398 R. Hooke — Law of Densities of Planetary Bodies. 



same error of angular measure, and the error would be one of 

 excess, so that, if we had the actual diameters of the satellites, 

 and should subtract them from the observed diameters, the 

 same difference would be obtained in the case of each satellite. 

 The writer has computed the diameters of these satellites from 

 the law of density, previously applied to the inner planets, and 

 the most recent values of the masses of the satellites relative 

 to that of Jupiter, and the following is a comparison of the 

 computed with the observed values, the latter being those 

 given in the ninth edition of the Encyclopaedia Britannica : 





Observed 



Computed 







diameter 



diameter 



Difference 





in miles. 



in miles. 



in miles. 



Satellite I 



2352 



1663 



689 



Satellite II 



2099 



1837 



262 



Satellite III 



3436 



2768 



668 



Satellite IV 



2929 



2214 ■ 



715 



It will be observed that the difference is about the same for 

 each satellite except the second, the diameter of which com- 

 putation makes larger than the first, but which observation 

 makes smaller. With the single exception just noted, the 

 result of the above test is confirmatory of the law of density 

 and the theory that these satellites have solidified, and there- 

 fore, under the adopted hypothesis, have the same surface 

 density as the inner planets and the moon. The apparent 

 want of coincidence in' the difference obtained for the second 

 satellite does not disprove the law of density, or its applica- 

 bility to these satellites, for the reason that several distin- 

 guished observers have observed this satellite to be larger than 

 the first, as the value of its mass indicates it should be.* The 

 values used for the masses of the satellites in the computation 

 of the diameters above given are as follows : 



(Mass of Jupiter=l.) 

 Satellite I 0-000016877 



Satellite II 0*000023227 



Satellite III 0-000088437 



Satellite IV 0-000042475 



The mean densities of the satellites of Jupiter are, accord- 

 ing to the above values of their masses and the computed diam- 

 eters already given, as follows: satellite I, 3 "22; satellite II, 

 3-29 ; satellite III, 3-66 ; satellite IV, 344. 



* There is, in all probability, a serious error either in the observed value of the 

 diameter, or in the assigned value of the mass of the second satellite of Jupiter, 

 as it is very improbable that in the same system of satellites, a satellite of given 

 volume should have a greater mass than one of larger volume. 



