/ 



. 



JBowditch on the permanency of the solar sptem 



Planets 



I'lic sun's 



Mean. J^ist 



.«?^^ 







2035810 

 S83137 

 S29630 



1846083 

 1067,09 



3359,40 



e, e^, &.C. 



Ternis of Uie Equation ^ Xtnas of the equation 



altered. 



s/ 



0.387100 0.205513 



0.723335 0.006885 



1. 0.01G814 



1.523693 0.093088 



5 £02778 0.048077 



9.538785 0.056223 



1^504: 119.183475 0.04658; 



1 



0.00000 00050 



1 



9 



88 



2 58000 



2 76000 



95000 



0.00000 01190 



16000 



30340 



10190 



2 00428 



2 76000 

 95000 



Constant quantity = 0.U0UO6 29148 |-M)0006 29148 



We cannot therefore conclude from the preceding equation^ 

 independent of other considerations of analogy, ihsiiiiiQ orhits of 

 all the planets will never vary from a circular form. 



A similar defect exists in the demonstration of the smallness 

 of the inclinations of the orbits of the planets, which has been in- 

 ferred from the equation 



"N 



constant 



<?• + m'. v 



given in § 61, Book I of thq ^' Mecanique Celeste,'' in which f,/ 



f 



&c. represent the inclinations of 



fixed pi 



* 



we may prove that some of the values of <p, V, &c 

 Tery great without affecting that equation sensibly, 



ay 



become 



the 



the values of e, e', &c. in the preceding equation 

 ccentricities. It may be observed that some of tl 



the fourth power of the eccentricities and inc 

 the two equations abovementioned, exceed 

 the second power which are retained, as is 



spection of the table : which is an addition 



terms of 

 elected in 



of the terms of 



d 



fr 



the in 



reason why those 



equations should be restricted to the three greater pi 

 maaner mentioned in this paper. 



the 



\. 



