632 PLATEAU ON THE PHENOMENA OP A FREE LIQUID MASS 



'J^ centims.jSO that the versed sine of the meridional convexity was 

 slightly greater than when this was 8 centims. The figure was 

 then found to be perfectly symmetrical, and it did not exhibit 

 any tendency to deformity ; whence it follows that the uniformity 

 in the densities had not experienced any appreciable alteration. 

 I recommenced, with still more care, the experiment with that 

 figure which was 8 centims. in height ; and I was enabled to 

 approach the cylindrical form still more nearly; but before it 

 was attained, the same phaenomena again presented themselves, 

 except that the alteration in form was effected in an inverted 

 manner, i. e. the figure became narrow at the upper part and 

 dilated at the base ; so that after the separation into two masses, 

 the perfect sphere existed in the lower ring and the lens in the 

 upper ring. On subsequently uniting, as before, the two masses, 

 and placing the rings at a distance of 7^ centims. apart, the 

 figure was again obtained in a regular and permanent form. 

 Thus when we try to obtain between two solid rings a liquid 

 cylinder the height of which is four times the diameter, the 

 figui'e always breaks up spontaneously, without any apparent 

 cause, even before it has attained the exactly cylindrical form. 

 Now as the cylinder is necessarily a figure of equilibrium, what- 

 ever may be the proportion of the height to the diameter, we 

 must conclude that the equilibrium of a cylinder the height of 

 which is four times the diameter is unstable. As the shorter 

 cylinders which I had obtained did not present analogous effects, 

 I was anxious so satisfy myself whether the cylinders were really 

 stable. I therefore again formed a cylinder 6 centims. in height 

 with the same rings ; but this, when left to itself for a full half 

 hour, presented a trace only of alteration in form, and this trace 

 appeared about a quarter of an hour after the formation of the 

 cylinder, and did not subsequently increase, which shows that 

 it was due to some slight accidental cause. 



The above facts lead us then to the following conclusions, — 

 1st, that the cylinder constitutes a figure the equilibrium of 

 which is stable when the proportion between its height and its 

 diameter is equal to 3, and with still gi-eater reason when this 

 proportion is les? than 3 ; 2nd, the cylinder constitutes a figure 

 the equilibrium of which is unstable when the proportion of its 

 height to its diameter is equal to 4, and with still greater reason 

 when it exceeds 4 ; 3rd, consequently there exists an interme- 

 diate relation, which corresponds to the passage from stability to 



