54 



Mr. A. M. Worthington on the [Dec. 18, 



In what follows I shall, for convenience, call the figure that would 

 be formed by bending a cylinder into an annulus, a cylindrical annulus, 

 while the form in which the liquid that has filled a groove is left 

 on the lower plate may be called a semi-cylindrical annulus. 



It seems reasonable to suppose that the first thing that will happen 

 to the liquid when liberated will be that it will spring from a semi- 

 cylindrical into a more or less cylindrical annulus, for there is a sharp 

 curvature of the surface at the edges bounding the flat and curved 

 portions, which will at once exert a pressure on the liquid, while the 

 force which causes it to split into drops being due to an unstable 

 equilibrium* must begin with a value equal to zero, and will therefore 

 be behindhand in its action. 



Since the cylindrical annulus must have the same volume as the 



semi-cylindrical, its diameter must be x diameter of the semi- 



d 



cylindrical annulus = ^/^ according to previous notation. 



Hence, if we apply Plateau's formula for the cylinder, we have — 



I 



n— 



-6 1 x — 



\ which gives for the 'first groove, 17'48 drops. 

 „ „ second „ 17 - 38 „ 



„ „ third „ 10-44 „ 



The only notable deviation from the number actually observed, is 

 in the case of the third groove, but even here 10 - 14 is within the 

 limits of observation, and a very possible value, since the plate, as has 

 been explained, could not be lifted up quickly enough to avoid all 

 friction. 



The observations, therefore, prove that at least for an annulus of 

 mercury lying on a glass plate, the law of splitting is practically the 

 same as that of a straight cylinder of the same thickness, being ex- 

 pressed by the formula n—- — ? — . 

 F J 64 xd 



Part IL 



In order to effect the liberation of a free annulus in air, the ap- 

 paratus shown in fig. 1 was used. 



A is a circular disk of hard wood, in which two annular grooves 

 were cut, whose cross section was of the form shown in fig. 2, the 

 lower part being circular. The width of the inner groove at the 



* The symmetry of the annulus implies equilibrium as regards segmentation. 



