WITHDRAWN FROM THE ACTION OF GRAVITY. 705 



with regard to our imaginary veins. Now I say that the sound 

 produced by a true vein will not differ from that which the cor- 

 responding imaginary vein would produce, if the charge is suffi- 

 cient relatively to the diameter of the orifice for the velocity of 

 transference of the liquid to augment very slightly from the con- 

 tracted section to a distance equal to the length of the divisions 

 of the imaginary vein. Then, in fact, within this extent, the two 

 causes which tend to modify the length of the divisions (§ 76), 

 i. e. the acceleration of the velocity of the liquid and the resulting 

 diminution in the diameter of the vein, will both be very small ; 

 and as they act in opposite directions, their resulting action will 

 be insensible, so that the divisions will freely acquire at their 

 origin the length corresponding to that of the corresponding 

 imaginary vein ; now it is clear that in this case the number of 

 divisions which will pass in a given time to the contracted sec- 

 tion will be the same in the real and the imaginary vein ; con- 

 sequently the sounds produced by both the veins will also be 

 identical. 



But in confining ourselves to very slightly viscid liquids, as 

 Mater, we know that the relation between the normal length of 

 the divisions of a cylinder imagined to exist under the conditions 

 of our laws and the diameter of this cylinder, must very pro- 

 bably differ but little from 4 ; consequently the same applies to 

 the relation between the length of the divisions of an imaginary 

 vein formed of one of these liquids and the diameter of the con- 

 tracted section of this vein. If, then, in a true vein formed 

 of one of these liquids, the increase in the velocity of trans- 

 ference is very slight at a distance from the contracted section 

 equal to 4 times the diameter of this section, the condition laid 

 down above will very probably be satisfied ; however, to avoid 

 any chance of being deceived, we will take, for instance, 6 times 

 this diameter. 



It is moreover clear, that if the condition, thus rendered pre- 

 cise, is fulfilled with regard to a given charge and orifice, it will 

 be so a fortiori for the same orifice and greater charges, and for 

 the same charge and smaller orifices. We arrive then at the 

 following conclusions : — 



I. When a series of veins, formed of a very slightly viscid 

 liquid, flow successively from the same orifice and under different 

 charges, if the least of them is sufficient for the velocity of trans- 

 ference of the liquid to augment very slightly, as far as a distance 



