282 Prof. Encke on Olbers's Method of 



d a 1 d 9 a! 



If for determining -j- and -j-g only three observations 



are used, we have only two equations according to our nota- 

 tion : 



a - a +T d7 + * T 7F + * T rf< a+ * 4T rf* 4 



from which they are to be found. Putting 

 a) — a = A a 



we have 



rf7=— 77V' * TT "d?-™ TT < t " t >7F • • • • 



d* 2 " tt't" * {T * } di? ™ KT TT +r ) dt* 



In these expressions the differential quotients are indepen- 

 dent of the greatness or smallness of the intervals of time, and 

 are to be considered as quantities of the order 0, or as quan- 

 tities of the same order with p, r 9 &c, which are to be deter- 

 mined by them. This will be the more the case as experi- 

 ence shows that their numerical value is really so considerable, 

 that even in that respect they cannot belong to any other 

 order. 



In the ephemerides of comets when calculated for every 

 fourth day, the fourth differences are still very sensible. But 

 as in this case the value of 1" in the fourth differential corre- 

 sponds in general to a value 



-j-g- and --7-j- will in most cases be greater than unity. 



df 



servations only are used, quantities of the first order are neg- 

 lected whenever the intervals of time are unequal. If these 

 latter are equal, quantities of the second order are, at any rate, 



neglected in the expressions for ——■ and , a . Theoretic 



Hence it follows that in the value of ■traN when three ob- 



