Two ellipsoids in which the principal sections lie in the same planes, and have the same foci, are called confocal.
The ellipsoid has important applications in dynamics, as a means of interpreting algebraic formulae for physical quantities; examples are the ellipsoids of strain and of gyration, and Poinsot's momental ellipsoid.
For example, all ellipsoids referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.
The ellipsoids (41) and (43) are reciprocal polars with respect to a sphere having O as centre.
During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and Laplace, had not carried the theory of the attraction of ellipsoids beyond the point which the geometry of Maclaurin had reached.
Legendre shows that Maclaurin's theorem with respect to confocal ellipsoids is true for any position of the external point when the ellipsoids are solids of revolution.
Obviously if the stars had been assumed to be ellipsoids they would have been found to overlap, as was the case for RR Centauri.
To these we may add Miss Emma Marwedel's wooden ellipsoids and hemispheres, already mentioned, which are satisfactory in size, and add the delights of color.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "ellipsoids" in a variety of sentences. We hope that you will now be able to make sentences using this word.
