XXXII GEELMUYDEN. ASTRONOMICAL OBSERVATIONS. [NORW. POL. EXP. 
tance D’ may be reduced to the standard aperture and distance by the for- 
(AV aa 
T—T = (a) | Beis eee (7) 
As to the application of the equations (1)... (6) only a few remarks 
mula 
are necessary. The standard distance D was taken as 5.20 and a small table 
formed for the function ¢ (equation (4)) with the argument log D’ from 0.60 
to 0.80. The standard aperture was taken as that of the Fram telescope 
2 
which is 7.4 em., and the quantity i) tabulated from A’=6.0 to 26 cm., 
the last being the largest aperture employed for the present observations. 
The fraction o in equation (1) was taken as 0.2; evidently the choice is not 
of great importance, the function & having a period equal to the time of 
revolution of Jupiter. 
The ellipticity of the different sections of the shadow has been calculated 
by Laplace in the chapters of Livre VIII containing the special theories for 
each Satellite, on the supposition that the ellipticity of Jupiter is 0.07150, the 
reciprocal of which is 14.025; but as Damoiseau states in the introduction to 
his Tables that he has employed the value 13.492, the numbers of Laplace 
were multiplied by 1.0395. More recent observations give a somewhat smaller 
ellipticity, but when using Damoiseau’s Tables his values should clearly be 
retained. 
The diameters of the Satellites employed were those determined by Mr. 
Barnarp with the great Lick refractor (Monthly Notices of the R. A. S., 
Vol. 55) compared with his value of Jupiter’s equatorial diameter (Astronomi- 
cal Journal, Vol. 14). As the values of @ for the four satellites, the equatorial 
semidiameter of Jupiter being taken as unity, are given by Damoiseau in the 
appendix to his Tables (p. 196), the fraction b could be calculated for the 
different Satellites. 
As it will be convenient to have a, the breadth of the standard invisible 
segment, expressed in terms of the Satellite’s radius, w must be expressed 
in the same units. If ¢ is the half duration of a central eclipse, as given by 
Damoiseau, and expressed in seconds, 
w=F 
