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



M K== h sin H + i sin I + etc. 



where the rate of change of the arguments H, I etc. is so little different from 

 the rate of change of v that they may be considered as equal during an 

 eclipse. Consequently 



i? = rj-- (h cos H + * cos T + etc.) = 



[h sin (H + 90) + i sin (7 + 90) + etc.]. 



Or the arguments which have already served for finding s will, when 

 they are jill augmented by 90, give cos y. 



In the figure A is the centre of the elliptic shadow, AD = a, C the centre 



o 



of the Satellite, CB the line of its relative motion, AB= . a, ABC = y. 



The Satellite is supposed to be in such a position that a certain fraction a 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 DAG = 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 a. It would not be difficult to take account of the phase 

 of the Satellite, which can never exceed 0.02 r, but it is also easily seen that 

 it is of no importance in this connection. The angle u can be determined 

 by the triangle ABC, where the angle ^1C-B = 90 -\- uy and 



cos (y u) _ sin y 

 AB ' ~~ 



Now as the elliptic radius corresponding to the direction u is, neglecting the 



