taken at the Lowell Observatory. 491 



matter composing the body is concentrated at its centre ; 

 the limit J</>, to that in which the body is homogeneous. 



Now, if: we know the body's equatorial radius and its 

 ellipticity, we can determine its volume, and from its mass 

 its mean density ; and if in addition we know its rate of 

 rotation, we can from its density and its rotation rate deduce 

 (// by the formula 



T 2 o 

 T 2 /> 



where the unaccented quantities refer to the Earth and the 

 accented to Jupiter. 



Gt/ 2 



For V = y-j — - f may thus be found, V being # 00115, and 



k being the constant of attraction ; and (j> r may be expressed 

 in terms of V / by a process which the reader will find given 

 in Tisserand's Mecanique Celeste. 



Tisserand's data for the densities &c. are not in accord- 

 ance with modern values. It is necessary, therefore, to 

 recalculate (p. Using, now, for Jupiter the most modern 

 determination of the equatorial radius and the ellipticity 

 which, as we have seen, the measures of the photographs 

 bear out, to wit : — 



a = 38" at Jupiter's mean distance, the solar parallax 

 at 8"'80, 

 = 89040 miles or 143300 km., 

 T = 9 h -842 at Jupiter's equator, 



and € =± i or V =^ 



where e = thc ellipticity —7 — and 77 the oblateness — , 



1 J b a 



we find $'= jjr^- 



The ellipticity is the more philosophic quantity to use, 

 although the oblateness is more commonly employed, because 

 the ellipticity associates itself directly with </>', and thus with 

 the planet's physical state. 



The limits then between which the ellipticity could lie are 



——^ and £^7, the former corresponding to total concen- 

 tration at the centre, the latter to homogeneity*. We thus 



* For anew and more exact method of determining these limits and (p, 

 see paper by the author appearing- in a following- number. 



