## Mechanism of the Heavens |

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Page 5

The velocity of a body moving uniformly , is the straight line or space over which it moves in a given interval of time ;

The velocity of a body moving uniformly , is the straight line or space over which it moves in a given interval of time ;

**hence**if the velocity v be the space moved over in one second or unit of time , vt is the space moved over in t ... Page 8

For , since the forces are proportional to the spaces , if a be the space described in one second , at will be the space described in t seconds ;

For , since the forces are proportional to the spaces , if a be the space described in one second , at will be the space described in t seconds ;

**hence**if at be equal to the space mA , and bt equal to mA mB the space mB , we have t = ... Page 11

Now the equation of the diagonal gives dr ( r - a ) 8r ( y b ) Sr dy dz

Now the equation of the diagonal gives dr ( r - a ) 8r ( y b ) Sr dy dz

**hence**the component forces of F are or F F ; dy Again , if F ' be another force acting on the particle at m in another direction r ' , its component forces parallel ... Page 20

E D B in ma ;

E D B in ma ;

**hence**at the end of that time the particle would be found in B , having described the fig . 17 . diagonal mB . Were the particle now left to itself , it would move uniformly to C in the next equal interval A of time ... Page 21

**Hence**when m is free , by article 68 , dir dz = Xdt ; d . dy = Ydt ; d . = Zdt ; ( 5 ) dt dl dt for the forces X , Y , Z , being perpendicular to each other , each one is independent of the action of the other two , and may be regarded ...### What people are saying - Write a review

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action angle appears arising assumed attraction axes axis becomes bodies cause centre of gravity changes co-ordinates coefficients computed consequently constant contain curve density depending described determined differential direction distance disturbing earth eccentricity ecliptic effect elements epoch equal equation expression fluid force functions give given greater hence inclination increase inequalities integral Jupiter Jupiter's known latitude less longitude mass matter mean motion moon move nearly nodes observation obtained omitted orbit parallax particle periodic planets position preceding pressure principal produce quantities radius ratio regard represented result revolve rotation satellites Saturn secular sine space square substituted supposed surface theory third tion true values variation varies vector velocity whence whole zero

### 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.