[ 4'8 3 
and biirfl: to its very Centre. If, on the contrary, its 
fame Side touched another cylindric Vortex by the 
Poles, they would both mix together, and would 
compofe but one Vortex. 
It is not fufficient for explaining the celeftial 
mmena\ becaufe it is allowed, that the tranflative Ve- 
locities of its Points cannot be in an inverted Ratio 
to the Roots of the Diftances, and that its centrifugal 
Force does not diminifh in the inverted Ratio of the 
Squares of thefe Diftances, <i^c. 
Corollary. 
Therefore the fpherical Vortex^ in order to be of 
Ufe, muft have other Properties than the cylindric : 
That is to fay, it muft have a relative Force to one 
and the fame Centre 5 for it is by this Force alone 
that it can be different from the cylindric Vortex. 
This Force, moreover, muft be equal in all the 
points of the fame fpherical Superficies j becaufe 
otherwife it might be burft and broke into in its weak 
Parts, as well as the cylindric, 
Theorem I. 
Even in the fpherical Vortex there is no relative 
Force to one and the fame Centre : That is to fay, 
that it has properly but an axifugal Force. 
Demonstration. 
The fpherical Vortex is compofed, as well as the 
cylindrical, of feveral parallel Circles, but with this 
Difference, that in the fpherical Vortex the Radii of 
the parallel Circles are not all equal, but on the con- 
’ ~ trary 
