126 Prof. Encke on Olbers's Method of 



by which we get 



1 -|- 2 sec v ^ 



But as sin y = r\ . p, the factor ^ — £, or the ratio j — ^ 



may be united with the table for the solution of Lambert's 

 equation. In the column of that table headed 



, , I + 2 secy 

 log v = log - r - 



its value for >j = to >j = 0*32 has been given. To continue 

 it further appeared quite unnecessary, in consideration of the 

 possible use which might be made of it. For the smallest va- 

 lue which in general may be admitted, viz. for r + r' = 1, 

 »j ss 0'32 corresponds already to an interval of 9 or 10 days. 



Taking into account only the first five decimals log v in- 

 creases very nearly as the square of >j, or for the same r -f r'» 

 nearly as the square of the time. If, on the contrary, we as- 

 sume a certain interval which for every single sector will rarely 

 be greater than seven days, we obtain for different (r + rO the 

 following table : 



Consequently log v likewise increases very nearly in the inverse 

 ratio of the cube of the radius vector. The terms of the se- 

 cond order prevail, therefore, on the whole very much. For 

 these terms the circumstance above noticed for the orbit of 

 the earth, viz. that for equal intervals they are entirely anni- 



