Chap. XVI.
HYDROSTATICS.
1097
I i* \
Although the columns EM, MG, G O, O I, IQ, QD, appear to unite themselvesagainst BE to surmount it, this latter is not in equilibrio with all the others, together orseparately, because they are divided among themselves, each tending to raise the other; thatis to say, the columns EM, M G, GO, () I, IQ, in likemanner unite with the first B E, against the single oneQD, because if each of these columns be opposed by allthe others, it is also supported by the others, and actsagainst each in particular: whence it follows that thecolumn E L, C D, composed of several small ones, lias nomore advantage over the single one B E than this hasover the preceding, which proves that a column of liquid,however large it may be, balances the last thread of thesame liquid when both are level, because the largercolumn is composed of threads similar to the first, whichoppose each other, and unite with the first against eachother as they all united against the first: all thecolumns of the same liquid are then in equilibrio, theirsurfaces are level, and as their surfaces are level, thesecolumns are in equilibrio.
If the vessel be of any other form than prismatic, it is only ne-cessary to conceive it divided by horizontal sections from thebottom X to the edge A C, in such a manner that each sectionmay be regarded as a small prism; pouring the liquid gentlyalong the edge of the vessel, it will level itself in the prism R X T;then in the second, N P, having the first for its base ; then in thethird, I O, which has the second for its base, and so on to thelast, A C.
If we have a siphon, whose branches A B, C D, E F, G H, wesuppose vertical, and of the same size, it cannot be doubtedthat the liquid poured into the first branch, A C, to a certainheight, L M, will mount in another branch, E G, to a heightN O, equal to the preceding; for on account ofthe pipe of communication CIKF, the co-lumn LC will raise the column NG until itis in equilibrio with it. These two columnsbeing equal in size, they must also be of thesame height, to weigh equally the two tubesA C and E G being to be regarded as the scalesof a balance which contain equal weights, andthe pipe of communication as the beam roundwhich the two columns of water are in equi-librio, and consequently their surfaces level.
M ith regard to the pipe of communication, itis evident that its length does not affect theequilibrium of the two columns: we may regard it as not existing, that is to say, as if thetwo branches of the siphon were contiguous, separated only by a diaphragm, for as long asthe communication is horizontal, the water contained cannot increase in one branch to theprejudice of the other.
If the first column A B C D were less than the second E F P Q, tlie columns of the sameliquid, KC and MP, would not the less be in equilibrio; for if we cut off from thesecond column another, M G, of the same size as the first, it is evident that the latter will
Fig. 1659.
Fig. 1660.
A n
Fig. 1661.
only have to oppose MG, which has the same base as itself: since the column MGwill be in equilibrio with the rest of the liquid of the branch E P, and also with thecolumn K C, the latter will be in equilibrio with the whole column MP.