Mathematical Tracts: Part 1. On Laplace's Coefficients, the Figure of the Earth, the Motion of a Rigid Body about Its Center of Gravity, and Precession and Nutation, Parte 1J. & J.J. Deighton, 1840 - 86 páginas |
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Mathematical Tracts: Part 1. on Laplace's Coefficients, the Figure ..., Parte 1 Matthew O'Brien No hay ninguna vista previa disponible - 2016 |
Términos y frases comunes
a₁ angle angular velocity assume axes center of gravity centrifugal force co-ordinates coincidence constant cos² denote determine diverging series dR dR dt dt dwi dt dx dy dz dy dt ea² Earth Earth's original fluidity ellipticity equations become evident force of gravity ƒª hence integral signs Laplace's coefficients Laplace's equation law of density limits Moon's motion multiplied nearly spherical neglecting the squares NUTATION observation particle polar axis pole Q₁ Q₂ Q₂h Q₂h² rational and integral respectively result retrograde motion rigid body rotation round its center series of Laplace's shew sin qa small quantities strata stratum substituting Sun's suppose u₁ u₂ unity values w₁ Y₁ Z₁ Z₂ zero αμ µ² µ³ μι Σδη Φε Φι аф ᏧᎾ
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Página iii - MATHEMATICAL TRACTS. On La Place's Coefficients; the Figure of the Earth ; the Motion of a Rigid Body about its Centre of Gravity ; Precession and Nutation. 8vo. 4*.
Página 3 - The most important of these results are,— The expression for the length of a meridian arc corresponding to a given difference of latitude, and the law of variation of the force of gravity at different points of the earth's surface.
Página 47 - ... which is itself a very small quantity. Now this very peculiar result thus capable of varied and extensive observation, and which agrees with it in a very remarkable manner, is arrived at on the hypothesis of the earth's original fluidity, from which we must conclude that the hypothesis is most...
Página 70 - ... a line drawn from the center of the earth to the sun represents practically the same direction as a line from the airplane to the sun.
Página 77 - This condition demands that the direction of the axis of the shadow shall be near the great circle joining the pole of the earth and the pole of the moon's orbit.
Página 47 - ... for the ellipticity of the earth, satisfy all these equations to a remarkable degree of accuracy, allowing for certain small errors which may easily be accounted for, and which, even considering them in the most unfavourable point of view, are very much smaller than 3 gg, which is itself a very small quantity.
Página 84 - At the equator 0 = $v ; and if we put G for gravity at the equator, m for the ratio of the centrifugal force to gravity at the equator, we get of a = mG, and...
Página 3 - Hence it is the duty of all thoughtful men to under.stand aright the laws of health, and the object of the following pages is to give an account of these laws.
Página 56 - ... shewn that if the form of the surface and the law of the variation of gravity be given independently, and if we suppose the earth to consist approximately of spherical strata of equal density, without which it seems impossible to account for the observed regularity of gravity at the surface, then the attraction on the moon follows as a necessary consequence, independently of any theory but that of universal gravitation. < Tract on the Figure of the...