XXVIII GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 
M—K=hsin H+ isin I+ ete. 
where the rate of change of the arguments H, J etc. is so little different from 
the rate of change of » that they may be considered as equal during an 
eclipse. Consequently 
ds awe 
dy i+e 
oS [h sin (H+ 90°) + 4 sin (I+ 90°) + ete]. 
(h cos H+ icos I+ etc.) = 
Or the arguments which have already served for finding s will, when 
they are all augmented by 90°, give cos y. 
In the figure A is the centre of the elliptic shadow, AD = a, C the centre 
of the Satellite, CB the line of its relative motion, AB= 5 oA Clay) 
The Satellite is supposed to be in such a position that a certain fraction o of 
its radius r is outside the shadow. The connection between the difference of 
observed times of a disappearance (or reappearance) and the variation of the 
breadth of the invisible segment depends on the angle DAC =u. This of 
course varies during the observations, but may here with sufficient accuracy 
be considered as constant for a given phenomenon, corresponding to a given 
value of the fraction o. It would not be difficult to take account of the phase 
of the Satellite, which can never exceed 0.02 7, but it is also easily seen that 
it is of no importance in this connection. The angle w can be determined 
by the triangle ABC, where the angle AC B= 90° + u—y and 
cos (y—u) __ sin 
AB AC ° 
Now as the elliptic radius corresponding to the direction w is, neglecting the 
