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Mv aim wilh lliis imoslijialinn \va« oxclnsivolv llio dotonniiialioii 

 of' till' iiicliiialioiis aiifl nodes of llic orliital planes of tlie satellites 

 and of the motions of these nodes. The plates of 1903 and 1904 

 were taken in order to provide a second epoch from which these 

 motions could he determined hv a comparison wilh the obser\'ations 

 of 1891. 



Tiie fine series of observations, made by Mr. Hkyan Cookson in 

 1901 and 1902 increases the weijiht of this determination considerably. 



I have already pointed out, in the fourth chapter of iny disserta- 

 tion, that the determination of the other elements, which must be 

 derived from the observed (jovicentric) longitudes, is probably sufTi- 

 ciently provided for by the observations of eclipses. Moreover from 

 the observations mentioned above sub 1. and 3. all elements were 

 determined. 



Eclipse-observations are however not well adapted for the deter- 

 mination of the inclinations and nodes, which must be derived 

 from the observed latitudes, as I have shown, 1. c. page 77. The 

 jn-incipal interest of the determination of the orbital planes lies in 

 the comparison with the observations of the large motions of the 

 nodes, which are demanded by the theory. Since these motions are 

 produced almost exclusively by the large polar compression of the 

 planet, the natural fundamental plane to which the latitudes must 

 be referred is the equator of Jupiter. 



If we i-efer the positions of the satellites to a system of co-ordinate 

 axes, of which the axis of // is the projection on the sphere of a 

 line perpendicular to this fundamental plane (i. e. of Jupiter's axis 

 of rotation), and the axis of ,t, is the great circle through the centre 

 of the planet perpendicular to the axis of y, then for the determina- 

 tion of the inclinations and nodes the y co-ordinates of the satellites 

 are alone important. Only these co-ordinates have therefore been 

 measured. The plate was, by means of the position-circle with which 

 the Repsold measuring machine of the Astronomical Laboratory at 

 Gi-oningen is provided, brought approximately in the position-angle 

 P + 90^, where P is the position-angle of Jupiter's adopted axis 

 of rotation. The plate then has a motion parallel to a straight line, 

 which nearly coincides with the axis of ,r, and which is defined by 

 the axis of the cylinder which guides the plate-holder in its motion. 

 The co-ordinates perpendicular to this straight line were then measured 

 by the micrometer screw. These diffei' from the co-ordinates y only 

 by small corrections (refraction, orientation and scale-value). In this 

 nietliod the measured quantities never exceed a few revolutions of 

 lh(< screw. All errors of réseau-lines, division eri'ors of the scales, 



