 | Henry Brougham Baron Brougham and Vaux, Edward John Routh - 1855 - 540 páginas
...as the square of the distance. Now if n=|, T : t :: R» : r*, or T2 : P :: R3 : r3 ; in other words the squares of the periodic times are as the cubes of the distances from the centre, which is the law discovered by Kepler from observation actually to prevail... | |
 | Augustus William Smith - 1855 - 340 páginas
...periodic time. 4°. If T2 oc r3, by substitution in (81), , r 1 , / GC — oc — ; */ ^ T2' or, when the squares of the periodic times are as the cubes of the distances from the center, the centrifugal force will be inversely as the square of the distance. 5°.... | |
 | Bartholomew Price - 1856 - 662 páginas
...accordance with the preceding conditions. In ellipses described about a centre of force in the focus the squares of the periodic times are as the cubes of the mean distances ; in this case however that law cannot hold, because the orbit described by the exterior... | |
 | 1856 - 496 páginas
...its motion around the sun are proportional to the time employed in the motion ; and, the other, that the squares of the periodic times are as the cubes of the distances. Order in relation to time is so manifest every23 where, that it is hardly necessary to specify... | |
 | James McCosh, George DICKIE (Botanist.) - 1856 - 570 páginas
...that line in its motion round the sun are proportional to the times employed in the motion ; and that the squares of the periodic times are as the cubes of the distances. The first of these is a law of forms, the other two are laws of numbers. The discoveries... | |
 | 1856 - 824 páginas
...ellipses ; that they describe round the sun in one focus areas proportional to the times ; and that the squares of the periodic times are as the cubes of the mean distances. Newton shows that these bodies are retained in their paths by a force varying inversely... | |
 | 1856 - 538 páginas
...variation to the conic section which must be described. He knows Kepler's wonderful discovery, that the squares of the periodic times are as the cubes of the distances of the planets i'rom the sun, and the mathematical deduction from this that the centripetal... | |
 | William Whewell - 1860 - 604 páginas
...reconcile Kepler's first two laws, of equal elliptical areas in equal times, with his third law, that the squares of the periodic times are as the cubes of the mean distances". Bernoulli, with his circular vortices, could accommodate the velocities at different... | |
 | Augustus William Smith - 1863 - 340 páginas
...the square of the periodic time. 4°. If T1 oc r', by substitution in (81), , r 1 /«P*?! or, when the squares of the periodic times are as the cubes of the distances from the center, the centrifugal force will be inversely as the square of the distance. 5°.... | |
 | Samuel Newth - 1864 - 392 páginas
...therefore, p= Hence, if several bodies move in different ellipses, about the same force in the focus, the squares of the periodic times are as the cubes of the major axes. 188. The values of p and p being the same for the hyperbola as for the ellipse, it follows... | |
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... the squares of the periodic times are as the cubes of the distances from the common centre, the centripetal forces will be inversely as the squares of the distances. 
