XXX GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 
eat rn ili ste (t) —.. 1... @) 
r 
the convergence of which will be sufficiently rapid for admissible values of h. 
If ¥ and h correspond to an observation at the distance D, 5’ and h/ 
to another distance D‘, then according to the above supposition 
as 
DPR TE 
from which it follows that 
E-() -Q)(ratete...) 
and 
D’ 
or, if for a moment Be is called f, 
wapnt+°.P+...). 
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 (F 
If. h for h’. 
If a disappearance or reappearance at the distance D is observed at the 
moment 7’ by means of a telescope of aperture A (in which case h =«) 
and the same phenomenon occurred at the moment 7’, for an aperture A, 
giving the invisible segment ¥,, it is assumed that the quantity of light is 
proportional to the square of the aperture, or 
2 A? = Aa; 
and further that the difference between the segments may be found with 
sufficient accuracy by a differential formula, or ©, — ¥—=d, where 
dr=2 /2 ir(1—3,) ah and dh = —k.di-= kT): 
