•WITHDRAWN FROM THE ACTION OF GRAVITY. 685 



of the constrictions of this vein, it must pass through the same 

 forms, and accomplish its moditications in the same time as any 

 one of the constrictions which would result from the transforma- 

 tion of a cylinder of the same diameter as the vein, formed of 

 the same liquid, and placed under the conditions in question. 



Now in the case of a cylinder of mercury, the time comprised 

 between the origin of the transformation and the instant of the 

 rupture of the lines is, in accordance with one of our laws, 

 exactly or apparently in proportion to the diameter of the cylin- 

 der ; and it is clear that this law is equally applicable to any one 

 of the constrictions in particular, or even simply to its neck, as 

 to the entire figure. If, then, we suppose our imaginary vein to 

 be formed of mercury, the time which the neck of each of its 

 constrictions will occupy in arriving at the instant of the rupture 

 of the line will be exactly or apparently in proportion to the 

 diameter which the vein would possess if the divisions in it wei'e 

 not formed, i. e. to that of the contracted section. Now as the 

 cylindi-ical form of the vein supposed to exist without divisions 

 only begins at the contracted section, it is only from this part 

 that the configuring actions arising from the instability of this 

 cylindrical form commence. We must therefore admit that the 

 liquid section which constitutes the neck of a constriction, does 

 not begin to undei-go the modifications which result from the 

 transformation until the instant at which it passes the contracted 

 section ; thus the interval under consideration commences at 

 this very instant. 



But this interval, comprised between the instant at which the 

 liquid section of which the neck of a constriction is formed, 

 passes the contracted section, and the instant of the rupture of 

 the line into which this constriction becomes converted, is that 

 which we have designated by 6, and in which the liquid section 

 traverses the distance D ; in our imaginary vein of mei'cury, the 

 time 6 will therefore be in proportion to the diameter of the 

 contracted section. 



Now we know that in a liquid vein, the diameter of the con- 

 tracted section may be regarded as proportional to that of the 

 orifice when the latter exceeds 6 millims,, and that above this 

 limit the proportionality does not alter very appreciably except 

 when the diameter of the orifice becomes less than a millimetre*. 



* In fact, the results obtained by Hachctte show (Ann. de Ckim. el de Phys., 

 t, iii. p. 78) that when the diameter of the oritice is equal to or greater than 



VOL. v. PART XXI. 3 A 



