■WITHDRAWN FROM THE ACTION OF GRAVITY. 693 



these two sections will include a division between them. After 

 another interval of time equal to the first, another division will 

 have passed to the contracted section ; but the first will even 

 then be shortened, so that its lower neck, in this second interval 

 of time, will have traversed a less space than the first. For the 

 same reason, the space traversed in a third interval of time equal 

 to the two others will be still smaller, and so on afterwards. The 

 movement of transference of the necks, and therefore that of the 

 divisions which they include two and two, will then constitute, 

 as I have stated, a retarded movement. 



Now the two causes which we have mentioned, and which act 

 concurrently upon the divisions, will necessarily combine their 

 effects. Consequently the velocity of transference of the divi- 

 sions will be intermediate between the accelerated velocity of the 

 liquid and the retarded velocity which w^ould result from the 

 second cause alone ; in the second place, the divisions will gra- 

 dually diminish in volume during their descent along the con- 

 tinuous portion, but according to a less rapid law than would be 

 the case under the isolated action of this second cause ; lastly, 

 the length of the divisions will follow a law intermediate be- 

 tween the gradual increase determined by the first cause and 

 the decrease produced by the second. 



77- We shall now investigate the manner in which these 

 modifications in the volume, length, and velocity of the divi- 

 sions, are capable of exerting an influence upon the laws regu- 

 lating the length of the continuous portion of the vein. 



We must first draw attention to the fact, that in our imaginary 

 veins, where the movement of transference of the liquid is sup- 

 posed to be uniform with all charges, the causes producing the 

 above modifications do not exist; consequently the divisions 

 must always descend with the same velocity as the liquid, with- 

 out varying in either volume or length in the course of the con- 

 tinuous part. Moreover, we must recollect, that after what has 

 been detailed in §§ 72, 74 and 75, Savart's laws are already 

 satisfied with regard to these veins commencing with very 

 feeble charges ; the first law in the case of any liquid whatever, 

 and the second in the case of mercury, very probably also in 

 that of any other very slightly viscid liquid, and perhaps even in 

 that of all liquids. 



Let us now recur to the true vein of the preceding section, 

 and let us begin by examining the influence exerted by the 



