270 THE FIGURES OF EQUILIBRimi OF A LIQUID MASS 



tion itself; we shall tlicn liave a second section at the origin of the first dilatation; 

 a tliird at the origin of the second constriction ; a fourth at the origin of the 

 second dilatation, and" so on; so that all the sections of the even series will 

 occupy the origins of the dilatations, all those of the odd series the origins of 

 the constrictions. The interval comprised between two consecutive sections of 

 the odd series will therefore include a constriction and a dilatation ; and as the 

 figure begins with a constriction and terminates with a dilatation, it is clear that 

 its entire length will be divided into a whole number of similar intervals. In 

 consequence of the exact regularity which we have supposed to exist in the 

 transformation, all the intervals in question will be equal in length ; and as the 

 moment at which we enter upon the consideration of the figure may be taken 

 arbitrarily from the origin of the phenomenon to the maximum of the depth of 

 the constrictions, it follows that the equality of length of the intervals subsists 

 during the whole of this period, and that, consequently, the sections which 

 terminate these intervals preserve during this period perfectly fixed positions. 

 Besides the parts of the figure respectively contained in each of the intervals 

 imdergoing identically and simultaneously the same modifications, the volumes 

 of all these parts remain equal to each other ; and as their sum is always equal 

 to the total volume of the liquid, it follows that, from the origin of the trans- 

 formation to the maximum of depth of the constrictions, each of these partial 

 volumes remains invariable, or, in other words, no portion of liquid passes 

 from any one interval into the adjacent ones. Thus, at the instant at which 

 we consider the figure, oh the one hand, the two sections Avhich terminate any 

 one interval will have preserved their primitive positions and their diameters ; 

 and on the other hand these sections will not have been traversed by any por- 

 tion of liquid. Matters will then have occurred in each interval in the same 

 manner as if the two sections by which it is terminated had been solid disks. 

 But the transformation cannot, ensue between two solid disks, if the proportion 

 of the distance which separates the disks to the diameter of the cylinder is less 

 than the limit of stability; the proportion of the length of our intervals and the 

 diameter of the cylinder cannot then be less than this limit. Now, the length 

 of an interval is evidently equal to that of a division ; for the first, in accord- 

 ance with what we have seen above, is the sum of the lengths of a dilatation 

 and a constriction ; and the second is the sum of the lengths of a dilatation and 

 two serai-constrictions, (§ 53 ;) the proportion of the length of a division to the 

 diameter of the cylinder cannot then be less than the limit of stability; and we 

 may remark here that this conclusion is equally true, whether the divisions are 

 able or not to assume exactly their normal length. 



58. Let us now attempt to ascertain the influence of the nature of the liqviid 

 and that of external circumstances, commencing with the latter. Our liquid 

 cylinder of mercury, along the whole of the line at which it touches the plate 

 of glass, must contract a tJight adherence to this plate, which adherence must 

 more or less impede the transformation. To discover whether this resistance 

 exerted any influence upon the normal length of the divisions, consequently 

 upon the proportion of the latter to the diameter of the cylinder, a simple 

 means presented itself, viz., to augment this resistance. To arrive at this 

 result, I arranged the apparatus in such a manner as to remove only one of 

 the strips of glass, so that the liquid figure then remained simultaneously in 

 CO tact with the plate and the other strip. I again repeated the experiment 

 ten times, using copper wires 1.05 millimeters in diameter, and giving the 

 cylinder a length of 100 millimeters. The fjllowing were the results : 



