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VII. — On the Theory of the Perturbations of the Playlets. By James Ivory, A.M. 
F.R.S. Instit. Reg. Sc. Paris. Corresp. et Reg. Sc. Gottin. Corresp. 
Read January 19, 1832. 
The perturbations of the planets is the subject of reiterated researches by all 
the great geometers who have raised up Physical Astronomy to its present 
elevation. They have been successful in determining the variations which the 
elements of the orbit of a disturbed planet undergo ; and in expressing these 
variations analytically, in the manner best adapted for computation. But the 
inquirer who turns his attention to this branch of study will find that it is 
made to depend upon a theory in mechanics, which is one of considerable 
analytical intricacy, known by the name of the Variation of the Arbitrary 
Constants. Considerations similar to those employed in this theory were 
found necessary in Physical Astronomy from its origin ; but the genius of 
Lagrange imagined and completed the analytical processes of general appli- 
cation. In a dynamical problem which is capable of an exact solution, such 
as a planet revolving by the central attraction of the sun, the formulas con- 
structed by Lagrange enable us to ascertain the alterations that will be in- 
duced on the original motions of the body, if we suppose it urged by new 
and very small forces, such as the irregular attractions of the other bodies of 
the planetary system. General views of this nature are very valuable, and 
contribute greatly to the advancement of science. But their application is 
sometimes attended with inconvenience. In particular cases, the general 
structure of the formulas may require a long train of calculation, in order 
to extricate the values of the quantities sought. It may be necessary for at- 
taining this end to pass through many differential equations, and to submit to 
much subordinate calculation. The remedy for this inconvenience seems to 
lie in separating the general principles from the analytical processes by which 
they are carried into effect. In some important problems, a great advantage, 
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