( 422 ) 



Yet it is evident that the accuracy of these elements is not equal to 

 the accuracy of those I could derive for previous returns of the comet. 

 In the first place the observations include only a period of 43 days, in 

 which the heliocentric motion of the comet with its large perihelion 

 distance was not even 12°. Secondly three observations with their 

 inevitable errors are in general only sufficient to obtain a mere 

 approximate idea of the orbit. We must admire the ability and 

 accuracy of the Heidelberg astronomers, who, from measurements on a 

 short focal photographic plate taken of a still wholly invisible nebula, 

 could deduce tlie position of the comet with an accuracy that could 

 be compared to that of micrometer measurements of objects several 

 hundred times brighter. Still we must bear in mind that the rejection 

 of only one of the 4 reference stars on the plate of the 28^^^ of August, 

 had an influence of 006 in « and 1"6 in declination, or of 2"39 

 in arc of a great circle. 



As a test to my calculations, I derived the 3 places finally by 

 direct computation from the obtained elements. 



Heliocentric aequatorial co-ordinates : 



X — [9.993 7648.63] sin {v + 77°37'28"36) 

 y — [9.876 2140.59] dn {v — 20 58 46.82) 

 z z= [9.832 7020.56] sm {v — 1 46 46.76) 



The following table contains the computed apparent places of the 

 comet and the differences Obs. — Comp. 



TABLE VII. 



The agreement between these differences found directly, and the 

 quantities obtained by substitution in the equations of condition forms 

 a sufficient control on the whole computation. 



The elements (i, n and tp. 



The elements from which the ephemeris for 1 906 has been derived 

 are those given in "Système VII" p. 78 of my Deuxième Mémoire, 

 reduced to 1906 by applying the perturbations, arising from the 

 action of Jupiter. The mean error of the obtained value for yc is so 



