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



2 = 1 V2T.fe*{l-A |_ A- ^ -...}... (a) 



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, 2' and h' 

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



fl 2 



from which it follows that 



2' 

 and 



or, if for a moment (-IT I is called f, 



*-/(' 



10 r 



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 Df can be reduced to the dis- 

 tance D by writing I jr J . 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, 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 



y J2 y A 2 



<^> t ^i * 4 ./I 1 j 



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

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



= 21/2 hr(l -\.dh and Ah = k.dt = k (TTJ. 

 \ 2r J 



