696 PLATEAU ON THE PH^ENOMENA OF A FREE LIQUID MASS 



the above two former; and supposing, on the contrary, that 

 acceleration occuiTed, this would produce an influence 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 uniform 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 contraiy, tends to make it increase less rapidly. Now 

 in virtue of their opposition, these two kinds of influences 

 will mutually neutralize each other to a greater or less extent ; 

 but in accordance with the diversity of the immediate causes 

 which respectively produce each of these influences, complete 

 neutralization must be regarded as very improbable ; which leads 

 us to the former conclusion, that, when the charges are suffi- 

 ciently weak, the law in question will differ from that of Savart; 

 but it will be impossible to decide a priori in what direction. 



In the second place, the primary cause of all the influences 

 which we have mentioned being the acceleration of the move- 

 ment of the liquid, it is clear that the resulting action of those 

 which act in the same direction, considered separately, 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 neu- 

 tralization 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, com- 

 mencing 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 transfei*ence 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 proportion 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 



