| Description | Seven engraved figures illustrating the following problems and theorems posed by Clairut in his paper on calculating the shapes of the planets, using calculus and expanding on the assumptions and conclusions of Isaac Newton on this subject:
Fig 1: Problem. To find the attraction which a homogeneous spheroid differing but very little from a sphere, exerts upon a corpuscle in the axis of revolution.
Fig 2: Problem. Supposing the spheroid not to be of homogeneous matter but composed of an infinite number of elliptical strata the attraction is required which this Spheroid exerts upon a corpuscle placed at the pole.
Fig 3: Theorem. A corpuscle being placed in any point of the surface of the foregoing spheroid will undergo the same attraction from this spheroid, as if it were placed at the pole of a second spheroid revolving about the axis N O, the
second axis being the radius of a circle equal in superficies to the elipsis FG suposing this second spheroid NGOF to have strata of the same densities as the first spheroid.
Fig 4: Problem. It is required to find the attraction which this circle exerts upon a corpuscle at N.
Fig 5: Problem. To find the Attraction which an elliptical spheroid exerts upon a corpuscle placed without its Surface.
Figs 6 and 7: Considering the effect of gravity placed on the spheroid
Relates to the paper 'Inquiry concerning the figure of such planets as revolve about an Axis supposing the Density continually to vary, from the Center towards the Surface'' by Alexis Claude Clairaut, translated by John Colson
Subject: Astronomy / Physics |