XXVI GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 



some doubt whether it would be safe to neglect it, but finally it was decided 

 to put it in the great bag of accidental errors, the most important of which 

 is, perhaps, the difference in the keenness of sight for the different observers. 

 It is true that the difference of absorption may have an effect of systematic 

 character, because the Planet's altitude in the high latitudes of the Fram 

 was of course on the average smaller than in Europe and Australia; but as 

 this effect will be of contrary sign for disappearance and reappearance, it 

 might be expected to make itself manifest and thus give the means for elimi- 

 nation from the whole mass of observations. 



The problem to be solved is firstly to find, by pairs of observations of 

 the same phenomenon, made with telescopes of different aperture, the breadth 

 of the invisible segment corresponding to a standard aperture and an arbitra- 

 rily chosen distance; then to apply the values found for disappearance (D) 

 and reappearance (R) of the different Satellites to all the continental observa- 

 tions taken during the period of polar observations, in order to deduce such 

 corrections to the predicted times that they will correspond to the telescope of 

 the Fram. A convenient form for the calculations has been found by the 

 following considerations. 



As the connection between the variation of the illuminated portion of a 

 Satellite, crossing the surface of the shadow, and the time, depends on the 

 position of the chord described by the Satellite's centre during the eclipse, 

 certain quantities must be taken out of Damoiseau's Tables, the foundation 

 of which is the theory of Laplace contained in Mfaanique Celeste, Livr. VIII. 

 For the quantities taken from this theory the notation of Laplace has been 

 retained as far as convenient. 



The signification of the letters employed below is : 



x the breadth of the invisible segment, as seen with a telescope of the 

 standard aperture A, when Jupiter is at the standard distance D from 

 the Earth, x may be expressed in parts of the Satellite's radius or in 

 some other convenient unit. 



T l and T^ the times for the same phenomenon observed by means of tele- 

 scopes of aperture A l and A 2 but as far as possible in similar circum- 

 stances in other respects. 



