220 THE FIGURES OF EQUILIBRIUM OF A LIQUID ' MASS 



proportion as tlic rotatory motion becomes weaker.* Thus, the difference of 

 the laws wliich govern the two sorts of attraction appears not to influence the 

 nature of the hgure taken by the mass that turns upon itself. 



19. A liquid mass can only assume and preserve an annular form under the 

 influence of a suflicient centrifugal force. 'J'hus, as we have seen, when the 

 resistance of the alcoholic liquid has diminished below a certain limit Oic velocity 

 of rotation of the ring of oil, the latter, obeying the preponderating action of the 

 molecular attraction, returns upon itself, loses its annular form, and reconstitutes 

 itself into an entire mass, first ellipsoidal and then spherical. But if, by a 

 method which I shall describe, we prevent the ring from agglomerating thus, 

 and still leave the action of its centrifugal force to diminish, we then witness 

 the appearance of other phenomena Avell meriting interest. In order to produce 

 them perfectly, in place of the disc of 35 millimetres, a disc of about 5 centime 



* I liad expected to be able to obtain a revolving isolated mass by means of another process, 

 viz : by forming a splMe of oil in the middle of a cylindrical flask so arranged as to he able 

 to turn upon its axis ; then causing this flask thus to turn with rapidity, until all the liquid 

 within, alcoholic mixture and mass of oil, had taken the same motion; then suddenly stop- 

 ping the llask. In eiVcct, it seems that then tlio alcoholic liquor being the first to lose its 

 rotatory moti'^n by the friction against the stationary sides of the flask, a moment must 

 occur when the mass of oil maintains an excess of angular velocity over the ambient liquid, 

 and that tlien the efilects of centrifugal force upon that mass may* manifest themselves. But 

 the experiuieut gives few results. First, it is extremely difficult to keep a mass of oil in the 

 middle of the flask. We keep it tolerably in the axis of the latter, because, if we liave suc- 

 ceeded in placing it so that its centre is Iktle removed from that axis, the rotation of the am- 

 bient liquiil brings it there, and then retains it there very well. But it is not the same in the 

 direction of the height of the flask. If a homogeneous alcoholic mixture be employed, and 

 the sphere of oil is placed, beibre turning the flask, a little higher or lower than. the middle of 

 the height of the latter, it quits its place when the flask turns to ascend, in the first case, or 

 to descend, in the second, until it comes to be dispersed against one of the two bases of the 

 flask. This cflect is attributable, I think, to the fact that the two bases exercising upon the 

 sections of liquid wiiich touch them a motive action much greater than that to which the 

 parallel sections of the interior of the mass are subjected, there ensues near these bases, at 

 the commencement of the rotation, an excess of centrifugal force which determines a ten- 

 dency upwards and downwards of the liquid near the axis. It is therefore necessary to en- 

 deavor to place the sphere of oil in a position very near to the midclle of the height of the 

 vessel. Unfortunately we cannot use for this purpose the process of superposition of the al- 

 coholic layers of unequal density, (ij 9;) for then, in the rotation of the flask, the denser in- 

 ferior layers come necessarily, by the excess of centrifugal force which results from their ex- 

 cess of density, to rise against the sides, causing the less dense liquid to occupy the axis; and 

 in this movement the mass of oil is drawn downwards, and is also dispersed upon the bottom 

 of the vessel. 



By employing a homogeneous alcoholic mixture and a sphere of oil of only about three 

 centimetres diameter, I liowever succeeded several times, by dint of patience, in giving to 

 this sphere a suflicieutly exact ])osition in the flask to be able to keep it at the same height 

 until it had itself taken the rotatory movement of the whole system. But then, when I 

 stopped the flask, a violent internal agitation was produced, which almost alwa3^s dispersed 

 the oil in innumerable spherules througliout the alcoholic liquid, or at least destroyed its form 

 in a completely irregular manner. I attribute these effects to the following cause. When 

 the flask is stopped, the portions of the alcoholic liquid which touch the sides and bases, losing 

 first their centrifugal force, the more internal portions, which still retain theirs, make their 

 way through them, dividing them, and this confusion is soon propagated to the axis, where 

 it gives rise either to the dispersion or to the irregular disfiguring of the mass of oil. 



In the cases in which I have been able to give a suitable position to the sphere of oil, I 

 "have observed a curious eftect; namely, that in the first instance of tlie rotation of tlie vessel 

 the mass of oil quits the spherical form, and becomes elongated in the direction of the axis 

 of rotation. This elongation is easy explained : the movement of rotation is communicated 

 to the j)ortions of the mixture which are nearest tlie axis above and below the mass of oil, 

 before being able to communicate itself witli the same intensity to the latter: hence, in the 

 different points of tins mass, there must result a less centrifugal force than in the points of 

 the alcoholic mixture sitiuited at the same distances from the axis of rotation. Thence a rush 

 of the oil to the axis, and an elongation of the mass of the latter in the direction of this same 

 axis. ]5ut, on continuing the rotation, the 41 comes to receive the same movement as the 

 surrounding liquid, and it also resumes gradually the spherical form. 



On stopping the flask, not suddenly, but in a rather rapid manner, I succeeded once in 

 obtainmg a result sufiiciently regular, and I observed, as I expected, the sphere become flat- 

 tened considerably in the direction of the axis of rotation. 



