Mechanism of the HeavensJ. Murray, 1831 - 621 pages |
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Page 25
... integral of the three equations of the motion of a particle being of the second order , will contain six arbitrary constant quantities , which are the data of the problem , and are determined in each case either by observation , or by ...
... integral of the three equations of the motion of a particle being of the second order , will contain six arbitrary constant quantities , which are the data of the problem , and are determined in each case either by observation , or by ...
Page 26
... integral of this equation can only be obtained when the first member is a complete differential , which it will be if all the forces acting on the particle , in whatever directions , be functions of its distance from their origin , S ...
... integral of this equation can only be obtained when the first member is a complete differential , which it will be if all the forces acting on the particle , in whatever directions , be functions of its distance from their origin , S ...
Page 28
... integral suds is a minimum ; and if it be constrained to move on a given surface , it will still move in the curve in which fuds is a minimum among all those that can be traced on the surface between the given points . To demonstrate ...
... integral suds is a minimum ; and if it be constrained to move on a given surface , it will still move in the curve in which fuds is a minimum among all those that can be traced on the surface between the given points . To demonstrate ...
Page 29
... integral is fuds = dx dx + dy sy + dz dz . dt dt dt If the given points A and B be moveable in space , the last member of this equation will determine their motion ; but if they be fixed points , the last member which is the variation ...
... integral is fuds = dx dx + dy sy + dz dz . dt dt dt If the given points A and B be moveable in space , the last member of this equation will determine their motion ; but if they be fixed points , the last member which is the variation ...
Page 31
... integral is and 2f ( x , y , z ) + c = vo , - A - v = 2f ( x , y , z ) – 2f ( a , b , c ) , as before . Hence , if the particle be urged by accelerating forces , the velocity is independent of the curve or surface on which the par ...
... integral is and 2f ( x , y , z ) + c = vo , - A - v = 2f ( x , y , z ) – 2f ( a , b , c ) , as before . Hence , if the particle be urged by accelerating forces , the velocity is independent of the curve or surface on which the par ...
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Common terms and phrases
A₁ action angle ascending node attraction axes axis 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 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 perturbations planets preceding equation radius vector ratio regard retrograde motion 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 δα δε δυ
Popular passages
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 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 xlix - An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London.
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 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.