WITHDRAWN FROM THE ACTION OF GRAVITY. 687 



We are therefore led to the following definitive conclusion : — 



In the case of mercury, and very probably also in that of all 

 other very slightly viscid liquids^ such as water, if for the same 

 charge increasing values are given to the diameter of the orifice, 

 from a value slightly less than a millimetre to some other deter- 

 minate value, and if the common charge be sufficiently great, 

 the length of the continuous part of the vein will be propor- 

 tionate to the diameter of the orifice. 



This conclusion is perhaps true in the case of any liquid what- 

 soever ; but the elements for deciding this question are wanting. 



Thus, with the restrictions contained in the above ermncia- 

 tion, the second law given by Savart results necessarily from the 

 properties of liquid cylinders ; and it is also evident, that if, in 

 the case of a common inconsiderable charge, the law becomes 

 modified, it must approximate towards that of Savart in propor- 

 tion as the value given to this charge is greater. 



75. We said (note to § 72) that we should return to the closely 

 approximative principle of equality between the length of the 

 continuous part of an imaginary vein and the corresponding 

 distance D, in order to establish this principle more clearly ; we 

 shall now do this. 



Let L be the length of the continuous part, and C the portion 

 common to this length and the distance D ; let also s be the in- 

 terval between the origins of the lengths L and D, i. e. the small 

 distance comprised between the orifice and the contracted sec- 

 tion ; and lastly, let i be the interval between the terminations 

 of these same lengths, i. e. the distance comprised between the 

 uppermost point of the rupture of the line and the middle of 

 this line ; we shall then have 



L=C + s, 



D = C + i; 



consequently 



L — D=«— i; 

 whence 



D=' + ^-? (>•) 



Let us now first approximatively value the quantity i in the 

 case of some particular liquid, and let us again take mercury. 

 After what was shown at the commencement of the preceding 

 section, the length of the divisions of an imaginary vein is equal 

 to the normal length of those of a cylinder of the same diameter 



3 A 2 



