Chase.] vJ [March 19, 



10. In most, if not in all, physical investigations wliich introduce con- 

 siderations of central force, velocity may be treated as a function of radius, 

 time and mass. 



v := F (r, t, m) . 



In undertaking to investigate successive conversions of spiritual, undu- 

 latory, and centripetal or centrifugal energy, astronomical phenomena fur- 

 nish the most abundant, extensive, and varied opportunities for observa- 

 tion and illustration. Unfortunately, there is so much uncertainty in re- 

 gard to the dimensions and densities of the principal heavenly bodies, that 

 we can point to few results which are so precise as would be desirable. 

 There are, however, some important indications of the operation of the 

 foregoing laws, which are confirmed by terrestrial phenomena that are 

 capable of very accurate measurement. 



In Searle's Outlines of Astronomy, page 403, the following figures are 

 quoted from the AnnaUn der Stermcarte in Leiden, on the authority of 

 Kaiser. "The apparent diameter of Mercury, at a distance equal to the 

 semi-axis major of Eartli's orbit, ranges, according to different observers, 

 from 5". 3 to 6".9 ; that of Venus from 16" 6 to 17".9 ; the apparent equa- 

 torial diameter of Mars from 9". 6 to 9". 2 ; its apparent polar diameter from 

 9". 4 to 9". 3. Similar disagreements appear in different estimates of the 

 apparent diameters of Jupiter, Saturn, Uranus, and Neptune, at a distance 

 for each planet equal to the semi-axis major of its orbit. Thus the equa- 

 torial diameter of Jupiter ranges from 39". 5 to 37". 1 ; its polar diameter 

 from 37". 9 to 35". 1 ; the equatorial diameter of Saturn from 18". 5 to 16".9 ; 

 its polar diameter from 16". 8 to 15". 1 ; the diameter of Uranus from 3". 9 

 to 3".6 ; that of Neptune from 3".5 to 4". 4." 



Kaiser adopts, as most probable values for the ratios of the several diame- 

 ters to Earth's diameter, figures which I have increased by one per cent., 

 in order to adapt them to more recent estimates of Sun's distance. These 

 increased figures are given under ?•(!), in the following table. Under 7'(II) 

 and in the subsequent columns, I give theoretical values which illustrate 

 simple harmonic deductions from the above general function of velocity. 



