( 660 ) 



also only relative positions of the satellites inter si', were deternfiined. 

 From these three series all elennents were derived, and all have 

 been used in the tinal discussion, the values being taken unaltered 

 from the definitive publications already quoted. The only exception 

 is the position of the fundamental plane for 1902, the inclination 

 of which on the ecliptic is 2°8'38", instead of 2°11'38", as printed in 

 Cape XII.2 page 191 '). 



3. Photographic plates, taken at the Cape Observatory in 1891 

 and 1903, measured and reduced by me, and })ublished in Cape 

 XII. 3. The quantities pi and qi alone were derived for each epoch. 

 These have been taken unaltered from Cape XII. 3. 



4. Photographic plares, taken at the Cape in 1904, measured and 

 reduced by me. From these plates were derived pi and qi, which 

 are published in Cape XII. 3, and l^ , 4 , h > which are published in 

 Gron. Puhl. 17. The published results have been adopted unaltered. 



In these last three series also only coordinates of the satellites 

 relatively to each other were used. The planet was not measured 

 by me. 



5. Photographic plates, taken at the Cape in 1902, measured and 

 reduced by Cookson, and published in Cape XII.4. This series 

 requires a closer consideration. 



Mr. CooKSON has measured on the plates differences of RA and 

 deck of the four satellites and Jupiter. The pointing on the planet 

 is, according to his own statement, "not very accurate" (Cape XII.4, 

 p. 24). But, according to the author, high accuracy is not required, 

 since it is eliminated in the reductions. This elimination, however, 

 is very incomplete. 



It is effected as follows. From the measured differences of R. A. 

 Xi — ^1, a preliminary solution is made, the resulting values of the 

 unknowns are substituted in the equations of condition, and residuals 

 are formed, which may be called dc; . The mean of these residuals 

 for any one plate, say (\j\ , is then considered to be the correction 

 ffj;^, to be applied to j',,, i.e. the error in the pointing on the 

 planet with reversed sigu. This mean is therefore subtracted from 

 the observed co-ordinates x^ — .t'^, . Now this method only eliminates 

 the accidental part of the correction <lc,^ . The systematic part is 

 already in the first approximation included in the values of the 



1) Tlie inclination and node referred to the equator are correct as printed, in the 

 reduction to the ecliptic some mistake must have occurred. The consequence of this 

 is that the inclination a;,, of the fundamental plane on the orbit of Jupiter requires 

 a correction of — 0\0093, instead of -i-0°.0375, as would appear from the printed 

 data of Gape XU.2. 



