WITHDRAWN FROM THE ACTION OP GRAVITY. 691 



of the continuous part of an imaginary vein of mercury only 

 exceeds the distance D by a quantity equal to 6 ten-thousandths 

 of the latter ; so that, for instance, if the diameter of the orifice 

 were such that the distance D were a metre, the length of the 

 continuous part would only differ from it by half a millimeti'e ; 

 and in consequence of the very small value we have attributed 

 to 6, even this probably exceeds the true difference. Lastly, if 

 we pass from mercury to some other liquid, the difference be- 

 tween L and D, or rather the proportion of this difference to D, 

 would necessarily vary in magnitude and direction with the 

 nature of the liquid ; but this proportion, as we have shown, 

 is so small, that we may safely admit that it will always be very 

 small in regard to any other liquid. 



76. Let us now go within the limit commencing with which 

 the real vein may be compared, in its continuous part, to the 

 corresponding imaginary vein (§ 'J3 and 74) ; in other words, 

 let us suppose the charge to be so inconsiderable, or the diameter 

 of the orifice to be so great, that the movement of transference, 

 in the extent of the continuous part of the real vein, is not per- 

 fectly uniform. The vein will also then tend to become thinner 

 from above downwards, and this diminution in thickness will 

 become visible upon the limpid portion. The question of the 

 laws which under these circumstances must regulate the length 

 of the continuous part, is very complicated ; we shall, however, 

 attempt to elucidate it to a certain point. 



Let us consider a division of the vein at the instant at which 

 its upper extremity passes the contracted section. The two 

 liquid sections between which the division in question is com- 

 prised separate from this position with different velocities ; for, 

 in the short path which the inferior section has traversed, its 

 velocity is even slightly augmented by the action of gravity. 

 Now it follows from this excess of velocity and the acceleration 

 of the motion, that the two sections will continue to separate 

 from each other more and more in proportion as they descend ; 

 or, in other words, that the portion of the liquid included be- 

 tween them will gradually become elongated during its motion 

 of transference. Consequently, if no other cause intervened, 

 each of the divisions, conveyed by the accelerated velocity of the 

 liquid, would gradually increase in length up to the instant of 

 the rupture of the line, and would preserve a constant volume 

 during its descent. 



