at which
370
Properties common to liquids and elastic fluids buoy
374
Method of determining the specific gravity of gases
377
BOOK VI
397
CHAP III
403
Of the Motion of Liquids in Open Channels
421
Investigation of the strength of the walls of a lock
428
Description of the gates of locks
429
Investigation of the proper angle for the leaves of the gates of locks
430
Principles on which the proper height of locks is deter mined
431
Principles that determine the size of locks
432
Defects of locks placed in juxtaposition
433
Mode of diminishing the waste of water in deep locks
434
Estimate of the waste of water in canals arising from leakage and evaporation
435
of Canals
437
Use of reservoirs in clarifying the water of canals
438
Culverts
439
Aqueducts
440
Wastegates
441
Inclined planes
442
Description of the lock of Betancourt CHAP VIII
443
Definition of the Resistance of a Fluid
444
Theory of the resistance of fluids
445
Experimental inferences of Bossut Analysis of the circumstances of the percussion of fluids
446
Circumstances of the resistance to bodies immersed in fluids
447
Circumstances of the resistance to bodies floating at the surface of liquids
448
Limit to the velocity with which bodies can move at the surface of liquids
449
Formulæ for the resistance of fluids by Bossut and Romme CHAP IX
450
Mode in which Waves may be formed at the surface of a liquid
451
Comparison between the motion of waves and the oscil lation of a liquid in a bent tube
452
Theory of the oscillations of a liquid in a bent tube
453
Application of the foregoing theory to the case of waves
454
Reflection of waves
455
Interference of systems of waves
456
Propagation of waves through vertical orifices
457
Examination of the phenomena of waves raised by the winds
458
Effect of inclined obstacles upon the motion of waves xxix
459
CHAP XI
479
Of the Winds
486
Land and Sea Breezes CHAP XIV
487
Cause of the existence of Vapour in the atmosphere
488
Phenomena of an atmosphere of vapour over a sphere of uniform temperature and surface
489
Phenomena in the case of an uniform decrease of tem perature from the poles to the equator
490
Influence of the aerial part of the atmosphere
491
Effects of diminution of temperature in rising in the aerial atmosphere
492
Motions in the aqueous atmosphere growing out of the unequal distribution of land and water
493
Influence of the winds on the distribution of vapour
494
Origin of springs and rivers
505

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Page 337 - SPECIFIC GRAVITY. THE Specific Gravity of a body, is the ratio of its weight to the weight of an equal volume of some other body assumed as a standard.
Page 498 - Our second remark is, that this difference of gravity becomes less as we ascend from the surface, and at a certain point is neutralized: while, on the other hand, the elasticity, which is equal at the surface, varies with the height ; and the Barometer stands higher, at equal elevations, in the equatorial than in the polar column.
Page 164 - There is an equilibrium upon the wheel and axle when the power is to the weight as the radius of the axle to the radius of the wheel.
Page 327 - He first established the truth that a body plunged in a fluid loses as much of its weight as is equal to the weight of an equal volume of the fluid it displaces.
Page 251 - ... would deviate from the horizontal as far as the mechanism would permit, and would afford no indication of approach to equality in the weights. With equal weights it would remain in equilibrium in any position. In virtue of possessing this last property, such a balance is called indifferent. Practically the distance between the centre of gravity and the point of suspension must not be less than a certain amount depending on the use for which the balance is designed. The proper distance is determined...
Page 130 - These are usually accounted six in number, viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 299 - Aroirdupois. 1 myriagramme = 22-0485 Ibs. Avoirdupois. 1 quintal = 1 cwt. 3 qrs. 25 Ibs. The unit of superficial measure is "the are, a surface of ten metres each way, or 100 square metres. The unit of measures of capacity is the litre, a vessel containing the cube of a tenth part of the metre, and equivalent, to 0-220097 parts of the British imperial gallon. The standard temperature is 32° F. All the divisions and multiples of the units are decimal.
Page 338 - This discovery furnished him with the method of determining the specific gravity of pure gold and pure silver. These being known, he had only to take the specific gravity of the crown, which (supposing no alteration in volume when the two...
Page 387 - From the foregoing statements it may be safely inferred that " the mean height of the barometer at the level of the sea being the same in every part of the globe...
Page 356 - ... fluid will be compelled to follow by the pressure of the atmosphere on its surface in the well. When the piston is again depressed, the water flows through the valve in it, and ascends into the barrel, and by the succeeding strokes of the piston is lifted up until it reaches and flows out of the spout, F. " Although in theory the limit of the height to which water may be raised by the sucking pump, from the surface of the fluid in the well to the highest position of the...

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