PREFACE. 



obtained before the computation of the elliptic elements was commenced. 

 Notwithstanding this, it seems somewhat strange that the general problem, 



To determine the orbit of a heavenly body, iviihmd, any hypothetical assumption, 

 from observations not embracing a great period of time, and not allowing a selection 

 ti.ith a view to the application of special methods, was almost wholly neglected up 

 to the beginning of the present century; or, at least, not treated by any one 

 in a manner worthy of its importance ; since it assuredly commended itself 

 to mathematicians by its difficulty and elegance, even if its great utility in 

 practice were not apparent. An opinion had universally prevailed that a 

 complete determination from observations embracing a short interval of time 

 was impossible, an ill-founded opinion, for it is now clearly shown that 

 the orbit of a heavenly body may be determined quite nearly from good 

 observations embracing only a few days ; and this without any hypothetical 

 assumption. 



Some ideas occurred to me in the month of September of the year 1801, 

 engaged at the time on a very different subject, which seemed to point to 

 the solution of the great problem of which I have spoken. Under such cir 

 cumstances we not unfrequently, for fear of being too much led away by 

 an attractive investigation, suffer the associations of ideas, which, more atten 

 tively considered, might have proved most fruitful in results, to be lost from 

 neglect. And the same fate might have befallen these conceptions, had they 

 not happily occurred at the most propitious moment for their preservation 

 and encouragement that could have been selected. For just about this time 

 the report of the new planet, discovered on the first day of January of that 

 year with the telescope at Palermo, was the subject of universal conversation; 



