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eclipse. This duration depends not only on lliose elements, but as 

 well on the form of the shadow-eone, i.e. on the geometrical com- 

 pression of the planet. This latter not being known with siiiKicient 

 accuracy, it is impossible to determine the latitudes from observations 

 of eclipses. The elements of the tirst gj'oup must therefore be derived 

 exclusively from heliometric or photographic extra-eclipse-observations 

 of the satellites. 



B. For the determination of the elements of group B, however, 

 the eclipses are very valuable. One eclipse-observation, which is a 

 determination of time, provides a much more accui-ate determination 

 of the longitude of the satellite than one extra-eclipse-observation. On 

 the other hand the latter can be repeated as often as the weather 

 and the available time of the observer permit, while eclipses only 

 occur in a limited number. Anotlier adNantage of eclipse-obser- 

 vations is that their accuracy is independent of the distance of 

 Jupiter from the earth, while the accuracy of extra-eclipse-observa- 

 tions is inversely proportional to that distance. Extra-eclipse-obser- 

 vations are thus generally combined in series extending over a few 

 months on both sides of the epoch of opposition. It must not be 

 forgotten, however, that away from the opposition the time during 

 w^hich Jupiter is above the horizon, and therefore the number of 

 observable eclipses, diminishes rapidly. 



B^or the tirst satellite, where eclipses are numerous, and microme- 

 trical observations least accurate, the advantage is vei-y probably on 

 the side of the eclipse-observations ; for the fourth, of which eclipses 

 are rare and extra-eclipse-observations are most accurate,') this ratio 

 is reversed. So long as nothing is known about the results derived 

 from the series of photometric eclipse-observations made at the 

 observatory of Harvai-d College in the years 1878 to 1903, it is not 

 possible to form a detinite judgment regarding the relative value of 

 the two kinds of observations. Anyhovv the attempt is justitied to 

 derive also the elements of group B exclusively from extra-eclipse- 

 observations. 



C. The four mean distances represent only one unknown quantity, 

 since the determination of their ratios from the mean motions (also 

 taking into consideration the uncertainty of the pertui'bations which 

 must be applied) is very much moi'e accurate than the direct deter- 



1) My meaning is, of course, that the delerminalion of the jovicentric place 

 of the satellite from extra-eclipse-observalions is most accurate for IV. This is due 

 only to the large mean ilislance, not to the observation itself. This latter, i.e. the 

 determination of the relative geocentric place, seems to be slightly more accurate 

 for U and III than for 1 and IV. 



