66 
plane of the symmetrical kind required, providing 
that the opposite pairs of equal circles are at the 
infinitesimal distance R from the central point of the figure, 
and that their radii are infinities of a second order in com- 
parison with R ; for, with these conditions, finite quantities, 
which are infinite in comparison with R, will be infinitesimal 
in comparison with the radii of the circles. Let a sphere of 
finite radius be described with its centre at the central 
point of the figure, then the part of the tube of which AB 
is the axis that is cut off by this sphere has the character- 
istics of our tubular ordinates ; and the part of the same 
sphere cut off by the space between the upper and lower 
circles forms circles of the nature of our circular ordinates. 
When the sphere becomes infinite and of radius greater 
than the diameter of the circles of the figure, the infinite 
ordinates — tubular aud circular, positive and negative — ■ 
will all go out into space altogether without the system, in 
obvious analogy with the sudden passage, in certain other- 
wise continuous variations, of -}- x and — x into each 
other. 
