214 THE FIGURES OF EQUILIBKIUM OF A LIQUID MASS ^ 



9. The apparatus being properly arranged, the next thing is to operate so as 

 to cause a sphere of oil to surround the disc in such manner that their two 

 centres are seiisiblj coincident. To attain this point, let us first endeavor, be- 

 fore introducing the disc into the vessel, to bring the centre of the sphere to 

 remain at the height at which that of the disc should be. It would be extremely 

 diilicult to accomplish this by suspending a sphere in a homogeneous alcoholic 

 mixture, as we have hitherto supposed; for then there is no reason why the 

 sphere should not stand higher or lower ; and, if even by chance it were placed 

 exactly at the desired height, the movements which would be produced on in- 

 troducing the disc would very probably change this height. It is, therefore, 

 necessary to employ a more sure process, and the following succeeded perfectly. 

 We bt"^in by causing the alcoholic mixture to contain a small excess of alcohol. 

 Then, the vessel being furnished Avith its Hd, and the stopper which closes the 

 central opening being lifted up, the mixture is introduced by this opening in 

 such quantity that the vessel bo not completely filled. A certain quantity of 

 a mixture, less charged Avith alcohol, and marking only 16° on the areometer 

 of Beaume, is then cautiously added. This, from its excess of density, falls to 

 the bottom of the vessel, Avhere it spreads itself in a horizontal layer. The oil 

 is then introduced, which, by reason of the small excess of alcohol contained in 

 the upper mixture, descends through the latter till it rests upon the denser layer 

 of tlu; lower mixture, either in a single mass or in several partial masses (§ 4.) 

 This bein'i" so, we unite, if the case i-equires it, the isolated spheres into a sin- 

 gle one ; then Ave stii' the liquor cautiously Avith a glass rod, so as to mix im- 

 perfectly the layer at the bottom Avith the higher layers, but Avithout dividing 

 the mass of oil, and the system is then left to rest. It Avill be seen that there 

 must hence result in the alcoholic liquor a state of density increasing from the 

 U])per layers of less density to the loAver of greater density than that of the 

 oil ; and that, in consequence, the mass of oil will necessarily remain in stable 

 equilibrium Avith respect to the vertical direction, in a certain layer whose mean 

 density is equal to its OAvn. Now, in performing the operation Avith the neces- 

 sary precautions — that is to say by stirring the liquid only a very little, then 

 leaving it to rest to observe the effect which results, again stirring it and leaving 

 it to rest, and so on ; lastly adding, if necessary, a small portion of mixture at 

 16°, or of pure alcohol, according to circumstances, Ave easily succeed in causing 

 the mass of oil to remain exactly at the desired height, and, as we have seen, 

 without tcrndency to a change of position in the vertical direction.* In geome- 

 trical strictness, truly, this mass of oil cannot then be any longer perfectly 

 spherical ; it must be flattened a little in the vertical direction; but, if Ave liaA'e 

 operated so that the increase of the densities is very feeble at the height at 

 which the oil stands — and we easily obtain that result by suitable trials — -the 

 flattening in question is completely insensible to the eye, and the mass appears 

 exactly spherical. 



Fur the experiments Avhich Ave have to describe, the most convenient diameter 

 to give to the sphere of oil is about 6 centimetres. We easily accomplish this 

 by first forming a less sphere, and adding successively fresh portions' of oil, 

 Avlrich Ave unite Avith the first. 



The next thing is to place the disc. This being attached by its axis to the 

 rod Avhich passes through the metallic stopper, (§ 8,) Ave begin by oiling it as 

 well as the axis, then introduce it slowly into the alcoholic liquid, and cause it 

 to penetrate by its edge into the sphere of oil. As the disc has previously 

 been oiled, the sphere envelopes it without difficulty, and, what is remarkable, 



* Tlic3 different liquid layers thus superjiosed tend of themselves, it is tnie, to mix ; but, as 

 they arc placed in the order of their densities, this spontaneous mixture proceeds only Avith 

 extreme slowness, and it requires a great many days for the liquor to become homogeneous. 

 No incouvenicuco thcreforo results from this for the experiments 



