WITHDEAWN FROM THE ACTION OF GRAVITY. 273 



6.35; and as, on tbe other hand, it must exceed 3, we might admit that it would 

 at least lie between the hitter number and 4, so that it would closely approxi- 

 mate the limit of stability. If, then, it were possible to exclude the viscidity 

 also, the new decrease which the proportion would then experience, would very 

 probably bring the latter to the very limit in question, or at least to a value 

 diti'ering but exceedingly little from it. Thus, on the one hand, the least value 

 of the proportion, that corresponding to the complete absence of resistances, 

 would not differ, or scarcely so, from the limit of stability; and oa the other 

 hand, under the influence of viscidity alone, the proportion appertaining to tha 

 mercury would be but little removed from this least value. Hence it is evident 

 that the hiiluence of the viscidity of mercury is small, which is moreover ex- 

 plained by the well-known feebleness of this same viscidity. 



We can now vmderstand in the case of other but very slightly viscid liquids, 

 such as water, alcohol, &c., where the viscidity is not able to form more than a 

 minimum resistance, that this viscidity, notwithstanding the differences in the 

 intensities of the 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 respectively corresponding tO' the various 

 very slightly viscid liquids cannot be very far removed from the limit of sta- 

 bility; and as the smallest whole number above this is 4, we may in regard to 

 these liquids adopt this number as representing the mean approximative proba- 

 ble value of the proportion in question. 



Starting from this value, calculation gives us the number 1.82 as the propor- 

 tion of the diameter of the isolated spheres which result from the transformation 

 to the diameter of the cylinder, and the number 2.18 for the proportion betAveen 

 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 unit}'. The propor- 

 tion of the normal length of the division to the diameter will then express this 

 normal length itself, and the proportion consiituting 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 commencement of the; preceding sec- 

 tion, 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 moment 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 constrigted or dilated, is necessa- 

 rily greater than half the limit of stability ; consequently the sutn of the lengths 

 of three contiguous portions, for instance two dilatations and the intermediate 

 constriction, 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 

 juxtaposition with a single constriction. This, in fact, r we have seen, always 

 took place in regard to the cylinder, in § 46, which was evidently in the above 

 condition, and the want of symmetry in its transformation now becomes ex])licable. 



62. As stated at the conclusion of § 48, we have yet to describe a remarkable 

 fact which always accompanies the end of the phenomenon of the transformation 

 of a liquid cylinder into isolated masses. 



In the transformation of large cylinders of oil, whether imperfect or exact, 

 (§ 44 to 46.) when the constricted part is considerably narrowed, and the sepa- 

 ration seems on the point of occurring, the two masses are seen to flow back 

 rapidly towards the rings or the disks; but they leave between them a cyliudri- 



18 s 



