The ellipsoid appears in the mathematical investigation of physical properties of media in which the particular property varies in three directions within the media; such properties are the elasticity, giving rise to the strain ellipsoid, thermal expansion, ellipsoid of expansion, thermal conduction, refractive index (see CRYSTALLOGRAPHY), &c. In mechanics, the ellipsoid of gyration or inertia is such that the perpendicular from the centre to a tangent plane is equal to the radius of gyration of the given body about the perpendicular as axis; the "momental ellipsoid," also termed the "inverse ellipsoid of inertia" or Poinsot's ellipsoid, has the perpendicular inversely proportional to the radius of gyration; the "equimomental ellipsoid" is such that its moments of inertia about all axes are the same as those of a given body. (See MECHANICS.) ELLIPTICITY, in astronomy, deviation from a circular or spherical form; applied to the elliptic orbits of heavenly bodies, or the spheroidal form of such bodies. (See also COMPRESSION.) ELLIS (originally SHARPE), ALEXANDER JOHN (1814-1890), English philologist, mathematician, musician and writer on phonetics, was born at Hoxton on the 14th of June 1814. He was educated at Shrewsbury, Eton, and Trinity College, Cambridge, and took his degree in high mathematical honours. He was connected with many learned societies as member or president, and was governor of University College, London. He was the first in England to reduce the study of phonetics to a science. His most important work, to which the greater part of his life was devoted, is _On Early English Pronunciation, with special reference to Shakespeare and Chaucer_ (1869-1889), in five parts, which he intended to supplement by a sixth, containing an abstract of the whole, an account of the views and criticisms of other inquirers in the same field, and a complete index, but ill-health prevented him from carrying out his intention. He had long been associated with Isaac Pitman in his attempts to reform English spelling, and published _A Plea for Phonotypy and Phonography_ (1845) and _A Plea for Phonetic Spelling_ (1848); and contributed the articles on "Phonetics" and "Speech-sounds" to the 9th edition of the _Ency. Brit._ He translated (with considerable additions) Helmholtz's _Sensations of Tone as a physiological Basis for the Theory of Music_ (2nd ed., 1885); and was the author of several smaller works on music, chiefly in connexion with his favourite subject phonetics. He died in London on the 28th of October 1890.