Mechanism of the HeavensJohn Murray, Albemarle-Street., 1831 - 621 pages |
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Page 31
... values in the end of article 69 , that equation becomes dr . dr + dy . d'y + dz.d2z dt2 = Xdr + Ydy + Zdã + R , { dx ... preceding equation ; and when the forces are functions of the distance , the integral is and 2f ( x , y , z ) + c ...
... values in the end of article 69 , that equation becomes dr . dr + dy . d'y + dz.d2z dt2 = Xdr + Ydy + Zdã + R , { dx ... preceding equation ; and when the forces are functions of the distance , the integral is and 2f ( x , y , z ) + c ...
Page 62
... preceding values of dr , dy , the result is ds = ds . you δε ᏧᎦ ds ds - • row = dw y - бу δι бу ds Ss - x δπ . бу or , multiplying by the momentum Fm , Fmds = Fm { y 3/2 бл x In the same manner with regard to the body m 62 [ Book I ...
... preceding values of dr , dy , the result is ds = ds . you δε ᏧᎦ ds ds - • row = dw y - бу δι бу ds Ss - x δπ . бу or , multiplying by the momentum Fm , Fmds = Fm { y 3/2 бл x In the same manner with regard to the body m 62 [ Book I ...
Page 67
... preceding values of ♬ 2 + ÿ2 + ~ are identical , or that or Σmx2 Emm ' ( x - x ) 2 ( Σmx ) 9 ( Σm ) = - Στη ( 2m ) 2 ( Emx ) Em . Emx2 - Emm ' ( x ' = Were there are only two planets , then - x ) * . Σmm + m ' , Σmx = mx + m'x ' , Emm ...
... preceding values of ♬ 2 + ÿ2 + ~ are identical , or that or Σmx2 Emm ' ( x - x ) 2 ( Σmx ) 9 ( Σm ) = - Στη ( 2m ) 2 ( Emx ) Em . Emx2 - Emm ' ( x ' = Were there are only two planets , then - x ) * . Σmm + m ' , Σmx = mx + m'x ' , Emm ...
Page 78
... values of and hence , if may be ; 90 ° be put for p , the line or ' will take the place of oy ' , the angle ror ' will become roy ' , and the preceding equation will give cos xoy ' cos 0 sin y cos - cos y sin p . Cos roz ' is found from ...
... values of and hence , if may be ; 90 ° be put for p , the line or ' will take the place of oy ' , the angle ror ' will become roy ' , and the preceding equation will give cos xoy ' cos 0 sin y cos - cos y sin p . Cos roz ' is found from ...
Page 88
... values of x ' , y ' , z ' , in functions of x , y , z , determined from the equations in article 163 be substituted in the preceding expressions , then if to abridge , S.x2dm = 12 Sy dmn2 Sz ៰ dm = s2 S.xydmf Sxzdmg there will result ...
... values of x ' , y ' , z ' , in functions of x , y , z , determined from the equations in article 163 be substituted in the preceding expressions , then if to abridge , S.x2dm = 12 Sy dmn2 Sz ៰ dm = s2 S.xydmf Sxzdmg there will result ...
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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 position preceding equation preceding values radius vector ratio regard rotation satellites Saturn secular inequalities secular variations sidereal sine spheroid square substituted surface system of bodies tangent terrestrial theory tion true longitude Uranus velocity whence 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.