286 Prof. Encke on Olbers's Method of 



, nd z ' .. . d z' 



'"'-K'HT Z " = *' + T ^T 



x - x V -T&J-V -6W*)- — 



a limitation which is immediately indicated by the absence of 

 ?•' in the final formulae. 



It is, therefore, clear that the author uses as many terms of 

 the terrestrial orbit as are required in practice, and in this 

 point his solution may be regarded as sufficient. But with 

 regard to the orbit of the comet, he evidently supposes that the 

 comet describes a straight line with uniform velocity. This sup- 

 position, however, which Boscovich had previously adopted *, 

 leads in the rarest cases only to an useful approximation. It 

 involves two false hypotheses, which in no case can agree with 

 the truth, the rectilinear motion, and uniform velocity, and on 

 that very account cannot stand by any means a comparison 

 with the supposition which is the groundwork of Olbers's me- 

 thod. 



The circumstance which gave rise to this paper naturally 

 led me to these remarks. They appear to be justified and even 

 to be called for by the warm and so well merited praise with 

 which the work of M. de Pontecoulant has been received like- 

 wise in Germany, and which might therefore easily cause the 

 merit of Olbers, which has remained unknown to the celebrated 

 author, to be put into the shade by his expressions on the sub- 

 ject. Now, indeed, that the greatest accuracy of calculation, 

 combined with the most convenient form, has been introduced 

 into almost all parts of astronomy, principally by Gauss and 

 Bessel, Olbers's method does not stand any more so preemi- 

 nent among the solutions of astronomical problems. But at 

 the time when it was first published those qualities were seldom 

 or never found united, and it has stood the severest test of 

 its excellence in the entire revolution of practical astronomy in 

 this century, without experiencing any sensible effect from it. 



* Olbers's Abhandlung, sect. 12 and sect. 16. 



