EXPERIMENTAL AND THEORETICAL RESEARCHES 
ON 
THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
WITHDRAWN FROM THE ACTION OF GRAVITY, &c. 
BY J. PLATEAU, PROFESSOR IN THE UNIVERSITY OF GHENT. 
TRANSLATED FOR THE SMITHSONIAN INSTITUTION FROM THE MEMOIRS OF THE ROYAL ACADEMY OF 
° BRUSSELS. 
SECOND SERIES. 
(CONTINUED FROM PAGE 285, SMITHSONIAN REPORT FOR 1863.) 
Application of the properties of liquid cylinders: theory of the constitution of 
liquid veins emitted from circular apertures. 
69. Let us now pass to the application which we have announced of most of 
the foregoing facts and laws. 
Let us consider a liquid vein flowing freely by the action of gravity from a 
circular orifice perforating the thin wall of the horizontal bottom of a vessel. 
The molecules of the liquid within the vessel, which flow from all sides towards 
the orifice, as we know, still retain, immediately after their exit, directions 
which are oblique to the plane of this orifice; whence there is produced a rapid 
constriction of the vein, commencing at the orifice and extending as far as a 
horizontal section, which has been improperly denominated the contracted sec- 
tion. When the molecules have arrived at this section, which is very near the 
orifice, they all tend to assume a common vertical direction, with a velocity cor- 
responding to the height of the liquid in the vessel; and they are, moreover, 
urged in this direction by their individual gravity. Hence, supposing the orifice 
to-be circular, the vein commencing at the contracted section tends to form an 
almost perfect cylinder, of any length; but this form is modified, as we now 
know, by the acceleration which gravity imparts to the velocity of the liquid, 
and the diameter of the vein, instead of being everywhere the same, decreases 
more or less in proportion as we recede from the contracted section. 
If the causes which we have detailed were alone in action, the vein would 
appear simply more and more attenuated in proportion as it is considered more 
distant from the contracted section, without losing either its limpidity or its 
continuity. But it results from our experiments, that a liquid figure of this 
kind, the form of which approximates to that of a very elongated cylinder, 
must become transformed into a series of isolated spheres, the centres of which 
are arranged upon the axis of the figure. In fact, we have here a liquid sub- 
mitted to the action of gravity; but it is evident that during the free descent 
of a liquid, gravity no longer presents any obstacle to the play of the: mole- 
cular attractions, and that the latter must then exert the same configuring 
actions upen the mass as if this mass were free from gravity and in a state of 
rest; this is the manner in which, for instance, drops of rain, during their fall, 
acquire the spherical form. But, for the preceding conclusion to be perfectly 
ERRATUM.—At page 207 of the Smithsonian Report for 1863, sixth line from the bottom, 
for “‘less than an,inch in a year,” read ‘‘less than an inch in a day.” Ag JE 
