1893.] Gravity of Fluid Bubbles through Liquids. 



15 



But in most of the experiments made the viscosity of the liquid 

 of which the column was composed was so much greater than that of 

 the bubble that the following form proved sufficiently accurate : 



-i . . 



~ *^ 84 5 



The value of these constant coefficients could be experimentally 

 found by a series of determinations of velocity through different 

 sized tubes, the same two substances being used throughout. 



Taking only three terms of the series, I have done this for the case 

 of air bubbles ascending through columns of glycerine of different 

 diameters, and I find that the constants thus determined are practically 

 the same as those required by my experiments Avith other substances. 

 Thus three terms would appear to be ample. 



In the following table is exhibited the time taken by a bubble of 

 air to ascend 1 cm. (the reciprocal of the velocity) through a column 

 of glycerine, the diameter of which is given in the top row. 



Table I. Air Glycerine. 



The third row was calculated by using the values of the constants 

 given below, which were themselves deduced from the second row by 

 the method of least squares. 



A! = 1-308 . gift 

 A 3 = 0-02322 . < 

 A 3 = 0-0009108 . 



The difference in density was 1*25, and the surface tension 63 dynes 

 per centimetre. Temperature was that of the air, and ranged between 

 10 and 14. For some sized tubes the agreement between the 

 observed and the number calculated is not good, but this is probably 

 due to variations in temperature. The viscosity of glycerine varies 

 rapidly with temperature. The importance of constant temperature 

 was not appreciated until most of the experiments made had been 

 completed. 



Having once determined the constant coefficients, it becomes possi- 

 ble to calculate the velocity of a bubble of any substance through a 

 tube of glycerine of given diameter. The only things now requisite 



