( 644 ) 



experienced l\y most observers to properly identify the comet in the 

 midst of numerous faint nebulae near the apparent orbit, made me 

 fear that such a rough ephemeris of the apparent places for 1906 

 might prove insuflicient for rediscovering it and observing it. 



In the autumn of 1905, I therefore resolved to derive the pertur- 

 bations which the comet would suffer on its path between the perihelion 

 passages of 1899 and 1906. The original plan of also computing the 

 perturbations arising from the action of Saturnus had to be given 

 up through lack of time. And so Jupiter remained the only disturbing 

 planet. The method I chose was that of the variation of the elliptic 

 constants ; I also chose an interval of 80 days, because former 

 investigations had shown that the accuracy, attainable by it was 

 more than sufficient for my purpose. In former researches we have 

 always adopted the rule that for each new epoch the small varia- 

 tions which the elements had undergone during the course of the 

 last interval were to be applied to them. The computations required 

 for this implied, however, an amount of labour not to be nnderrated, 

 and as in this case the computations could have only a preliminarj- 

 character I could leave aside these small corrections by which in this 

 case only small quantities of the second order were neglected. Thus 

 the above mentioned system VII was used as a basis for the com- 

 putation of perturbations for the entire revolution. The places of 

 the disturbing planet are taken from the Nautical Almanac; the 

 longitudes only were reduced to the equinox of 1900.0 by applying 

 the precession. The neglection of the small corrections for nutation 

 and for the variation in the obliquity of the ecliptic cannot have 

 any perceptible influence on (he perturbations caused by the planet. 



Instead of the elaborate tables of perturbations 1 shall for shortness 



communicate only the summed series, namely the quantities ^^f for 



the mean daily motion and the quantities {/' for the other elements. 



By working out each table the reader will be able to form a judgment 



on the accuracy reached. The initial constants printed in big figures, 



which in the construction of the tables were derived from the first 



dE 

 values of — , {E representing one of the 6 elements) and from their 



dt 



differences up to f^^' are chosen so that the integi'als disappear for 

 1899 September 9 as lower limit. Up to 1900 February 16 the 

 derivatives could be borrowed from the tables which I have commu- 

 nicated in my Deuxième Mémoire ps. 26 — 32 ; with regai-d, however 



to the interval chosen now I had to multiply — by 4, and the 



dt 



other derivatives of the elements by 2. 



