( 720 ) 



ment^). In estimating the probable errors I have taken into account 

 as accurately as I could the imperfections as well of the theory on 

 which the left-hand members of the equations of condition depend 

 as of the observations from which the rigiit-hand members are derived. 

 It has been my aim to estimate true probable eri-ors, i. e. the 

 masses (C) are those which with our present knowledge of the 

 system I consider the most probable, and I consider it equally pro- 

 bable that the deviation of the values (6') from the truth is smaller 

 than the stated p. e., as that it exceeds this quantity. 



The above contains all that can be derived from modern extra- 

 eclipse observations. The resulting \alues of the inclinations and nodes, 

 and of the mass of the system, i.e. the groups A and C of unknowns, 

 must be considered as final, so far as the observational data at 

 present available go. The results for the other unknowns (those of 

 group B) cannot be accepted as final until they are confirmed by the 

 reduction of the photometric eclipse observations of the Harvard 

 observatory. With regard to the inclinations and nodes, I have already 

 pointed out in Cape XII. 3 (page 121) that a new determijiation 

 about the year 1920 is desirable. For the determination of ???., it will 

 be necessary, as was pointed out by me in my dissertation, p. 82 

 and 85, to supplement the modern observations by a determination 

 of //j and k^ about 1790 from a re-redaction of old eclipses. Of these 

 an amply sufficient number exists. Between the years 1772 and 

 1799 I have found in the literature of the epoch records of 63 

 eclipses of which the immersion and emersion have been observed 

 by the same person, and about one third of these have been observed 

 by more than one observer. 



In order to derive entirely satisfactO)"y results it will also be neces- 

 sary to revise Souillart's analytical theory, as pointed out by me 

 in Gron. Publ. 17, page 118. 



The masses and elements derived in the above, though not to be 

 considered as final, still doubtlessly are much nearer to the truth 

 than those used in Souillart's theory. It therefore seemed desirable 

 to introduce them into the expressions for the latitudes, longitudes 

 and radii-vectores as given by that theory. To take account of the 

 uncertainties of the masses I give the coefficients as functions of the 

 small quantities q and A,-, which are defined by 



1) "The probable error arising from the uncertainty of such judgments must be 

 included among the possible unavoidab'e sources of error." Newcomb, Astronomical 

 Papers of the American Ephemeris, Vol. 5, Part 4, page 398. 



[Note added in the English translation]. 



