364 Prof. J. Plateau on the Figures of Equilibrium 



to the last. The last three ratios were, on the contrary, below 

 the theoretical limit, but also successively approached it ; and 

 with them the character of stability was recognized, although 

 likewise becoming less and less marked from one to another. 

 Lastly, with the theoretical ratio 3* 14 itself neither of these 

 characters was exhibited : in this case, as with the lower ratios, 

 the exact cylinder was arrived at without difficulty; but when 

 this cylinder was left to itself, it began, after remaining appa- 

 rently unaltered for a few seconds, to change, at first with ex- 

 treme slowness, but afterwards gradually more and more quickly. 

 The figure divided itself as usual into a bulging and a constricted 

 portion, and the change of shape continued until complete separa- 

 tion had taken place. The results of experiment accordingly 

 agreed completely with that of calculation. 



As I proved in my Second Series, a liquid cylinder, of which 

 the length is considerable as compared with its diameter, sepa- 

 rates of its own accord into bulging portions alternating with 

 constricted portions, both becoming more and more distinct until 

 the whole figure is changed into a succession of isolated spheres. 

 I then arrived at the following conclusions, — that a cylinder of 

 indefinite length, with its surface entirely free, and formed of a 

 liquid without weight and completely devoid of viscosity, would 

 in all probability transform itself in such a way that the sum of 

 the lengths of an enlargement and a contraction would be equal 

 to that which corresponds to the limit of stability. But I showed 

 at the same time that the sum of these lengths increases with 

 the resistances, either external or internal, that retard the trans- 

 formation. Now in the present Series, supposing a cylinder of 

 indefinite length, or only of very great length, formed of a real 

 liquid, and therefore one in which the transformation is neces- 

 sarily interfered with, at least by viscosity, and assuming that at 

 the commencement of this transformation the meridian line of 

 the figure is still a curve of sines, I investigate mathematically 

 the difference between the capillary pressures exerted by a con- 

 tracted and those exerted by an expanded portion ; and in this 

 way 1 find that the excess of the former above the latter increases 

 with the length of the contracted and expanded portions. It 

 will thus be understood how, when there are resistances, the 

 transformation spontaneously adjusts itself so as to overcome 

 them, increasing the difference of the pressures by an increase 

 in the length of the contracted and enlarged portions. 



Experiment, moreover, confirms the result of the above calcu- 

 lation, leaving out of account any hypothesis as to the nature of 

 the orginal meridian line. I have in fact established that if cy- 

 linders of oil are formed between the same pair of disks, exceed- 

 ing to a greater and greater extent the limit of stability, as can 



