328 Mr. H. S. Allen on the Motion of 



small, the surface-tension is great enough to keep its form 

 sensibly spherical. Further, any effect due to the existence 

 of waves on the surface has to be disregarded. 



All these effects would have to be considered in a complete 

 solution of the problem ; but it appears certain that in the 

 slow motion of a small bubble they would enter only as cor- 

 rections to the velocity calculated for a solid sphere with a 

 definite amount of slipping at the surface. 



5. Method of determining the Velocity of Small Bubbles. 



The apparatus used is shown in the diagram (fig. 1) . A is 

 a long glass tube whose bore is very large compared with the 

 diameter of the bubbles observed. It is closed at the lower 

 end by a cork through which pass two tubes, one serving to 

 draw off the liquid, and the other to furnish the bubbles. This 

 second tube ends within the receiver in a fine capillary tube, 

 while outside it is connected with a pressure-tube containing 

 mercury. 



The method of procedure for the production of bubbles is as 

 follows: — The pressure-tube, including the lower part of the 

 T-piece, is filled with mercury, and the pinch-cock is closed. 

 The capillary tube, made by drawing out one end of a short piece 

 of clean tubing of the same bore as the T-piece, is securely 

 attached to the upper end of the latter by a rubber joint. 

 The cork is then inserted and the receiver filled with the 

 liquid to be used. By raising the pressure-tube and opening 

 ike pineh-eock the air enclosed in the vertical limb of the 

 T-piece is driven out in a stream of bubbles. The pressure- 

 tube is lowered until this stream just ceases, and the pinch- 

 cock is again closed. The pressure of the fingers on the 

 rubber tube is then sufficient to form the bubbles when 

 required. In this way single bubbles or groups of two or 

 three can be detached at will. The bubbles are so small that 

 the air enclosed is sufficient to produce a very large number ; 

 but if necessary more air can be introduced by lowering the 

 pressure-tube and opening the clamp at the free end of the 

 T-piece. 



As the pressure employed in starting the bubbles is some- 

 times as much as an atmosphere, care must be taken to see 

 that all joints are perfectly secure. 



There is a considerable fascination in watching the forma- 

 tion and ascent of these bubbles. The smaller bubbles ascend 

 with extreme steadiness ; but when large bubbles are formed 

 from a comparatively wide capillary they ascend in a spiral 

 curve round the tube, and are seen to be in continual 



