PREFACE. XV 



and soon afterwards the observations made by that distinguished astronomer 

 PIAZZI from the above date to the eleventh of February were published. No 

 where in the annals of astronomy do we meet with so great an opportunity, 

 and a greater one could hardly be imagined, for showing most strikingly, the 

 value of this problem, than in this crisis and urgent necessity, when all hope 

 of discovering in the heavens this planetary atom, among innumerable small 

 stars after the lapse of nearly a year, rested solely upon a sufficiently ap 

 proximate knowledge of its orbit to be based upon these very few observa 

 tions. Could I ever have found a more seasonable opportunity to test the 

 practical value of my conceptions, than now in employing them for the de 

 termination of the orbit of the planet Ceres, which during these forty-one 

 days had described a geocentric arc of only three degrees, and after the 

 lapse of a year must be looked for in a region of the heavens very remote 

 from that in which it was last seen ? This first application of the method 

 was made in the month of October, 1801, and the first clear night, when 

 the planet was sought for* as directed by the numbers deduced from it, re 

 stored the fugitive to observation. Three other new planets, subsequently 

 discovered, furnished new opportunities for examining and verifying the effi 

 ciency and generality of the method. 



Several astronomers wished me to publish the methods employed in these 

 calculations immediately after the second discovery of Ceres ; but many 

 things other occupations, the desire of treating the subject more fully at 

 some subsequent period, and, especially, the hope that a further prosecution 

 of this investigation would raise various parts of the solution to a greater 



By de ZACH, December 7, 1801. 



2 



