WITHDRAWN FROM THE ACTION OF GRAVITY. 367 
: , Mire trices 
limit of such increase, when the diameter becomes infinite, the term N will com- 
pletely disappear for all points of the meridian line; which, as regards this entire 
eel 1 : 
line, will reduce the equation of equilibrium to uM C; the radius of curvature 
Bt 
will be then strictly constant, and we shall arrive at*this singular result, that the 
total meridian line will be condensed into a single circumference of a circle ; and 
as the latter will be situated at an infinite distance from the axis of revolution, 
we perceive that the figure generated will be simply a cylinder. Thus the 
second limit of the variations of the nodoid is the cylinder; but this cylinder is 
placed transversely in relation to the axis of the nodoid from which it is derived, 
. and that axis is infinitely removed from it; while the cylinder which forms the 
second limit of the variations of the unduloid (§8) has for its axis that of the 
latter figure. 
§ 36. For the partial realization of a nodoid whose complete meridian line 
shall be of the kind represented by Fig. 40, it is not necessary that the absolute 
Lig. 40 
PRERRRERRR 
DY) 9) 
CL ) 
TRIN 
LD) 
Hl 
a> 
Kes 
diameter of the solid ring should be very considerable; it is sufficient that this 
diameter be large relatively to the length of the meridian node. For, if we 
reflect that, in this latter, the curvature continues to diminish (§ 26) from the 
summit to the points where the tangents are parallel to the axis of symmetry, 
and that, from thence to the other extremity of the node, it is less than at those 
points, we shall perceive that if the leagth of this same node is small in relation 
to the radius of the solid ring, its width will be still smaller, and that at its 
summit the radius of curvature will be extremely small in comparison with the 
distance from that summit to the centre of the ring, a distance which constitutes 
the perpendicular. At the summit, then, the term V will be inconsiderable in 
Te. ae 
regard to the term ‘i and the value of the quantity MN will depend chiefly 
cb ! : 
on that of x? but it is at the summit that the perpendicular is least; therefore, 
upon the rest of the node and upon the arcs which unite this node with the 
pbeegee Pie : 
nodes neighboring on the complete meridian line, the term > will have still less 
influence, and consequently, in the whole extent of that line, the curvature will 
vary but slightly. 
The liquid ring momentarily obtained in a solid ring 70 millimetres in diame- 
ter, by piercing a disk reduced almost to a film, (2d series, § 19,) constitutes a 
partial nodoid of the kind which we are considering; this liquid ring has, in 
effect, but little size relatively to the radius of the solidring. It is also evidently 
a concave portion of a nodoid of this kind which we realize in the experiments 
of § 25, when the disks are very near one another, and we stop the exhaustion 
of oil at the point where the extreme elements of the meridian are are sloped on 
the faces of the disks at their borders. Such, too, is the figure realized in the 
experiments of § 31, when the distance of the disks is very small and. the extreme 
elements of the meridian are are inclined as nearly as possible on the prolonga- 
tions of the solid faces. Here, however, the meridian are does not appertain to 
