MECHANISM OF THE HEAVENS BY Mary Fairfax Greig Somerville 1780-1872 Second Edition Edited by Russell McNeil 2001 Mary Fairfax Greig Somerville 1780-1872 Print, CD-ROM and WWW Versions Copyright © 2001 by Russell McNeil All rights reserved No part of this work may be produced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher Published by Malaspina Great Books, 3516 Wiltshire Dr., Nanaimo, BC, Canada, V9T 5K1 Manufactured in Canada ISBN 1-896886-40-X (Print version) ISBN 1-896886-38-8 (CD-ROM Version) ISBN 1-896886-36-1 (WWW Version) TO HENRY, LORD BROUGHAM AND VAUX, LORD HIGH CHANCELLOR OF GREAT BRITAIN, _ This Work, undertaken at His Lordship's request, is inscribed as a testimony of the Author's esteem and regard Although it has unavoidably exceeded the limits of the Publications of the Society for the Diffusion of Useful Knowledge, for which it was originally intended, his Lordship still thinks it may tend to promote the views of the Society in its present form To concur with that Society in the diffusion of useful knowledge, would be the highest ambition of the Author, MARY SOMERVILLE Royal Hospital, Chelsea, 21st July, 1831 To my three children Liam, Bronwyn and Rose Siubhan TABLE OF CONTENTS _ Art Page ACKNOWLEDGEMENTS xvii FOREWORD TO THE SECOND EDITION xix Notes to Foreword xxiii GLOSSARY OF SYMBOLS & LIST OF IMAGES PRELIMINARY DISSERTATION Notes to Preliminary Dissertation xxvii 36 INTRODUCTION PHYSICAL ASTRONOMY Notes to Introduction 41 42 BOOK I − DYNAMICS Foreword to Book I The Figure of the Earth The Rotation of the Earth The Sun, Moon, Planets and Satellites 45 45 50 57 BOOK I: CHAPTER I DEFINITIONS, AXIOMS, &c 22 39 43 12 48 51 56 Definitions Uniform Motion Composition and Resolution of Forces The General Principles of Equilibrium On Pressure On the Normal Equilibrium of a Particle on a curved Surface Virtual Velocities Variations Notes to Bk I, Chap I 65 66 67 71 73 74 74 76 77 78 BOOK I: CHAPTER II VARIABLE MOTION 60 Definitions 79 Art 63 68 69 75 79 81 83 84 85 93 96 97 99 100 100 106 109 113 Page Central Force Demonstration: perpetually varying central force Demonstration: force and acceleration General Equations of the Motions of a Particle of Matter Demonstration: general equations both free and constrained Demonstration: resolution of forces Principle of Least Action Motion of a Particle on a Curved Surface Radius of Curvature Pressure of a Particle Moving on a Curved Surface Demonstration: tangent and normal components Centrifugal Force Demonstration: centrifugal force and central force Motion of Projectiles Demonstration: effect of air resistance Theory of Falling Bodies Comparison of Centrifugal Force with Gravity Simple Pendulum Demonstration: impelled initial velocity Isochronous Curve Curve of Quickest Descent Notes to Bk I, Chap II 79 79 80 81 81 85 87 89 90 93 93 93 96 96 96 99 100 101 101 105 108 109 BOOK I: CHAPTER III ON THE EQUILIBRIUM OF A SYSTEM OF BODIES 114 119 120 121 122 123 124 125 127 128 130 131 132 135 vi Definitions and Axioms Reaction equal and contrary to Action Mass proportional to Weight Density Mass proportional to the Volume into the Density Specific Gravity Equilibrium of two Bodies Demonstration: lever Equilibrium of a System of Bodies Demonstration: equilibrium Rotatory Pressure On the Lever Demonstration: moments Projections of Lines and Surfaces Equilibrium of a System of Bodies invariably united Demonstration: equilibrium about a point On the Centre of Gravity Mechanism of the Heavens 111 111 112 112 112 112 113 113 113 113 115 116 116 116 117 117 120 Table of Contents Art 137 138 143 Page On the Position and Properties of the Centre of Gravity Demonstration: centre of gravity displaced from origin of co-ordinates Equilibrium of a Solid Body Notes to Bk I, Chap III 121 122 124 124 BOOK I: CHAPTER IV MOTION OF A SYSTEM OF BODIES 144 151 153 158 165 168 Introduction On the Motion of a System of Bodies in all possible Mathematical relations between Force and Velocity Demonstration: uniform motion of centre of gravity Demonstration: as a consequence of the law of reaction and action On the Constancy of Areas Demonstration: general equation of a system of bodies Demonstration: general equations for a system moving uniformly On the motion of a system in all possible relations between force and velocity Notes to Bk I, Chap IV 127 129 129 130 131 132 136 138 139 BOOK I: CHAPTER V THE MOTION OF A SOLID BODY OF ANY FORM WHATEVER 169 174 176 181 202 216 222 Introduction Determination of the general Equations of the Motion of the Centre of Gravity of a Solid in Space Rotation of a Solid Demonstration: three permanent axes of rotation Rotation of a Solid not subject to the action of Disturbing Forces, and at liberty to revolve freely about a Fixed Point, being its Centre of Gravity, or not Rotation of a Solid which turns nearly round one of its principal Axes, as the Earth and the Planets, but not subject to the action of accelerating Forces Compound Pendulums Notes to Bk I, Chap V 141 142 143 145 156 163 166 168 BOOK I: CHAPTER VI ON THE EQUILIBRIUM OF FLUIDS 225 231 233 238 239 240 Definitions, &c Equilibrium of Fluids Equation of Equilibrium Equations of Condition Equilibrium of homogeneous Fluids Equilibrium of heterogeneous Fluids Demonstration: relationship between pressure and density Mary Somerville 169 169 170 171 172 172 172 vii Art 246 Page Equilibrium of Fluids in Rotation Notes to Bk I, Chap VI 174 175 BOOK I: CHAPTER VII MOTION OF FLUIDS 248 250 252 257 258 260 261 263 266 267 269 272 278 280 291 293 296 302 306 307 General Equation of the Motion of Fluids Equation of Continuity Development of the Equation of Continuity Second form of the Equation of the Motions of Fluids Integration of the Equations of the Motions of Fluids Demonstration: integration of equations when exact differential Theory of small Undulations of Fluids Rotation of a Homogeneous Fluid Determination of the Oscillations of a Homogeneous Fluid covering a Spheroid, the whole in rotation about an axis; supposing the fluid to be slightly deranged from its state of equilibrium by the action of very small forces Action of the Sun and Moon Determination of the general Equation of the Oscillation of all parts of the Fluids covering the Earth Equation at the Surface Continuity of Fluids Oscillations of the Oceans On the Atmosphere Density of the Atmosphere Equilibrium of the Atmosphere Oscillations of the Atmosphere Oscillations of the Mercury in the Barometer Conclusion Notes to Bk I, Chap VII 177 178 178 181 182 183 184 185 186 186 187 189 191 192 197 197 198 201 203 204 204 BOOK II − UNIVERSAL GRAVITATION Foreword to Book II Gravitation Elliptical Orbits Perturbations of the Planets 207 207 210 212 BOOK II: CHAPTER I PROGRESS OF ASTRONOMY 308 viii Historical Review Notes to Bk II, Chap I 219 223 Mechanism of the Heavens Table of Contents Art 309 326 332 BOOK II: CHAPTER II ON THE LAW OF UNIVERSAL GRAVITATION Kepler’s Laws On Parallax Force of Gravitation at the Moon Notes to Bk II, Chap II Page 225 223 236 240 BOOK II: CHAPTER III DIFFERENTIAL EQUATIONS OF A SYSTEM OF BODIES 344 352 354 Introduction Motion of the Centre of Gravity Attraction of Spheroids Notes to Bk II, Chap III 241 246 249 252 BOOK II: CHAPTER IV ON THE ELLIPTICAL MOTION OF THE PLANETS 359 365 374 378 379 386 387 388 392 397 398 399 400 401 404 405 406 407 408 Introduction Motion of one Body Determination of the Elements of Elliptical Motion Elements of the Orbit Equations of Elliptical Motion Determination of the Eccentric Anomaly in functions of the Mean Anomaly Determination of the Radius Vector in functions of the Mean Anomaly Kepler’s Problem−To find a Value of the true Anomaly in functions of the Mean Anomaly True Longitude and Radius Vector in functions of the Mean Longitude Determination of the Position of the Orbit in space Projected Longitude in Functions of true Longitude True Longitude in Functions of projected Longitude Projected Longitude in Functions of Mean Longitude Latitude Curtate Distances Motion of Comets Arbitrary Constant Quantities of Elliptical Motion, or Elements of the Orbits Co-ordinates of a Planet Determination of the Elements of Elliptical Motion Velocity of Bodies moving in Conic Sections Notes to Bk II, Chap IV Mary Somerville 255 256 261 266 266 268 270 272 275 276 277 277 277 278 278 279 279 280 280 282 284 ix Art BOOKII: CHAPTER V THEORY OF THE PERTURBATIONS OF THE PLANETS 410 417 422 428 452 455 Introduction Demonstration of Lagrange’s Theorem Variation of the Elements, whatever the Eccentricities and Inclinations may be Variations of the Elliptical Elements of the Orbits of the Planets Determination of the Coefficients of the Series R Coefficients of the series R Notes to Bk II, Chap V Page 287 288 291 297 317 323 327 BOOK II: CHAPTER VI SECULAR INEQUALITIES IN THE ELEMENTS OF THE ORBITS 462 473 480 481 488 498 499 510 511 512 515 525 Stability of the Solar System, with regard to the Mean Motions of The Planets and the greater axes of their Orbits Differential Equations of the Secular Inequalities in the Eccentricities, Inclinations, Longitudes of the Perihelia and Nodes, which are the annual and sidereal variations of these four elements Approximate Values of the Secular Variations in these four Elements in Series, ascending according to the powers of the Time Finite Values of the Differential Equations relative to the eccentricities and longitudes of the Perihelia Stability of the Solar System with regard to the Form of the Orbits Secular Variations in the Inclinations of the Orbits and Longitudes of their Nodes Stability of the Solar System with regard to the Inclination of the Orbits Annual and Sidereal Variations in the Elements of the Orbits, with regard to the variable Plane of the Ecliptic Motion of the Orbits of two Planets Secular Variations in the Longitude of the Epoch Stability of the System, whatever may be the powers of the Disturbing Masses The Invariable Plane Notes to Bk II, Chap VI 329 336 340 341 346 351 352 355 357 357 360 365 367 BOOK II: CHAPTER V11 PERIODIC VARIATIONS IN THE ELEMENTS OF THE ORBITS 529 Variations depending on the first Powers of the Eccentricities and Inclinations Notes to Bk II, Chap VII 371 375 BOOK II: CHAPTER VIII PERTURBATIONS OF THE PLANETS 532 536 x Introduction Perturbations in the Radius Vector Mechanism of the Heavens 377 378 Basic Bibliography 772 Mechanism of the Heavens SUBJECT INDEX BY ARTICLE _ Article Aberration of light Acceleration of moon’s mean motion Action, equal and contrary to re-action Activity of matter Anomaly, mean, defined true, defined in functions of mean anomaly eccentric, defined in functions of mean anomaly Aphelion, defined Arbitrary constant quantities of elliptical motion Arc, projected Arcs, circular, convertible into time introduced by integration into series of perturbations Areas, principle of, in a system of bodies in a rotating body consists in exists, when centre of gravity moves in space in the elliptical motion of the planets the first of Kepler’s laws Areas, variation of, a test of disturbing forces sum of, zero on two of the co-ordinate planes and a maximum on the third Argument, defined Aries, first point of Astronomy, progress of Astronomical tables, formation of correction of Atmosphere, density of height and oscillations of Atmospheres of planets Attraction of spheroids of a planet and its satellites Axes of co-ordinates method of changing Axes, permanent, of rotation Axis, instantaneous, of rotation Axis, major of orbits, not affected by secular variations periodical variations in 951 748 119 382 382 388 383 386 316 73 370, 405 548 213 540, 555 158 176 161 165 368 309 180 164 394 359 308 661 662 293 302 655 354 354 25 162, 194 182, 189 194, 199 462 428, 439 Subject Index by Article permanent change in 555 Barometer, oscillations of 306 Centre of gravity, of a system position and properties of conservation of motion of, in a solid motion of the same, as if the masses of the planets were united in it of a planet and its satellites distance of primitive impulse from Circular motion Coefficients of the series expressing the disturbing action of the planets development of numerical values of, for Jupiter Comets, areas described by Continuity of fluids Co-ordinate planes Co-ordinates of a planet of the moon Curtate distance, defined in functions of latitude Curve of quickest descent Cycloid, properties Day, length of invariable Data for computing the celestial motions Density of sun and planets Disturbing forces development of acting on moon acting on Jupiter’s satellites Disturbed rotation of a solid motion of fluids motion of atmosphere Earth, the figure of Earth, the inequalities in the motion of rotation compression not homogeneous Eccentricity, defined Eccentricities of planetary orbits Eclipses, general theory of of Jupiter’s satellites 774 Mechanism of the Heavens 135 137 165 174 352 352 208 385 449 452 620 321 250, 278 25 406 691 362 401 113 110 795 596 121 607 346 445 677 809 198 266 302 B1 Fwd 642 193, 213 774, 775 774, 776 318 612 925 918 Subject Index by Article Ecliptic, defined obliquity of, its secular variation Elements of the orbits of three comets Elements of planetary orbits defined enumeration of determination of, from the arbitrary constant quantities of elliptical motion from the initial velocity and direction of projection from observation variations of, whatever be the eccentricities and inclinations when the eccentricities and inclinations are small differential equations of the periodic variations of secular variations of annual and sidereal variations of ditto, with regard to variable ecliptic integrals of ditto approximate values of, in functions of the time secular variations of, depending on the square of the disturbing forces Elliptical Orbits, general overview Ellipticity of sun, effects on the motions of the planets Epoch, defined longitude of, defined secular variation of equation of Equator, defined Equation of centre, defined expression of of Jupiter’s satellites Equations of condition Equinoctial points defined Equilibrium, general principles of of a particle of a particle on a surface of a system of bodies of a system invariably united of two bodies of a solid of fluids of homogeneous fluids of heterogeneous fluids of a fluid mass in rotation Ethereal medium, effects of, on solar system Falling bodies, theory of Fixed plane defined Fluids, small undulations of oscillations of, covering the earth 359 648 618 362 378 374 407 609 422 429 439 441 473 510 483, 498 480 580 B2 Fwd 592 362, 393 362 512 512 192 382 391 835 238 359 39 22, 54 48 116, 125 132 124 143 231 239 240 246 788 99 364 261 266 Mary Somerville 775 Subject Index by Article Force, exerted by matter analytical expression of direction and intensity of central a function of the distance of gravity, instantaneous transmission of of gravity, varies inversely as the square of the distance centrifugal moving living, or impetus of a system conservation of proportional to velocity Forces, resolution and composition of Gravitation general overview proportional to attracting mass at surface of sun and planets intensity of at the moon intensity of on earth, determined by the length of the seconds pendulum varies as the square of the sine of the latitude Gyration, centre and radius of Homogeneous spheroid, its compression 14 63 39 792 338 85 118 146 78 14 22 309 B2 Fwd 337 608 332 108 107 210 774 Impetus, definition of, true measure of labour Impetus of a revolving solid Inclination of an orbit defined Inclinations of planetary orbits of lunar orbit constant Invariable plane, defined, its properties in a revolving solid of solar system Isochronous curve 146 181 362 613 728 166 204, 210 525 109 Jupiter compression of Jupiter and Saturn, Theory of computation of the perturbations of great inequality of, analytical and numerical periodical variations in the elements of the orbits of same depending on the squares of the disturbing forces secular variations of, depending on the squares of the masses limits and periods of the secular variations of Jupiter’s satellites, Theory of relation among their mean motions and longitude 651 918 571 619 573, 628 572 578 580 633 798 801 776 Mechanism of the Heavens Subject Index by Article orbits of, nearly circular move nearly in the plane of the planet’s equator fixed planes of motion of nodes and apsides of, caused by the compression of primary development of the disturbing forces acting on perturbations in the longitudes and radii vectores of equations, whence are obtained secular variations in the form of the orbits of libration of perturbations of, in latitude equations, which give the secular variations in the positions of the orbits of effects of the precession and nutation of their primary on the motions of effects of the displacement of Jupiter’s orbit on the motions of numerical values of the perturbations of determination of the masses of eclipses of 808 803 803, 869 802 801 818 841 843 859 874 863 868 885 889 919 Kepler’s problem of finding the true anomaly of a planet Laws satellites obey 388 309, 323 324 Lagrange’s theorem of the variation of the elliptical elements Latitude defined of a planet perturbations of the planets in of Jupiter and Saturn in of the moon of Jupiter’s satellites Least action, principle of Lever Light, principle of least action, applied to the refraction of velocity of effects of the velocity of, on the solar system Longitude, defined mean, defined true, defined true, in functions of mean projected, in functions of true longitude, and vice versâ true, of moon true, of Jupiter’s satellites of the perihelion, node and epoch defined Longitudes of the perihelia, nodes and epochs Lunar perturbations Lunar theory equation of the tables of the sun 417 361 400 559 576, 577 766 878 78 130 80 951 792 360 392 393 392 398 757 821 362 614 B3 Fwd 665 644 Mary Somerville 777 Subject Index by Article Magnitude of the sun Mars Mass, definition of proportional to the product of the volume and the density of moon Masses of the planets Mean place of a planet, defined motion of a planet, defined motions of planets motions, ratio of those of Jupiter and Saturn distance of a planet, defined distances of planets Mercury transits of Meridian, defined Momentum, defined Moments of inertia, of a solid greatest and least, belong to the principle axes of rotation Moon, phases of circular motion of Moon, elliptical motion of effects of sun’s action on analytical investigation of the inequalities of co-ordinates of secular variations in the form of the orbit of the position of the orbit of the mean longitude of, in functions of her true longitude true longitude of, in functions of her mean longitude latitude of, in functions of her true longitude mean longitude parallax of, in functions of her true longitude mean longitude constant part of equatorial parallax of distance of, from the earth ratios among the secular variations of immense periods of secular variations of apparent diameter of acceleration of motion of perigee of nodes of effects of the variation in the eccentricity of the earth’s orbit on motions of variation of evection of annual equation of lesser inequalities of 778 Mechanism of the Heavens 350 649 120 122 744 597 381 380 610 571 384 611 635 636 329 115 176 189 666 667 673 676 687 691 720 727 736 757 739 766 741 768 742 744 751 753 746 748 749 750 754 760 759 761 763 Subject Index by Article inclination of orbit of, constant inequalities of, from the spheroidal form of the earth nutation of the orbit of, from the action of the terrestrial equator inequalities of, from the action of the planets effects of secular variation in the plane of the ecliptic on of an ethereal medium on the motions of of the resistance of light on the motions of of the successive transmission of the gravitating force on the motions Newtonian theory of Moon’s perigee and nodes not affected by the ether, nor by transmission of gravity Motion, defined uniform variable of a free particle of a particle on a surface of projectiles Motion of a system of bodies of centre of gravity of a system of bodies of centre of gravity of a solid of a system, in all possible relations between force and velocity of a solid rotatory of fluids in a conic section of a system of bodies, mutually attracting each other of centre of gravity of solar system elliptical, of planets general equations of finite equations of perturbed, general equations of of comets of sun in space of a planet and satellites, the same as if they were all united in their common centre of gravity Neptune, discovery of New planets Nodes of a planet’s orbit defined line of Normal Numerical values of the perturbations of Jupiter of the motions of Jupiter’s satellites of the motions of the moon Nutation of the earth’s axis 755, 786 770 778 780 786 788 793 794 797 793 18 60 69 81 96 144 151 174 168 169 176 248 317 345 352 359 365 384 347 404 366 353 352 B1 Fwd 650 362 362 47 619 885 735 193 Mary Somerville 779 Subject Index by Article Obliquity of ecliptic variation of limited Observation, elements of the planetary orbits determined by Orbits of planets and comets, conic sections position of, in space of Jupiter and Saturn, variations of determination of the motion of two, inclined at any angle Orbit, terrestrial, secular variations of Parallax, defined horizontal defined lunar solar, determined from the transit of Venus lunar inequalities Pendulum, simple oscillations of compound Penumbra Period of an inequality depends on its argument of great inequality of Jupiter and Saturn of secular variations of the orbits of Jupiter and Saturn Periodic time defined variations in the elements of the planetary orbits depend on configurations of the bodies general expressions of Periodicity of sines and cosines of circular arcs Perihelion defined Perturbations of planets, general overview Perturbations of planets, theory of determination of by Lagrange’s method depending on the squares of eccentricities and inclinations depending on the cubes of the same arbitrary constants of from the form of the sun action of the satellites Plane of greatest rotatory pressure (also called the Invariable Plane) invariable, always remains parallel to itself Planets mean distances of mean sidereal motions of longitudes of, at epoch masses of densities of periodic times of 780 Mechanism of the Heavens 603 648 648 596 309 397 633 511 646 326 327 768 639 743 103 109 222 932 566 571 633 319 529 412 439 215 316 B2 Fwd 410 546 533 559 563 539 592 594 204 525 635 611 609 888 606 507 610 Subject Index by Article Pluto, discovery of Precession of equinoxes Pressure of a particle moving on a surface Principle axis of a solid properties of Primitive impulse Problem of the three bodies equations of solution of approximate Projectiles Projection of lines and surfaces Quadratures, defined B1 Fwd 648 43 84 180 189 207 349 417 351 96 131 318 Radius of curvature defined its expression Radius vector defined finite value of in functions of mean anomaly longitude in a parabola Rotation of the earth Rotation of the moon Rotation of the planets Rotation of a solid nearly about a principle axis and translation independent of each other of a homogeneous fluid of the same when disturbed by foreign forces stable and unstable of the earth, the measure of time Rotatory pressure defined zero in equilibrio Saturn Satellites, observe Kepler’s laws of Jupiter, Saturn, Uranus and Neptune of Jupiter of Jupiter, theory of of Saturn of Uranus of Neptune not sensibly disturb their primaries with the exception of the moon Secular variations defined depend on configuration of orbit Mary Somerville 83 83 312 314 387 392 404 B1 Fwd B3 Fwd B4 Fwd 176 216 175 263 266 179, 180 20 129 132 652 324 B4 Fwd B4 Fwd 798 956 958 B4 Fwd 594 413 413 781 Subject Index by Article general expressions of of elements during the period of the perturbations depending on squares of disturbing forces in the earth’s orbit Sidereal revolutions of planets Semi-diameters of sun and planets Solar System, general overview of the sun, moon, planets and satellites Specific gravity Stability of solar system, with regard to mean motions and greater axes with regard to the forms of the orbits positions of the orbits whatever may be the powers of the disturbing forces Stars, fixed, their action on solar system Sun Tides Time, its measure convertible into degrees of the oscillations of a pendulum of falling through circular arcs Uranus 443 566 581 646 610 607 B1 Fwd 123 462 488 499 515 659 656 268, 280 20 213 107 111 653 958 satellites of Variation, secular, of the plane of the ecliptic of the arbitrary constant quantities determines the period and secular changes, both of translation and rotation Variations, method of Velocity, defined variable uniform angular in a conic section Virtual velocities defined real variations Venus transits of 786 Weight defined 120 Year, Julian 609 782 Mechanism of the Heavens 443 56 60 171 408 51 59 637 637 NAME INDEX Achilles, 38 Adams, John, xxiii, 62, 215, 218, 496, 503 Agassiz, Louis, 500 Agnesi, Maria, 736 Airy, George, xxiii, 57, 58-59, 759 d’Alembert, Jean, 110, 743, 766 Ampère, Andre, xx Arnett, Bill, 609 Apollonius, 736 Arago, Dominique, xx, xxiii, 38, 480, 496 Archimedes, 549 Aristarchus, 38, 510, 549 Aristotle, 223, 754, 769 Aristyllus, 38 Babbage, Charles, xix, xxiii, xxiv, 18, 741, 757 Bacon, Francis, 7, 37, 769 Bailly, Jean, 24, 38 Baily, Francis, 49, 58-59 Battani, [al-], 429 Becquerel, Antoine, xx Bellarmino, Cardinal, 42 Berkeley, George, 487, 497 Bernard, Claude, 769 Bernoulli, Jean, xxiv, 76, 78 Bessel, Friedrich, 38, 58, 479, 496, 497, 605 Biot, Jean, xx, xxiii, 96, 110 478, 495, 496 Black, John, 223 Bond, William, 604, 608 Born, Max, 769 Bouguer, Pierre, 47, 488, 497 Bouvard, Alexis, xx, 559, 570, 725, 751 Bowditch, Nathaniel, xxiii, 729, 732, 767-769 Bradley, James, 22, 38, 443, 568, 577-578, 588, 598, 722-724 Brahe, Tycho, 37, 39, 220, 223, 232, 495, 566, 567, 569 Brewster, David, xx, xxiii Brinkley, John, 58, 757 Brougham, Henry, iv, xxv, 729, 732, 737, 760 Bruno, Giordano, 769 Buckley, Arabella, 45, 207, 499, 603 Buffon, Georges-Louis, 560, 571 Buller, Charles, 732-735 Burckhardt, Johann, 557, 570, 577 Burg, M., 557, 559, 570, 577, 588 Caccini, Tommaso, 41 Caesar, Julius, 23 Cardano, Girolamo, 769 Carpenter, Dr., 50, 500 Casper, Barry, 769 Cassini, Giovanni, 488, 497, 604-605 Cavendish, Henry, 49 Challise, Mr., 759 Charles II, 37 Châtelet, Gabrielle-Émilie, 736 Chiron, 24, 38 Clairaut, Alexis, 32, 39, 560, 571, 743 Clarke, A R., 48 Claussen, Mr., 451 Cook, James, 14, 38 Copernicus, Nicolas, 219, 223, 549, 769 Croll, Mr., 53 Cuvier, Georges, xx Damoiseau, Théodore, 515, 549, 557, 561, 563, 564, 767 Dana, James, 500 Darwin, Charles, xx, 54, 500, 769 Dawes, Mr., 604 Delambre, Jean, 31, 39 366, 443, 559, 645, 714, 723-724, 740, 751, 768 Delaunay, Mr., 503 Descartes, René, 597, 602, 769 Diophantus, 736 Dixon, Jeremiah, 589 Dreyer, J., 769 Dzielska, Maria, 769 Einstein, Albert, 78, 215, 604 Encke, Johann, 450, 452, 597, 602, 750 Name Index Eratosthenes, 13, 38, 48 Euclid, 38 Eudoxus, 24, 38 Euler, Leonhard, xix, xxiv, 78, 89, 110, 148, 411, 597, 743-745, 758 Everest, George, 48 Faraday, Michael, xx, 175, 769 Farghani, [al-], 429 Fermat, Pierre de, 89, 109 Flamsteed, John, 411, 429 Fresne l, Augustin, 29, 38, 39, 597 Galilei, Galileo, 41, 100, 219, 221, 223, 611, 650, 723, 750, 769 Galilei, Giulia Ammannati, 41 Galilei, Maria Celeste, 41 Galilei, Vincenzo, 41 Galle, Johann, 62, 215, 218 Galloway, Thomas, 736-752 Gambart, Mr., 451 Gassendi, Pierre, 223 Gauss, Carl, 443, 451, 497 Gay-Lussac, Joseph, xx, 96, 110 George III, 39 Gray, Asa, 500 Gregory, Mr., 757 Hesiod, 477, 496 Hevelius, Johannes, 32, 39 Hildegard von Bingen, 769 Hind, J R., 218 Hipparchus, 19, 21, 38, 51-52, 412, 561, 599 Hirsch, Meier, 758 Homer, 477, 496 Hooke, Robert, 110, 221, 223, 597 Hopkins, Mr., 55-56 Huygens, Christiaan, 89, 110, 221, 597, 601 Hypatia of Alexandria, 736 Irving, Washington, xx Ivory, James, 45, 48, 758 Jacob, Captain, 604 Johnston, Ian, 41 Junis, Ibn, 25, 39, 559 Kant, Immanuel, 769 Kater, Henry, 25, 39 Kepler, Johannes, 2, 6, 14, 37, 208, 210, 216, 220, 223, 225-226, 230-232, 240, 245, 272, 348, 447-448, 493, 495-496, 502, 603, 671-672, 723, 725-726, 742, 769 Kuhn, Thomas, 769 Lacaille, Nicolas, 235, 240 Lacroix, Silvestre, xix, xxiv, 103, 110, 758 Hamilton, William, xx, 78, 759 Lagrange, Joseph, xix, 7, 37, 78, 204, 217, 273, Halley, Edmond, 32, 38, 39, 411, 450, 474, 285, 288, 308, 377, 411, 724, 741, 743, 559, 571, 748, 766 744-748, 751, 754, 757, 765-766 Hansen, Mr., 503 Lahire, Philippe de, 32, 39 Harding, Mr., 37, 484, 607 Lalande, Joseph, 568, 571 Harding, Sandra, 769 Lambert, Johann, 411, 428, 765 Hawking, Stephen, xxiv Landen, John, 756 Hayek, F., 769 Laplace, Pierre, xix, xxiii, 7, 10, 24, 27-28, 41, Heath, Thomas, 769 42-43, 45, 138, 204, 217, 219, 221, Hellins, Mr., 756 222, 240, 365, 377, 398, 411-412, 454, Henry, Joseph, xx 476, 488, 497, 499, 503, 558-559, 561, Henry, Madeleine, 769 564, 568, 578, 588, 597, 601, 603, 720, Herschel, Caroline, xx, 34, 39 724-725, 729-733, 735-737, 741-754, Herschel, John, xix, xxiii- xxiv, 34, 39, 52, 54, 762-767 398, 604, 608, 753-768 Lassell, William, 62, 604, 608-609 Herschel, William, xxiii, 32-34, 39, 441, 485, Legendre, Adrien-Marie, ix, 494, 497 486-488, 605, 608, 724, 726 Leibniz, Gottfried, xix, xxiii, 37, 39, 78, 769 784 Mechanism of the Heavens Name Index Leslie, John, xxiii, 20, 38, 56 Leverrier, Urbain, 62, 215, 217-218, 496 Lubbock, John, 365-366, 369, 597, 602, 759 Lyell, Charles, 53, 54 Lyon, Captain, 31 McKinley, Jane, xxv, 769 Mackintosh, James, 1, 37 Maclaurin, Colin, 284 Martineau, Harriet, xx Maskelyne, Nevil, 37, 366, 369, 443, 496, 557, 577, 588 Mason, Charles, 588, 589 Mathieu, Emile, xxiii Maupertuis, Pierre, 89 Mayer, Julius, 494 Mazotti, Mr., 597, 750 Maxwell, James, xx-xxiii, xxv, 55, 604, 605, 769 Milne-Edwards, William, xxi Mill, John Stuart, xxi Milton, John, 477, 498 Moulton, Forest, 469 Murray, John, 45 Plato, 769 Playfair, John, xxiii, 7, 37, 741, 757, 763 Poincaré, Henri, 769 Poinsot, Louis, xxiii Poisson, Siméon, xx, xxiii, 204, 217, 336, 365, 735, 744, 746 Pontécoulant, Philippe, 257, 284, 469, 735, 739, 741, 744-745, 747 Ptolemy, 6, 24, 37, 89, 216, 223, 411, 429, 502, 559, 563, 566, 769 Qurrah, Thabit ibn, 429 Robinson, Professor, 757 Roëmer, Mr., 722 Salt, Henry, 25, 38 Savart, Félix, 110 Sayre, Anne, 769 Scrope, George, 56 Segner, Jan, 148, 168 Shröeter, Mr., 480, 487, 603, 607 Sime, Ruth, 769 Snow, C P., 769 Somerville, Mary, xix- xxii, xxiii, xxiv, xxv, 38, 39, 45, 60, 110, 175, 207, 215, 217, 218, 221, 451-452, 499-500, 570, 603, 604, 729-753, 760-769 Somerville, Martha, xxiii, 769 Somerville, William, xxiii South, James, 34, 39 Spence, W., 757-758 Stein, Dorothy, 769 Struve, Friedrich, 17, 34, 38, 48, 485, 496, 605, 609 Napier, John, 169, 757 Nasmyth, Mr., 500 Noer, Richard, 769 Newton, Isaac, xix, xxiii- xxiv, 1-3, 7, 36, 38, 39, 41, 45, 62, 89, 104, 110, 207, 219, 221, 223, 231-232, 412, 489, 495, 499, 566, 571, 599, 601, 604, 729, 736-737, 742, 749-750, 753-756, 759, 762, 766, 769 Nightingale, Florence, xxi North, John, 469 Timocharis, 21, 38 Thomson, William, 55, 56 Olbers, Wilhelm, 37, 484, 497 Vince, Mr., 756, 758 Parry, William, 31, 39 Vinci, Leonardo da, 769 Patterson, Elizabeth, xxv, 175, 732, 736, 769 Peacock, George, xix, xxiii, xxiv Wallace, William, xxiii, xxv, 736 Perkins, Jacob, 36, 38 Wargesten, Mr., 235 Piazzi, Giuseppe, 37, 484, 497 Waring, Edward, 756 Plana, Giovanni, 429, 503 Wheatstone, Charles, xxi, Mary Somerville 785 Name Index Planck, Max, 604, 769 Whewell, William, xix, xxiv White, Michael, 769 Wollaston, William, 33, 39, 197 Wood, Dr., 735, 758 Woodhouse, Professor, 478, 757, 759 Wren, Christopher, 110 Young, Thomas, 20, 25, 29-30, 38, 56, 184, 597, 759 786 Mechanism of the Heavens ... account of the reciprocal action of matter, the stability of the system depends on the intensity of the primitive momentum of the planets, and the ratio of their masses to that of the sun: for the. .. the prolongation of one of the axes of the spheroid The plane of the equator is inclined to the plane of the ecliptic at an angle of about 23o 8′ , and the inclination of the lunar orbit on the. .. motions of the earth and Venus, by the same method as for the eclipses of the sun In fact the ratio of the distances of Venus and the sun from the earth at the time of the transit, are known from the