Referee report by G. B. Airy on 'Of Such Ellipsoids Consisting of Homogeneous Matter as are Capable of Having the Resultant of the Attraction of the Mass upon a Particle in the Surface, and a Centrifugal Force Caused by Revolving about One of the Axes, Made Perpendicular to the Surface' by J. Ivory
between the three axes of an <s>spheroid <\s> ellipsoid to insure this condition, that if from any point of the surface a normal be drawn and produced till it meet the largest principal section, and if from the same point there be drawn and similarly produced a line representing the direction of the whole attraction of the ellipsoid, the line in the principal section joining the points at which these lines intersect the principal section may be parallel to the <s>line<\s> perpendicular from the <s>same<\s> point in question upon the smallest axis <s>which<\s> of the <s>spheroid<\s> ellipsoid.” In the second Section, the mathematical condition is worked out. The equation obtained is the same as that which M. Liouville has obtained by forming the differential equation for the external <s>d<\s> surface depending on the attraction and centrifugal force, comparing this with the differential equation of the surface of the ellipsoid, and eliminating the centrifugal force from the two equations obtained by this comparison. I should prefer Mr. Ivory’s as a statement of the fundamental geometrical condition (instead of first introducing the centrifugal force and afterwards eliminating it), except for the reason that <s>one<\s> another of the necessary conditions, namely the proportionality of the line in the principal section to the perpendicular upon the smallest axis, though it appears as a result of the investigation, cannot be made a condition for the problem. The third section merely contains the substitution of the expressions <s>for<\s>, in definite integrals, for the principal attractions of the ellipsoid. The fourth section is employed on the case of spheroids of revolution.
Referee report by G. B. Airy on 'Of Such Ellipsoids Consisting of Homogeneous Matter as are Capable of Having the Resultant of the Attraction of the Mass upon a Particle in the Surface, and a Centrifugal Force Caused by Revolving about One of the Axes, Made Perpendicular to the Surface' by J. Ivory, 1838. From The Royal Society, RR/1/120