WITHDRAWN FROM THE ACTION OF GRAVITY. 697 



as that at which the acceleration of the movement of the liquid 

 may be neglected. But I say further, that the variation in 

 question will very probably take place in a much greater pro- 

 portion than that of the diameters of the orifices. 



For, let h' be the charge with which the approximative uni- 

 formity of the movement of transference begins in the case 

 of a given orifice and liquid, and 6' the corresponding value of 6. 

 The charge h', as we have seen, should be such that \/ Igli 

 may be very considerable in regard to g& , or, in other words, 



that the proportion — ^— may be very great. Let us now take 



an orifice of less diameter, and let A" denote the charge which 

 fulfills in regard to this second orifice the same condition as li 

 with regard to the former ; let also ^" denote what Q becomes in 

 the case of the new orifice. If we wish, in the movement of the 

 liquid, in the continuous portion of the vein which flows from 

 the latter to have the same degree of uniformity as in the con- 

 tinuous portion of the preceding one, we must evidently make 



But the time 6, at least in the case of mercury, is proportionate 

 to the diameter of the contracted section, consequently to 

 that of the orifice (§ 74) ; hence, in the case of this liquid, we 



may substitute for ^ that of the squares of the diameters of 



the two orifices ; whence it follows that in passing from any de- 

 terminate orifice to one which is less, the charge under consi- 

 deration will decrease as the square of the diameter of the orifice. 

 Now it must be considered as very probable that the weakest 

 charge at which Savart's law begins to be realized will decrease 

 in an analogous manner, i. e. in a much greater proportion than 

 that of the diameters. As we have several times stated, we 

 are not aware whether the considerations relative to mercury 

 are applicable or not to all other liquids ; but we know at least 

 that they are very probably so to all those the viscosity of which 



