Ball — On Laplace^ s Perturbations of Jupiter^ s Satellites. 567 



There is one difference between this expression and that arrived 

 at by Laplace's analysis. In Laplace's form we have the coefficient 



{hi - kn'f - iV^- 



In this form we have 



2nr 



{hi - hi J - N"' 



Now as N^ n the difference is inappreciable, but it is curious to 

 observe the source whence this discrepancy has arisen. It is due to 

 the retention of some terms of the second order, while others have 

 been discarded. If all be discarded save only where N occurs in the 

 denominator of certain terms in Zr^ then the two expressions become 

 identical. 



