fifty roots of an equation of which Airy had been able to calculate only two. Other memoirs followed: "On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids," in which he shows for the first time how to take account of the equations of motion, of differences of pressure in different directions due to the viscosity of the fluid; and the resulting equations constitute the complete foundation of the hydrokinetics of the present day. "On the theory of oscillatory waves," in which he investigates the steep waves of the deep sea where the elevations are narrower than the hollows and the height of an elevation exceeds the depth of a hollow. "On the formation of the central spot of Newton's rings beyond the critical angle," his earliest investigation in the wave-theory of light. "On the dynamical theory of diffraction," containing the mathematical theory of the propagation of motion in a homogeneous elastic solid; also an experimental investigation from which he concluded that the plane of polarization is the plane perpendicular to the direction of vibration in plane-polarized light, agreeing with Fresnel's position as opposed to that of MacCullagh.
To the Cambridge and Dublin Mathematical Journal he contributed the following papers: "On the motion of a piston and of the air in a cylinder"; "On a formula for determining the optical constants of doubly refracting crystals"; "On attractions and on Ciairault's theorem." A series of notes on hydrodynamics was prepared supplementary to a report on that subject which he presented to the British Association in 1846. Shorter papers he communicated to the Philosophical Magazine, two of which are the aberration of light and the constitution of the luminiferous ether viewed with reference to that phenomenon. On the theory of the emission of light, the explanation of aberration is simple; in these papers he attempts an explanation which shall be in accordance with the undulatory theory without making the startling supposition that the earth in its motion round the sun experiences no resistance from the ether.
In 1849 the Lucasian Chair of Mathematics at Cambridge fell vacant—the chair filled by Sir Isaac Newton 180 years
