12 Mr. F. T. Trouton. On the Motion under f June 1, 



IV. " On the Motion under Gravity of Fluid Bubbles through 

 Vertical Columns of Liquid of a different Density." By 

 F. T. TROUTON. Communicated by Professor FITZGERALD, 

 F.R.S. Received May 3, 1893. 



The kind of motion herein referred to can be observed by means 

 simply of a glass tube, closed- at one end, and provided with a stopper. 

 If the tube be filled with water to nearly the top, closed, and then 

 placed upside down, the enclosed bubble of air while ascending to 

 the top can be observed, and the speed of ascent ascertained between 

 two measured marks. 



By enclosing different volumes of air it was found that the speed 

 depended on the length of the bubble. The relation connecting the 

 volume of the bubble with its speed of ascent was experimentally 

 investigated. The speed, as will be seen from experiments subse- 

 quently described, may be taken within limits as a periodic function 

 of the volume of the bubble. Bubbles greater than a certain thing 

 all have the same velocity. 



Experiments have also been made with other liquids. By mixing 

 two liquids, such as water and glycerine, a series of determinations 

 of speed with liquids of gradually increasing viscosity can be made. 

 In these experiments the size of the bubble was outside the periodic 

 limit. Contrary to expectation it was found that as the viscosity of 

 water was increased by adding glycerine, the velocity increased 

 instead of diminished. With tubes of about 0*7 cm. in diameter, it 

 is not until the viscosity of the solution used is about eight times 

 that of water that the velocity comes to be less than that through 

 pure water. From this state the velocity was found to be inversely 

 proportional to the viscosity of the solution, other things the same. 



Instead of air the bubble may be of some liquid which does not 

 too readily mix with that of which the column consists. In this 

 way experiments were made to investigate the relation between the 

 speed of ascent and the difference in density of the liquids, and also 

 whether surface tension may have any influence. 



The consideration of the subject may then conveniently be divided 

 into two parts. The first part will deal with the dependence of the 

 speed with which the bubble travels through the liquid column on 

 the physical properties of the two fluids concerned in the phenomenon. 

 The second part will refer to the connexion between the size or 

 volume of the bubble and its speed. 



