658 PLATEAU ON THE PHENOMENA OF A FREE LIQUID MASS 



configuring forces, will also exert only a feeble influence upon 

 the proportion in question. Hence it results that in the absence 

 of all external resistance, the values of this proportion respect- 

 ively corresponding to the various very slightly viscid liquids, 

 cannot be very far removed from the limit of stability ; and as 

 the smallest whole number above this is 4, we may in regard to 

 these Uquids adopt this number as representing the mean ap- 

 proximative probable value of the proportion in question. 



Starting from this value, calculation gives us the number 1'82 

 as the proportion of the diameter of the isolated spheres which 

 result from the ti'ansformation to the diameter of the cylinder, 

 and the number 2* 18 for the proportion between the distance of 

 two adjacent spheres and this diameter. 



61. There is another consequence arising from our discussion. 

 For the sake of simplicity, let the diameter of the cylinder be 

 taken as unity. The proportion of the normal length of the di- 

 vision to the diameter will then express this normal length itself, 

 and the proportion constituting the limit of stability will express 

 the length corresponding to this limit. This admitted, let us 

 resume the conclusion at which we arrived at the commence- 

 ment of the preceding section, which conclusion we shall 

 consequently express here by stating that in the case of all 

 liquids the normal length of the divisions always exceeds the 

 limit of stability ; we must recollect in the second place, that 

 the sum of the lengths of one constriction and one dilatation is 

 equal to that of a division (§ 57) ; and thirdly, at the first mo- 

 ment of the transformation, the length of one constriction is 

 equal to that of a dilatation (§ 46). Now, it follows from all these 

 propositions, that when the transformation of a cylinder begins 

 to take place, the length of a single portion, whether constricted 

 or dilated, is necessarily greater than half the limit of stability ; 

 consequently the sum of the lengths of three contiguous por- 

 tions, for instance two dilatations and the intermediate constric- 

 tion, is once and a half greater than this same limit. Hence, 

 lastly, if the distance of the solid bases is comprised between 

 once and once and a half the limit of stability, it is impossible 

 for the limit of stability to give rise to three portions, and it will 

 consequently only be able to produce a single dilatation in juxta- 

 position with a single consti'iction. This, in fact, as we have 

 seen, always took place in regard to the cylinder in § 46, which 

 was evidently in the above condition, and the want of sym- 

 metry in its transformation now becomes explicable. 



