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 ou! of Damoiseau’s Tables, the foundation 
of which is the theory of Laplace contained in Mécanique Céleste, 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: 
a 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. a may be expressed in parts of the Satellite’s radius or in 
some other convenient unit. 
Tf, and T, the times for the same phenomenon observed by means of tele- 
scopes of aperture A, and A, but as far as possible in similar circum- 
stances in other respects, 
