(414 ) 



If we consider the quotient log M{g) -. log g as an approximate 

 (but always too small) value of the number A{g) of prime numbers 

 less than g, to Kronecker's result 



2 



^ id) = 7- — -2" log 2 sin jiQn 

 log gn<q 



we may add 



:g\ 2 

 A\ - ] = :S log 2 cos jtQu ■ 



^ 2 



Astronomy. — "Researches on the orbit of the periodic comet Holmes 

 and on the perturbations of its elliptic motion. IV." By Dr. 

 H. J. ZwiERS. (Communicated by Prof. H. G. van de Sande 

 Bakhuyzen). 



At the meeting of the Academy on the 27 January of 1906, a com- 

 munication was made of my preliminary researches on the pertur- 

 bations of the comet Holmes, during the period of its invisibility 

 from January 1900 till January 1906, and also of an ephemeris of 

 its apparent places from the :i^'of May till the Sl^t of December 1906. 

 This time again this computation led to its rediscovery. Owing to 

 its large distance from the earth and the resulting faintness of its 

 light, there seemed to be only a small chance for its observation 

 during the first months. This proved to be true, as not before the 

 30^^ of August of this year, the Leiden observatory received a 

 telegram, that the comet was found by prof. Max Wolf at the 

 observatory Koenigstuhl near Heidelberg, on a photograph taken in 

 the night of the 28^'^ of August of a part of the heavens where 

 according to the ephemeris it ought to be found. The roughly 

 measured place 



« = 61° 51' d= + 42°28' 



for 13''52'"1 local time, appeared to be in sufficient agreement with 

 the calculation. 



Afterwards the place of the comet has been twice photographically 

 determined : on the 25*'' of September and on the 10^'^ of October, 

 and each time prof. Wolf was so kind, to communicate immediately 

 to me the places as they had been obtained, after carefully measur- 

 ing the plates. Although Wolf declared in a note to the observed 



