VOL. XXVII.] PHILOSOPHICAL TRANSACTIONS. Qyg 



Prop. II. The Point of Contact between a Sphere and a Plane is infinitely 

 greater than that between a Circle and a Tangent. — Let a be the point of con- 

 tact between the sphere adqf and the plane bc, fig. 9. About the sphere de- 

 scribe the cylinder npgm. Draw kh to represent a circle parallel to the plane. 

 Let the circle be supposed to move, till it becomes coincident with the plane. 

 The cylindrical surface khgm will always be equal to the spherical surface dap. 

 Now when these surfaces become infinitely small, one terminates in the point of 

 contact, and the other in the periphery of the base of the cylinder. Therefore 

 the point of contact is equal to the periphery of the base of the cylinder, equal 

 to a periphery which has the same diameter as the sphere, and by consequence is 

 infinitely greater than any point of contact between a circle and a tangent. 



G. E. D. 



Prop. III. The Points of Contact by Spheres of different Magnitude, are to 

 each other as the Diameters of the Spheres. — For by the 2d prop, the points of 

 contact are equal to the peripheries of such diameters ; whose proportion is the 

 same as the diameters. 



An Experiment, concerning the Angle required to suspend a Drop of Oil of 

 Oranges, at certain Stations, between tivo Glass Planes, placed in the form of 

 a IVedge. By Mr. Fr. Hauhsbee, F. R. S. N° 334, p. 473. 



I procured two glass planes, that measured a radius of 20 inches each ; their 

 breadth was about 3 inches : that which I used for the lower plane, was placed 

 with its surface parallel to the centre of its axis, and to the horizon. The 

 planes being very clean, they were rubbed with a linen cloth dipped in oil of 

 oranges : then a drop or two of the same oil being let fall on the lower plane 

 near the axis, the other plane was laid on it ; and as soon as it touched the oil, 

 the drop spread itself considerably between both their surfaces. Then the upper 

 plane being raised a little at the same end by a screw, the oil immediately at- 

 tracted itself into a body, forming a globule contiguous to both surfaces, and 

 began to move toward the touching ends. When it had arrived 2 inches from 

 the axis, an elevation of J 5 minutes at the touching ends stopped its progress, 

 and it remained there without motion any way. The planes being let fall again, 

 the drop moved forward till it came to 4 inches from the centre ; then an ele- 

 vation of 25 minutes was required to give it a fixed station. At 6 inches it re- 

 quired an angle of 35 minutes ; at 8, of 45 minutes ; at 10, a degree. At 12 

 inches from the axis, the elevation was 1 degree 45 minutes ; and so on, at the 

 several stations, as they stand in the annexed table. This after numerous trials, 

 I take to be the most correct, though the others succeeded very nearly the 



