WITHDEAWN FROM THE ACTION OP GRAVITY. 219 



it ahvaya liolds within it a multitude of small bubbles of alcoholic liquor, wliicli 

 borne along by the oil that surrounds them, render the movements of the difter- 

 ent points of the mass perfectly observable. Now, if the experiments which 

 we have described be repeated with the aid. of a sphere of oil thus tilled with 

 alcoholic bubbles, the following results are observed. So long as we give to 

 the disc such slight velocities only as are sufficient to produce a simple flatten- 

 ing, there is not a great diiference of angular velocity between the portions 

 next to the axis and the portions adjoining the equator ; but this ditlerence 

 becomes very considerable when the disc turns more ra-pidly, and the bourrelet 

 and the ring are developed. 



We may thus prove, by means of the small alcoholic bubbles, that the mean 

 angular velocity is established in the ring once formed, and that all the points 

 of the latter perform their revolutions in the same time. 



Furthermore, in our experiments upon the masses of oil, there are two foreign 

 fofces which act, in addition to the causes which we have noticed, to facilitate 

 the development of the bourrelet and of the ring. One is the resistance of the 

 ambient liquid, which contributes to weaken the angular velocity of the equa- 

 tor of the mass ; the other is the action of the hand which keeps up the motion 

 of rotation of the disc, and consequently hinders the central portions of the 

 mass from participating gradually in the slackening of the equatorial portions. 

 But that which is produced by these two foreign forces would be equally pro- 

 duced by a greater initial velocity of rotation if we could annul them. 



IS. When, by the aid of a moderate velocity of the disc, we limit ourselves 

 to producing the flattening of the mass, the two foreign forced of which we have 

 just spoken necessarily hinder the latter from attaining an angular velocity 

 equal in all its points, even though we keep turning the disc. The result is, 

 that the mass cannot take exactly the figure which would correspond to that 

 equality of angular velocity. That which it adopts is a figure of revolution ; 

 but on placing the eye at the height of the centre of the mass, it is easily recog- 

 nized that it is not an ellipsoid. The curvature at the equator is too small, 

 and this is the more evident in proportion as the flattening is more consider- 

 able. 



Now, is this difference between the figure thus produced and that which would 

 correspond to the case of universal gravitation solely the result of the action of 

 the two foreign forces in question, or is it in part caused by the difference of the 

 laws which the two kinds of attraction follow ? In other words, if we could 

 eliminate or render insensible the difi"ereuces of angular velocity of the several 

 parts of the mass of oil, would the figure produced be an ellipsoid or not? Now, 

 we should render these differences of angular velocity insensible if we could 

 impress a movement of rotation on a mass of oil suspended in an isolated man- 

 ner, without interior system, in the alcoholic liquid, and then leave it to itself. 

 In this case the resistance of the ambient liquid would be exercised, indeed, 

 on the exterior of the mass ; but nothing maintaining the constancy of velocity 

 of the central parts, these, by virtue of the strong self-adherence of the oil, 

 would participate eventually in the slackening of the exterior portions, and we 

 might consider the mass as having each Instant an angular velocity equal 

 throughout. 



Now, it is very easy to realize the above by availing ourselves of the fact 

 that, when the ring of oil is formed, it returns, after some time, upon itself, (§11.) 

 At the instant when the ring is well developed, and when we have just stopped 

 the disc, we lift the latter cautiously by means of the metallic stopper which 

 bears its axis. Then the mass of oil, which is again formed by the return of 

 the ring upon itself, continues still to repilve for some time, completely isolated 

 the ambient liquid. Its figure is then, as well as the eye can judge of it, a 

 perfect ellipsoid of revolution, which gradually approximates to a sphere in 



