The mathematical principles of mechanical philosophy (Google eBook)

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Contents

Six equations of equilibrium of a rigid body
31
One point of the body fixed
33
GO Two points or an axis in the body fixed
34
Gl Conditions of equilibrium when a body rests on a plane
35
The principal moment of the forces
36
CHAPTER III
39
Principle of Virtual Velocities
41
Conditions of stable and unstable equilibrium
45
Centre of gravity highest or lowest when in equilibrium
46
The equilibrium stable or unstable according as the centre of gravity is in its lowest or highest position
47
Lagranges proof of Virtual Velocities
48
Conditions of equilibrium deduced from the principle of Virtual Velocities
50
CHAPTER IV
52
Coordinates of the centre of gravity and the calculation of them in various coses Integration between limits explained and illus trated
55
GuldinusProperties
68
CHAPTER V
71
Three species of lever
74
requisites for a good balance
75
Graduation of the steelyard 99 Robervals Balance
78
CHAPTER VI
91
Arch explanation of terms
97
Conditions of equilibrium of an arch that it may not break
104
Common Catenary Property of its centre of gravity Tension
112
CHAPTER VII
122
CHAPTER VIII
139
ARTICLE TAGS
141
Attraction of a homogeneous oblate spheroid of any ellipticity on
149
Formulse for the attraction of any heterogeneous mass
156
Calculation of V for a homogeneous sphere
162
A function of n J cos a J n sin w can be expanded
169
UTICLE PACE
177
Dynamical measure of force
183
Measure of impulsive accelerating force
190
Mean of obtaining equations to calculate motion
205
Rectilinear motion under the action of gravity and central forces
211
Curvilinear motion under the action of gravity
217
Properties of central orbits
223
ARTICLE P0
225
The law of force found when the orbit is known Force in
231
CHAPTER III
241
Method of determining the elements of an orbit from observation
247
Time in a parabolic orbit about the foens
254
Brief history of lunar inequalities 200
261
IfTKLk PACK 299 Effect on the periodic time of the Moon 205
265
Effect on the velocity in the circular orbit
266
Effect on the form of the circular orbit
267
The ratio of the axes of the oval orbit
268
The velocity in the oval orbit Moons Variation
269
Effect on the inclination and line of nodes
271
34 Calculation of the motion of the nodes
273
Calculation of the inclination of the Moons orbit
277
CHAPTER V
278
introduction of the constants c and g
294
Integration of the equations second approximation
297
Distance of the Moon from the Earth
298
Geometrical interpretation of the terms in the formula? for the dist ance and longitude of the Moon Progression of the line of Apsides The Variation ...
303
Error in the calculated progression of the apsides
304
Notices of inequalities of the third and higher orders
305
The centre of gravity of the Earth and Moon nearly describes an ellipse about the Sun
306
Means of determining the mass of the Moon
309
ARTICI K ViCf 349 Comparison of the methods used in the Lunar and Planetary Theories
310
Explanation of the process of integration
311
Integration of the equations for an undisturbed planet
313
Elements of the orbit in terms of the arbitrary constants
316
Integration of the equations for a disturbed planet
318
Transformation of the differential coefficients of R
321
Variations of the elements
324
Method of expanding R
329
The form of the terms and the order of magnitude of the co efficients in this expansion The constant part of U
331
Effect of the terms of R after the first periodical
338
Jupiter and Saturn the Earth and Venus
340
Equations for calculating the secular variations
342
and of the eccentricities and inclinations The fact that the planets re volve about the Sun in the same direction ensures the Stability of the System
345
The masses and elements of the heavenly bodies
351
CHAPTER VII
357
oscillations are isochronous
359
Motion ona circulararc
361
measuring of heights and depths
363
Oscillation of a pendulum in a cycloid
366
CHAPTER VIII
381
Formulas for the transformation of coordinates
387
Properties of the principal moments of inertia
395
Motion about a fixed axis The angular accelerating force
401
Equations for calculating the angular velocities about the principal
413
Stability of the Earths rotation
423
The length of the mean day is invariable
429
The inclination of the Earths axis to the lunar orbit is nearly
435
477 Plane of Princifml Moments and Invariable Plane The action
442
and remarks The Conservation of vis viva
445
Principle of Least Action or of Stationary Action
452
Coexistence of Small Vibra
460
CHAPTER XIII
469
Impact of spheres
475
Motion of centre of gravity Conservation of Motion of Centre
481
HYDROSTATICS
509
CHAPTER II
517
The figure of a moss of fluid revolving about an axis through
530
Calculation of the ellipticity
537
Additional theorems
543
Equations for calculating the ellipticity 526
547
CHAPTER III
549
HYDRODYNAMICS
555
Equations for calculating the motion of an elastic fluid the
561
The ellipticity of the strata increases from the centre to
627

Common terms and phrases

Popular passages

Page 505 - A uniform ladder, 10 feet long, rests with one end against a smooth vertical wall and the other on the ground, the coefficient of friction between the ladder and the ground being J.
Page x - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.
Page 236 - Gravitation is, that every particle of matter attracts every other particle with a force which varies directly as the mass of the attracting particle, and inversely as the square of the distance.
Page 66 - ... is the length of the path described by the centre of gravity of the area.
Page 4 - ... method, and the forces are called kinetic forces. Weight is the name given to the pressure which the attraction of the earth causes a body to exert. Hence, since static forces produce pressure, we may take, as the unit of force, a pressure of one pound (Art. 11). Therefore, the magnitude of a force may be measured statically by the pressure it will produce upon some body, and expressed in pounds. This is called the Static...
Page 69 - The portions of the lever into which the fulcrum divides it are called the arms of the lever : when the arms are in the same straight line, it is called a straight lever, and in other cases a bent lever.
Page 83 - Mechanical Power is the Wedge. This is a triangular prism, and is used to separate obstacles by introducing its edge between them and then thrusting the wedge forward. This is effected by the blow of a hammer or other such means, which produces a violent pressure for a short time, sufficient to overcome the greatest forces. 168.
Page 6 - If two forces act on a body in opposite directions their resultant is equal to their difference and acts in the direction of the greater; thus two forces acting in opposite directions and equal to 9 and 4 Ibs.
Page 229 - Hence the orbit described about this centre of force will be an ellipse, parabola, or hyperbola according as the velocity is less than, equal to, or greater than that from infinity.
Page 71 - ... grate. Scissors, shears, nippers, pincers, and other similar instruments are composed of two levers of the first kind; the fulcrum being the joint or pivot, and the weight the resistance of the substance to be cut or seized ; the power being the fingers applied at the other end of the levers. The brake of a pump is a lever of the first kind; the pump-rods and piston being the weight to be raised.

References from web pages

John Henry Pratt: Biography and Much More from Answers.com
He wrote Pratt's Mechanical Philosophy, full title: The Mathematical Principles of Mechanical Philosophy and their application to Elementary Mechanics and ...
www.answers.com/ topic/ john-henry-pratt

THE CLERK MAXWELL COLLECTION
236) Pratt, jh The mathematical principles of mechanical philosophy, 2nd ed. 1845. 237) Preece, wh & Sivewright, J. Telegraphy. 1876. ...
www.clerkmaxwellfoundation.org/ JCMLibrary.pdf

THE ORIGINS OF WATER WAVE THEORY - Annual Review of Fluid ...
The Mathematical Principles of Mechanical Philosophy; And Their Application to the Theory of Universal Gravitation. Cambridge, UK: Deighton. Rankine WJM. ...
arjournals.annualreviews.org/ doi/ pdf/ 10.1146/ annurev.fluid.36.050802.122118

John Henry Pratt —— 维客(wiki)
He wrote Pratt's Mechanical Philosophy, full title: The Mathematical Principles of Mechanical Philosophy and their application to Elementary Mechanics and ...
www.wiki.cn/ wiki/ John_Henry_Pratt

Bibliographic information