WITHDRAWN FROM THE ACTION OF GRAVITY. 297 
the molecules of the liquid to undergo these alternate 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 conginuous portion would be longer than in the cor- 
responding imaginary vein; whence it follows, 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 por- 
tion, 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 considered, 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 accele- 
rated velocity of the liquid; but it would be difficult to decide, @ priori, 
whether this intermediate velocity preserves any retardation or whether it pre- 
sents any acceleration. However, admitting that retardation exists, the latter, 
tending evidently to diminish the length of the continuous portion, would pro- 
duce an influence in the same direction as the above two former; and sup- 
posing, on the contrary, that acceleration occurred, this would produce an influ- 
ence in the same direction as the third. 
78. To sum up, then: when the charges are less considerable than those 
which would render the movement of transference of the liquid perfectly uni- 
form in the continuous part of the vein, two opposite kinds of influences affect 
the law, according to which the length of this continuous portion varies with 
the charge, the first tending to make this length increase more rapidly than the 
square root of the charge, whilst the second, on the contrary, teuds to make it 
increase less rapidly. Now in virtue of their opposition, these two kinds of in- 
fluences will mutually neutralize each other to a greater or less extent; but in 
accordance with the diversity of the immediate causes which respectively pro- 
duce each of these influences, complete neutralization must be regarded as very 
improbable; which leads us to the former conclusion, that, when the charges 
are sufficiently weak, the law in question will differ from that of Savart; but 
it will be impossible to decide @ priori in what direction. 
In the second place, the primary cause of all the influences which we have 
mentioned being the acceleration of the movement of the liquid, it is ciear that 
the resulting action of those which act in the same direction, considered sepa- 
rately, decreases in proportion to the augmentation of the charge, and may be 
neglected, commencing with the first of the charges under which the movement 
of the liquid becomes perfectly uniform in the continuous portion. Now what 
remains of the mutual neutralization of the two resulting opposed actions is 
necessarily less, and probably considerably so, than each of them in particular; 
whence we must believe that this excess may be neglected, commencing with 
a much less charge. We then arrive at this second conclusion, that Savart’s 
first law will undoubtedly begin to be true in the case of a charge which will 
still leave a very marked acceleration in the movement of transference of the 
liquid in the continuous portion. 
Lastly, this result, in connexion with a principle which we have established 
at the end of § 73, furnishes us with a third conclusion, viz., that the charge at 
which the vein begins in reality to satisfy Savart’s first law will be less in pro- 
portion to the size of the orifice; for it is evident that, in passing from one 
orifice to the other, this charge must vary in the same manner as that at which 
the acceleration of the movement of the liquid may be neglected. - But I Ey 
further, that the variation in question will very probably take place in a much 
greater proportion than that of the diameters of the orifices. 
For, let 2’ be the charge with which the approximative uniformity of the move- 
ment of transference begins in the case of a given orifice and liquid, and 6’ the 
