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



tance D 1 may be reduced to the standard aperture and distance by the for- 

 mula 



As to the application of the equations (1) ... (6) only a few remarks 

 are necessary. The standard distance D was taken as 5.20 and a small table 

 formed for the function c (equation (4)) with the argument logD' from 0.60 



to 0.80. The standard aperture was taken as that of the From telescope 



(74x2 

 -ji J tabulated from A' = 6.0 to 26 cm., 



the last being the largest aperture employed for the present observations. 

 The fraction a in equation (1) was taken as 0.2; evidently the choice is not 

 of great importance, the function k 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 0.07130, 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. 

 BARNARD 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 a 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 6 could be calculated for the 

 different Satellites. 



As it will be convenient to have x, the breadth of the standard invisible 

 segment, expressed in terms of the Satellite's radius, vo must be expressed 

 in the same units. If i is the half duration of a central eclipse, as given by 

 Damoiseau, and expressed in seconds, 



