which arc neither Spherical nor Cylindrical. 31 



iron wire. This is done by introducing the ring into a sphere 

 of oil, of sufficiently large diameter, and afterwards subtracting 

 a portion of the liquid. When, by gradual absorption, the 

 thickness of the lens has been reduced to about a sixth of the 

 diameter of the ring, the former is pierced in its centre in a 

 manner indicated in the memoir ; the oil then takes the form of 

 an annular figure, whose meridian curve, rounded on the side 

 of the axis of revolution, has a sharp point on the side of the 

 solid ring ; it is in fact the meridian curve of the figure gene- 

 rated by our loop. 



The hquid figure thus obtained, however, only exists for a few 

 seconds, showing thereby that it is unstable ; it soon becomes 

 deformed, and finally disunited on one side. 



On examining what becomes of the branches of the curve after 

 their intersection at the point of the loop, I find that each, pre- 

 serving the character of its curvature, recedes to a maximum 

 distance from the axis of revolution, and afterwards returns 

 towards this axis so as to form an arc convex outwards. I have 

 realized the portion generated by this arc by introducing a mass 

 of oil between two discs, rendering the same first cylindrical, 

 and afterwards causing one of the discs to approach the other. 

 The liquid figure then becomes bulged, and the meridian con- 

 vexity increasing as the distance between the discs diminishes, 

 it passes through the form of a portion of a sphere, after which 

 it constitutes successively the figui'es generated by a portion of 

 the arc in question, afterwards that generated by the whole arc, 

 and finally it attains a figure generated by a more extended arc 

 of the complete meridian curve. These successive arcs, however, 

 belong to different cases of the equilibrium-figure. 



I further show that the arc in question — in accordance with 

 the appearance of the realized figures — is perfectly symmetrical 

 on each side of its middle point, so that the curve has another 

 axis of symmetry passing through this point, and perpendicular 

 to the axis of revolution. 



Hence we must clearly conclude that our arc which comes 

 from a loop arrives at a second, identical with the first ; that 

 this second is followed in the same manner by a third, and so 

 ou indefinitely. The complete meridian curve, therefore, con- 

 sists of an indefinite series of equal loops, connected by equal 



arcs, and arranged alongside the axis of revolution (fig. 2). In 



