252 Wisconsin Academy of Sciences, Arts and Letters. 



case its interior heat has not escaped the figures above given for crust den- 

 sity ruust be made larger. 



36. The rrust density of Jupiter's satellites. 



The diameters of Jupiter's sa'ellites in orders of Nos. per Loomis is in 

 miles, 2436, 2187, 3576 and 3057. There is some uncertainty about these di- 

 ameters, and Newcomb says they vary from 230 ) to 3700 miles. The mean 

 densities of these satellites in order, per diameters of Loomis is, 1.05, 1.90, 

 1.70 and 1.32. The averages of these mean densities is 1.49, or a little 

 more ihan the meaa density of Jupiter, which is 1.3S. The surface gravity 

 of these satellites is very ^mall, hence the center density can not be very 

 much greater han the crust density. The average crust density can not 

 vary much from 1.30. 



37. As already obtaine 1, the near surface or crust density of Mercury 

 is about 5, Venus at present average temperature, 3, or at zero 3.20, the 

 Earth at present average temperature, 2.96, or at zero 3.20, the Moon at zero 

 3.20, Mars at zero 3.20, and the average of Jupiter's satellites 1.20. From 

 these results I see away back in the past a large ring around the sun; this 

 ring separated into three, like the rings now around Saturn ; and from 

 these three came the triplet planets, Mars, the Earth and Venus.* 



CONCLUSION. 



During the delay of two years in the publication of this 

 Eeport of the Academy of Sciences, Arts and Letters, I 

 have added three chapters to this paper. As it stands the 

 title is inappropriate, and the introduction fails to give due 

 credit to the paper as presented. The Attraction and the 

 Figure of Equilibrium of a Rotating Fluid Mass, and the 

 Interior Density and Temperature of the Earth, is a more 

 appropriate title. Measured by my reading of what has 

 been written on the subject, this investigation attains not 

 only some new final results, but it opens, by its new meth- 

 ods, a new field for valuable deductions. The new way of 

 finding any diameter of the ellipse is a change from the com- 

 plex to the simple. The system using chord and wedge ele- 

 ments of attraction instead of shell elements is a grand step 

 of advance in simplification. By the new system mathe- 



* It is due the author to say that the chapters of this paper were written 

 at periods separated by months. The last chapter was composed after the 

 previous ones had passed from his hands, and he was forced to keep up the 

 connection with the other chapter-^, partially from memory. His excuse 

 for not unifying the p iper under an appropriate title is want of time. 



