304 NEWTON S PRINC1PIA. 



selves elliptical. The fluid between two elliptic curves of 

 motion must always keep between them, and therefore 

 the velocity must be greatest where the distance between 

 the paths is least. But by Kepler s law the velocity is 

 such that the areas described are proportional to the time. 

 These two conclusions can be shown not to agree. As an 

 example, let us take the three orbits of Venus, Earth, 

 and Mars. &quot; At the beginning of the sign of Virgo, 

 where the aphelion of Mars is at present,&quot; says Newton, 

 &quot; the distance between the orbits of Mars and Venus is to 

 the distance between the same orbits at the beginning of 

 the sign of Pisces as 3 to 2. Therefore the matter of the 

 vortex between those orbits ought to be swifter at the be 

 ginning of Pisces than at the beginning of Virgo in the 

 ratio of 3 : 2. Therefore the velocity of the Earth at the 

 beginning of Pisces should be to its velocity in the begin 

 ning of Virgo in the same ratio. But judging from the 

 Sun s diurnal motion, we know that the Earth is swifter at 

 the beginning of Virgo than at the beginning of Pisces. 

 Hence the hypothesis of vortices is not reconcileable with 

 astronomical phenomena.&quot; 



If a body be carried round a vortex, it must have the 

 same density as the fluid along its path. In that case it 

 may be regarded as a piece of solidified fluid, and its cen 

 trifugal force is just balanced by the pressures on its two 

 sides. But if the density be different, this balancing no 

 longer takes place. The centrifugal force will be greater 

 or less than the difference of pressures, according as the 

 density of the body is greater or less than that of the fluid. 

 Hence the body will recede from or approach to the centre 

 according as its density is greater or less than that of the 

 fluid. If the strata of fluid be not placed so that their 

 densities increased with the distance, not only would they 

 themselves be in an unstable state, but the globes also, if 



