## Mechanism of the HeavensJ. Murray, 1831 - 621 pages |

### From inside the book

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Page 78

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**substituted**in the value of cos roz ' sin 0 sin y . + cos y cos & } + cos y sin } + z ' sin 0 sin y . y and z are found to be x , it becomes x = x ' { cos 0 sin o sin y ' { cos 0 cos sin ¥ - In the same manner , the values of y = x ... Page 79

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**substitution**be made , and the angles y and so assumed that sin @ cos c ' √ c2 + c22 + c1 / 2 " с - - c ' √ c2 + c22 + c'l2 ' √ c2 + c22 + c ' ' sin @ sin = it follows that cos 0 = whence Em x'dy ' — y'dr ' = c2 + c12 + c / 12 , ( 27 ) ... Page 80

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**substitution**be made in it becomes ( xď2y — ydx \ dt Ση [ yd2x } TE.md'y ' - ÿEΣmd2x ' dt2 = Σm . ( Yx ' - Σm ( xY - yX ) + Em , x'd3y ' - y'd2x ' dt Xy ' ) + a.ΣmY - y . EmX . But in consequence of the preceding equations it is reduced ... Page 87

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**substituted**, they will be the same sums , when projected on the new co - ordinate planes x'oy ' , x'oz ' , y'oz ' . The angles 0 , 4 , and 4 , introduced by this change are arbi- trary , so that the position of the new axes ox ' , oy ... Page 88

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**substituted**in the preceding expressions , then if to abridge , S.xdm = 1a Sy'dm = n2 Sz3dm = s2 S.xydmf Sxzdm = g there will result Syzdmh , cos p.S.x'z'dm - sin p.S.y'z'dm = ( 2n2 ) sin o sin cos y + fsin e ( cos y - + cos ( g cos h ...### Other editions - View all

### Common terms and phrases

A₁ action angle ascending node attraction axes axis B₁ becomes c'mv centre of gravity centrifugal force co-ordinates coefficients comets computed conic sections consequently cosines curve density depending determined differential direction disturbing forces dR dR dt dt earth eccentricity ecliptic elements epoch equal equilibrium equinoxes expression fixed plane fluid functions give hence inclination indefinitely small integral Jupiter latitude mass mean anomaly mean distance mean longitude mean motion moon moon's move nearly observation omitted orbit of Jupiter oscillations parallax particle perigee perihelion periodic inequalities perturbations planets preceding equation preceding values radius vector ratio regard rotation satellites Saturn secular inequalities secular variations sidereal sine spheroid square substituted surface system of bodies terrestrial theory tion true longitude Uranus velocity whence zero

### Popular passages

Page xviii - ... that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles.

Page vii - His works, but trace, with precision, the operation of His laws, use the globe he inhabits as a base wherewith to measure the magnitude and distance of the sun and planets, and make the diameter of the earth's orbit the first step of a scale by which he may ascend to the starry firmament. Such pursuits, while they ennoble the mind, at the same time inculcate humility, by showing that there is a barrier which no energy, mental or physical, can ever enable us to pass: that, however profoundly we may...

Page xv - That day, as other solemn days, they spent In song and dance about the sacred hill ; Mystical dance, which yonder starry sphere Of planets, and of fix'd, in all her wheels Resembles nearest, mazes intricate, Eccentric, intervolved, yet regular Then most, when most irregular they seem ; And in their motions harmony divine So smooths her charming tones, that God's own ear Listens delighted.

Page xlix - An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London.

Page lxiv - Jupiter ; it then gradually diminished in splendor, and having exhibited all the variety of tints that indicate the changes of combustion, vanished sixteen months after its discovery, without altering its position. It is impossible to imagine anything more tremendous than a conflagration that could be visible at such a distance.

Page xiv - But, in the midst of all these vicissitudes, the length of the major axes and the mean motions of the planets remain permanently independent of secular changes. They are so connected by Kepler's law, of the squares of the periodic times being proportional to the cubes of the mean distances of the planets from the sun, that one cannot vary without affecting the other.

Page lxix - If the attraction of the sun for the огпtre of the earth, and of the hemisphere diametrically opposite to him, were diminished by a difficulty in penetrating the interposed matter, the tides would be more obviously affected. Its attraction is the same also, whatever the substances of the celestial bodies may be; for if the action of...

Page vi - is to inspire the love of truth, of wisdom, of beauty — especially of goodness, the highest beauty — and of that supreme and eternal Mind, which contains all truth and wisdom, all beauty and goodness. By the love or delightful contemplation and pursuit of these transcendent aims, for their own sake only, the mind of man is raised from low and perishable objects, and prepared for those high destinies which are appointed for all those who are capable of them.

Page xii - ... depends upon the velocity with which they were first propelled in space. Had that velocity been such as to make the planets move in orbits of unstable equilibrium, their mutual attractions might have changed them into parabolas, or even hyperbolas, so that the earth and planets might, ages ago, have been sweeping far from our sun through the abyss of space.

Page xxxvi - ... the waters back to their sources ; and thus again by removing matter to a greater distance from the centre, destroy the velocity generated by its previous approach ; so that the descent of the rivers does not affect the earth's rotation.