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

                                It contains nothing which has not been known many years:
and might as well have been omitted.
The fifth section contains the discussion of the equations as 
applied to the general case. A new substitution is made 
for the constant upon which the proportion of the three axes 
depends and which gives facilities for the examination of 
particular points. First it is shewn that there is an infinite 
number of forms for the ellipsoid (each requiring a 
peculiar velocity of rotation). Secondly, the limiting proportion 
of the axes is found; this occurs when the equatoreal axes 
are equal, each being = polar axis x 1.715. Thirdly it is 
shewn that if one equatoreal axis be smaller than this quantity, the 
other will be greater: and that when one is indefinitely near 
to equality with the polar axis, the other will be indefinitely 
great. Fourthly it is shewn, by an investigation conducted 
with great skill, that to any velocity of rotation there 
corresponds but one proportion of the axes and <u>vice versa<\u>:
that for the limiting proportion above-mentioned there is a certain 
velocity, and that as the inequality of the equatoreal axes 
increases, the velocity of rotation must be diminished,
till in the case of one axis infinitely long the velocity is 
0. With this, Mr. Ivory’s investigation closes. The whole 
of this section is curious and valuable.
From the statement above it appears that the paper 
is not to be considered as an original memoir so much