WITHDRAWN FROM THE ACTION OF GRAVITY. 695 



preceding. In virtue of the excess which the velocity of the liquid 

 acquires above that of the divisions, the liquid passes, as we have 

 seen, from one division to the other, so that any one portion tra- 

 verses successively, sometimes the narrower canal of a constric- 

 tion, sometimes the larger space of a dilatation. But as the liquid 

 thus moves in a conduit the dimensions of which are alternately 

 smaller and larger, its velocity must be greater in the constricted 

 parts, and less in the dilated parts, than if the divisions did not 

 exist ; whence this singular consequence results, that the velo- 

 city of transference of the liquid, instead of being uniformly 

 accelerated, is subjected, in the course of the continuous part, to 

 a series of particular variations which render it alternately greater 

 and less than that which a solid body falling from a point situated 

 at the elevation of the liquid in the vessel would have. More- 

 over, the liquid molecules, instead of moving in the direction of 

 lines presenting a very slight curvature, and always in the same 

 direction, as they would do if the divisions were absent, will 

 necessarily describe sinuous lines in their passages from division 

 to division. Now the configuring forces emanating from the 

 superficial layer of the vein, and which produce the divisions, 

 cannot force the molecules of the liquid to undergo these alter- 

 nate changes of direction and velocity, without expending a part 

 of their own action; so that things will go on as if these forces 

 experienced a loss in intensity. If then the influence in question 

 were alone exerted, the transformation would be effected with 

 less rapidity, and therefore the continuous portion would be 

 longer than in the corresponding imaginary vein ; whence it fol- 

 lows, that in passing from the charge under consideration to a 

 charge which would establish the approximative uniformity of 

 the movement of transference of the liquid in the continuous 

 portion, the length of this portion of the vein would increase in 

 a less proportion than that of the square roots of the two charges. 

 With regard to the transference of the divisions, separately con- 

 sidered, we are well aware that it must be intermediate between 

 the retarded velocity which would result from the free shortening 

 of these divisions, and the accelerated velocity of the liquid ; but 

 it would be difficult to decide a priori whether this intermediate 

 velocity preserves any retardation or whether it presents any 

 acceleration. However, admitting that retardation exists, the 

 latter, tending evidently to diminish the length of the continuous 

 portion, would produce an influence in the same direction as 



