since the internal fluid-pressure is also everywhere identical, that the expression (1ã₤ãã₤ R ã₤+ã₤1ã₤ãã₤ Rÿ£¢ãý ) for the cylinder is equal to the corôÙreôÙsponôÙding expression, which we may call (1ã₤ãã₤ r ã₤+ã₤1ã₤ãã₤ rÿ£¢ãý ), in the case of the terminal spheres. But in the cylinder 1ã₤ãã₤ Rÿ£¢ãý =ã₤0, and in the sphere 1ã₤ãã₤ r =ã₤1ã₤ãã₤ rÿ£¢ãý . Therefore our relation of equality becomes 1ã₤ãã₤ R =ã₤2ã₤ãã₤ r , or r =ã₤2ã R ; that is to say, the sphere in question has just twice the radius of the cylinder of which it forms a cap.
And if Ob, the radius of the sphere, be equal to twice the radius (Oa) of the cylinder, it follows that the angle aOb is an angle of 60ô¯, and bOc is also an angle of 60ô¯; that is to say, the arc bc is equal to (ÿ£¢1ÿ£¢ãÿ£¢3)ãü. In other words, the spherical disc which (under the given conditions) caps our cylinder, is not a portion taken at haphazard, but is neither more nor less than that portion of a sphere which is subtended by a cone of 60ô¯. Moreover, it is plain that the height of the spherical cap, de,
where R is the radius of our cylinder, or one-half the radius of our spherical cap: in other words the normal height of the spherical cap over the end of the cylindrical cell is just a very little more than one-eighth of the diameter of the cylinder, or of the radius of the