asheinin/The_Mathematical_Principles_of_Natural_Philosophy_1846

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OF
THE SYSTEM OF THE WORLD.
* * *
That the matter of the heavens is fluid, 511
The principle of circular motion in free spaces, 512
The effects of centripetal forces, 512
The certainty of the argument, 514
What follows from the supposed diurnal motion of the stars, 514
The incongruous consequences of this supposition, 514
That there is a centripetal force really directed to the centre of every planet, 515
Centripetal forces decrease in duplicate proportion of distances from the centre of every planet, 516
That the superior planets are revolved about the sun, and by radii drawn to the sun describe areas proportional to the times, 517
That the force which governs the superior planets is directed not to the earth, but to the sun, 518
That the circum-solar force throughout all the regions of the planets decreaseth in the duplicate proportion of the distances from the sun, 519
That the circum-terrestrial force decreases in the duplicate proportion of the distances from the earth proved in the hypothesis of the earth s being at rest, 519
The same proved in the hypothesis of the earth's motion, 520
The decrement of the forces in the duplicate proportion of the distances from the earth and planets, proved from the eccentricity of the planets, and the very slow motion of their apses, 520
The quantity of the forces tending towards the several planets : the circum-solar very great, 521
The circum-terrestrial force very small, 521
The apparent diameters of the planets, 521
The correction of the apparent diameters, 522
Why the density is greater in some of the planets and less in others; but the forces in all are as their quantities of matter, 524
Another analogy between the forces and bodies, proved in the celestial bodies, 525
Proved in terrestrial bodies, 525
The affinity of those analogies, 526
And coincidence, 526
That the forces of small bodies are insensible, 527
Which, notwithstanding, there are forces tending towards all terrestrial bodies proportional to their quantities of matter, 528
Proved that the same forces tend towards the celestial bodies, 528
That from the surfaces of the planets, reckoning outward, their forces decrease in the duplicate, but, reckoning inward, in the simple proportion of the distances from their centres, 529
The quantities of the forces and of the motions arising in the several cases, 529
That all the planets revolve about the sun, 529
That the common centre of gravity of all the planets is quiescent. That the sun is agitated with a very slow motion. This motion defined, 531
That the planets, nevertheless, are revolved in ellipses having their foci in the sun; and by radii drawn to the sun describe areas proportional to the times, 531
Of the dimensions of the orbits, and of the motions of their aphelions and nodes, 532
All the motions of the moon that have hitherto been observed by astronomers derived from the foregoing principles, 532
As also some other unequable motions that hitherto have not been observed, 533
And the distance of the moon from the earth to any given time, 533
The motions of the satellites of Jupiter and Saturn derived from the motions of our moon, 534
That the planets, in respect of the fixed stars, are revolved by equable motions about their proper axes. And that (perhaps) those motions are the most fit for the equation of time, 534
The moon likewise is revolved by a diurnal motion about its axis, and its libration thence arises, 535
That the sea ought twice to flow, and twice to ebb, every day; that the highest water must fall out in the third hour after the appulse of the luminaries to the meridian of the place, 535
The precession of the equinoxes, and the libratory motion of the axes of the earth and planet, 535
and that at the third hour after the appulse of the moon to the meridian of the place. But that out of the syzygies and quadratures those greatest and least tides deviate a little from that third hour towards the third hour after the appulse of the sun to the meridian, 536
That the tides are greatest when the luminaries are in their perigees, 536
That the tides are greatest about the equinoxes, 536
That out of the equator the tides are greater and less alternately, 537
That, by the conservation of the impressed motion, the difference of the tides is diminished; and that hence it may happen that the greatest menstrual tide will be the third after the syzygy, 538
That the motions of the sea may be retarded by impediments in its channels, 538
That from the impediments of channels and shores various phænomena do arise, as that the sea may flow but once every day, 539
That the times of the tides within the channels of rivers are more unequal than in the ocean, 540
That the tides are greater in greater and deeper seas; greater on the shores of continents than at islands in the middle of the sea; and yet greater in shallow bays that open with wide inlets to the sea, 540
The force of the sun to disturb the motions of the moon, computed from the foregoing principles, 542
The force of the sun to move the sea computed, 543
The height of the tide under the equator arising from the force of the sun computed, 544
The height of the tides under the parallels arising from the sun s force computed, 545
The proportion of the tides under the equator, in the syzygies and quadratures, arising from the joint forces of both sun and moon, 545
The force of the moon to excite tides, and the height of the water thence arising, computed, 545
That those forces of the sun and moon are scarcely sensible by any other effect beside the tides which they raise in the sea, 546
That the body of the moon is about six times more dense than the body of the sun, 547
That the moon is more dense than the earth in a ratio of about three to two, 547
Of the distance of the fixed stars, 547
That the comets, as often as they become visible to us, are nearer than Jupiter, proved from their parallax in longitude, 548
The same proved from their parallax in latitude. 549
The same proved otherwise by the parallax, 550
From the light of the comets heads it is proved that they descend to the orbit of Saturn, 550
And also below the orb of Jupiter, and sometimes below the orb of the earth, 551
The same proved from the extraordinary splendor of their tails when they are near the sun, 551
The same proved from the light of their heads, as being greater, cæteris paribus, when they come near to the sun, 553
The same confirmed by the great number of comets seen in the region of the sun, 555
This also confirmed by the greater magnitude and splendor of the tails after the conjunction of the heads with the sun than before, 555
That the tails arise from the atmospheres of the comets, 556
That the air and vapour in the celestial spaces is of an immense rarity; and that a small quantity of vapour may be sufficient to explain all the phænomena of the tails of comets, 558
After what manner the tails of comets may arise from the atmospheres of their heads, 559
That the tails do indeed arise from those atmospheres, proved from several of their phænomena, 559
That comets do sometimes descend below the orbit of Mercury, proved from their tails, 560
That the comets move in conic sections, having one focus in the centre of the sun, and by radii drawn to that centre do describe areas proportional to the times, 561
That those conic sections are near to parabolas, proved from the velocity of the comets, 561
In what space of time comets describing parabolic trajectories pass through the sphere of the orbis magnus, 562
At what time comets enter into and pass out of the sphere of the orbis magnus, 563
With what velocity the comets of 1680 passed through the sphere of the orbis magnus, 564
That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, 564
With what velocity comets are carried, shewed by more examples, 565
The investigation of the trajectory of comets proposed, 566
Lemmas premised to the solution of the problem, 567
The problem resolved, 570
* * *
INDEX TO THE PRINCIPIA.
* * *
Æquinoxes, their præcession—the cause of that motion shewn, 413
“ the quantity of that motion computed from the causes, 458
Air, its density at any height, collected by Prop. XXII, Book II, and its density at the height of one semi-diameter of the earth, shewn, 489
“ its elastic force, what cause it may be attributed to, 302
“ its gravity compared with that of water, 489
“ its resistance, collected by experiments of pendulums, 315
“ the same more accurately by experiments of falling bodies, and a theory, 355
Angles of contact not all of the same kind, but some infinitely less than others, 101
Apsides, their motion shewn, 172, 173
Areas which revolving bodies, by radii drawn to the centre of force describe, compared with the times of description, 103, 105, 106,
195, 200

OF

THE SYSTEM OF THE WORLD.

* * *

That the matter of the heavens is fluid, 511

The principle of circular motion in free spaces, 512

The effects of centripetal forces, 512

The certainty of the argument, 514

What follows from the supposed diurnal motion of the stars, 514

The incongruous consequences of this supposition, 514

That there is a centripetal force really directed to the centre of every planet, 515

Centripetal forces decrease in duplicate proportion of distances from the centre of every planet, 516

That the superior planets are revolved about the sun, and by radii drawn to the sun describe areas proportional to the times, 517

That the force which governs the superior planets is directed not to the earth, but to the sun, 518

That the circum-solar force throughout all the regions of the planets decreaseth in the duplicate proportion of the distances from the sun, 519

That the circum-terrestrial force decreases in the duplicate proportion of the distances from the earth proved in the hypothesis of the earth s being at rest, 519

The same proved in the hypothesis of the earth's motion, 520

The decrement of the forces in the duplicate proportion of the distances from the earth and planets, proved from the eccentricity of the planets, and the very slow motion of their apses, 520

The quantity of the forces tending towards the several planets : the circum-solar very great, 521

The circum-terrestrial force very small, 521

The apparent diameters of the planets, 521

The correction of the apparent diameters, 522

Why the density is greater in some of the planets and less in others; but the forces in all are as their quantities of matter, 524

Another analogy between the forces and bodies, proved in the celestial bodies, 525

Proved in terrestrial bodies, 525

The affinity of those analogies, 526

And coincidence, 526

That the forces of small bodies are insensible, 527

Which, notwithstanding, there are forces tending towards all terrestrial bodies proportional to their quantities of matter, 528

Proved that the same forces tend towards the celestial bodies, 528

That from the surfaces of the planets, reckoning outward, their forces decrease in the duplicate, but, reckoning inward, in the simple proportion of the distances from their centres, 529

The quantities of the forces and of the motions arising in the several cases, 529

That all the planets revolve about the sun, 529

That the common centre of gravity of all the planets is quiescent. That the sun is agitated with a very slow motion. This motion defined, 531

That the planets, nevertheless, are revolved in ellipses having their foci in the sun; and by radii drawn to the sun describe areas proportional to the times, 531

Of the dimensions of the orbits, and of the motions of their aphelions and nodes, 532

All the motions of the moon that have hitherto been observed by astronomers derived from the foregoing principles, 532

As also some other unequable motions that hitherto have not been observed, 533

And the distance of the moon from the earth to any given time, 533

The motions of the satellites of Jupiter and Saturn derived from the motions of our moon, 534

That the planets, in respect of the fixed stars, are revolved by equable motions about their proper axes. And that (perhaps) those motions are the most fit for the equation of time, 534

The moon likewise is revolved by a diurnal motion about its axis, and its libration thence arises, 535

That the sea ought twice to flow, and twice to ebb, every day; that the highest water must fall out in the third hour after the appulse of the luminaries to the meridian of the place, 535

The precession of the equinoxes, and the libratory motion of the axes of the earth and planet, 535

and that at the third hour after the appulse of the moon to the meridian of the place. But that out of the syzygies and quadratures those greatest and least tides deviate a little from that third hour towards the third hour after the appulse of the sun to the meridian, 536

That the tides are greatest when the luminaries are in their perigees, 536

That the tides are greatest about the equinoxes, 536

That out of the equator the tides are greater and less alternately, 537

That, by the conservation of the impressed motion, the difference of the tides is diminished; and that hence it may happen that the greatest menstrual tide will be the third after the syzygy, 538

That the motions of the sea may be retarded by impediments in its channels, 538

That from the impediments of channels and shores various phænomena do arise, as that the sea may flow but once every day, 539

That the times of the tides within the channels of rivers are more unequal than in the ocean, 540

That the tides are greater in greater and deeper seas; greater on the shores of continents than at islands in the middle of the sea; and yet greater in shallow bays that open with wide inlets to the sea, 540

The force of the sun to disturb the motions of the moon, computed from the foregoing principles, 542

The force of the sun to move the sea computed, 543

The height of the tide under the equator arising from the force of the sun computed, 544

The height of the tides under the parallels arising from the sun s force computed, 545

The proportion of the tides under the equator, in the syzygies and quadratures, arising from the joint forces of both sun and moon, 545

The force of the moon to excite tides, and the height of the water thence arising, computed, 545

That those forces of the sun and moon are scarcely sensible by any other effect beside the tides which they raise in the sea, 546

That the body of the moon is about six times more dense than the body of the sun, 547

That the moon is more dense than the earth in a ratio of about three to two, 547

Of the distance of the fixed stars, 547

That the comets, as often as they become visible to us, are nearer than Jupiter, proved from their parallax in longitude, 548

The same proved from their parallax in latitude. 549

The same proved otherwise by the parallax, 550

From the light of the comets heads it is proved that they descend to the orbit of Saturn, 550

And also below the orb of Jupiter, and sometimes below the orb of the earth, 551

The same proved from the extraordinary splendor of their tails when they are near the sun, 551

The same proved from the light of their heads, as being greater, cæteris paribus, when they come near to the sun, 553

The same confirmed by the great number of comets seen in the region of the sun, 555

This also confirmed by the greater magnitude and splendor of the tails after the conjunction of the heads with the sun than before, 555

That the tails arise from the atmospheres of the comets, 556

That the air and vapour in the celestial spaces is of an immense rarity; and that a small quantity of vapour may be sufficient to explain all the phænomena of the tails of comets, 558

After what manner the tails of comets may arise from the atmospheres of their heads, 559

That the tails do indeed arise from those atmospheres, proved from several of their phænomena, 559

That comets do sometimes descend below the orbit of Mercury, proved from their tails, 560

That the comets move in conic sections, having one focus in the centre of the sun, and by radii drawn to that centre do describe areas proportional to the times, 561

That those conic sections are near to parabolas, proved from the velocity of the comets, 561

In what space of time comets describing parabolic trajectories pass through the sphere of the orbis magnus, 562

At what time comets enter into and pass out of the sphere of the orbis magnus, 563

With what velocity the comets of 1680 passed through the sphere of the orbis magnus, 564

That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, 564

With what velocity comets are carried, shewed by more examples, 565

The investigation of the trajectory of comets proposed, 566

Lemmas premised to the solution of the problem, 567

The problem resolved, 570

* * *

INDEX TO THE PRINCIPIA.

* * *

Æquinoxes, their præcession—the cause of that motion shewn, 413

“ the quantity of that motion computed from the causes, 458

Air, its density at any height, collected by Prop. XXII, Book II, and its density at the height of one semi-diameter of the earth, shewn, 489

“ its elastic force, what cause it may be attributed to, 302

“ its gravity compared with that of water, 489

“ its resistance, collected by experiments of pendulums, 315

“ the same more accurately by experiments of falling bodies, and a theory, 355

Angles of contact not all of the same kind, but some infinitely less than others, 101

Apsides, their motion shewn, 172, 173

Areas which revolving bodies, by radii drawn to the centre of force describe, compared with the times of description, 103, 105, 106,

195, 200