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



~ A r " T * T VrJ '/' 



the convergence of which will be sufficiently rapid for admissible values of h. 

 If 2 and h correspond to an observation at the distance D, S' and h' 

 to another distance D', then according to the above supposition 



from which it follows that 



and 



or, if for a moment [jr\ is called 



f-'- 1 ('+**?*+) 



Now, when D is the mean distance of Jupiter from the Sun, which is 

 also a mean distance from the Earth, the numerical value of the coefficient 

 of - can never exceed 0.04, and as h is certainly only a fraction of r for 

 all but the smallest telescopes, the second term may safely be neglected. 

 Consequently an observation at the distance D' can be reduced to the dis- 



tance D by writing \jr\ . h for h'. 



If a disappearance or reappearance at the distance D is observed at the 

 moment T by means of a telescope of aperture A (in which case h = x) 

 and the same phenomenon occurred at the moment T t for an aperture A t 

 giving the invisible segment 2 lt it is assumed that the quantity of light is 

 proportional to the square of the aperture, or 



.A 2 = Z l .AS, 



and further that the difference between the segments may be found with 

 sufficient accuracy by a differential formula, or 2 V S = d S, where 



= 21/2 



2 M 1 a^l-* 1 * and d ^ = k.At = k (TT t ). 



