t 



■ ■ 



Boicditch on the permanency of tM solav system, 711 



left hand side of this equation U small, therefore the sum, or the con- 

 stant quantity on the right hand side must also he small, consequent, 

 ly each term of the equation must always be small; whence it has 

 been inferred, that the eccentricities of all the planets must always 

 he small, or in other words, that the orbits will never vary much 

 from a circular form, so that these orbits may be considered as 

 perfectly stable, in respect to the eccentricities, which will oscil- 

 late abourfhe mean values, from which they will vary but very 

 little. 



But the deduction thus made from the preceding equalioa 

 does not appear to be warranted to the extent usually given to it. 

 If it had been confined to the three largest planets, Jupiter, Sat- 

 urn, and Uranus, it would have been correct ; but that equation 

 may be satisfied supposing the orbits of the planets Mercury, 

 Venus, the Earth and Mars to be extremely elliptical, parabolic, 

 or even hyperpolic. To prove this, Ihc values of the terms 

 M e'^Val w! e'^ Vo', &c. corresponding to the planets were computed 

 roughly, as in the following table, column 0, using the values ol 

 m, m', m^% &c. a, a% &c. e, e', &c. given in the second edition of La 

 Place's 'Exposition of the system of the world. In col. 6, the val- 

 lies of the same terms are computed, supposing the orbits of Mer« 

 cury, Venus, the Earth and Mars to be parabolic, or that e = e* 

 Q^ —X e^^ = 1^ and tbea by reducing the eccentricity of Jupiter 



less than one sixth part, the sum of the terms of the equation be- 

 comes the same as in col. 5. 



.^ 



* 



