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

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                                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.
                            
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Manuscript details

Author
James Ivory
Reference
RR/1/120
Series
RR
Date
1838
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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

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