the Motion of Spheres throtifjh Liquids. 7G9 



admitted to the main tube until any turbulence introduced 

 by inverting the tube should have subsided. The procedure 

 then consisted in obtaining a small bubble in the s'em, in- 

 verting the tube, and timing the transits across fine lines 

 etched on the main tube. The tube \yas again inverted and 

 the bubble allowed to come to rest when about one-third of 

 the return distance had been traversed, where it was measured 

 as it rested against the side of the tube. This completed one 

 observation. The bubble was then returned into the stem 

 and the operation repeated until, owing to its erosion, the 

 bubble had become too small to follow. 



The chief errors in this method are introduced in the 

 measurement of the size of the bubble, and in the assumption 

 of no circulation in the liquid. The flattening of the bubble 

 against the side of the tube becomes noticeable with the 

 larger bubbles, hence we have to restrict ourselves to small 

 ones. The errors due to circulation need be feared only in 

 liquids of low viscosity, for observations on small specks of 

 lint introduced into the tube showed that the turbulence 

 caused by slowly inverting the tube had, in the case of the 

 more viscous liquids, completely vanished before the bubble 

 had emerged from the stem. With the less viscous liquids, 

 however, this is the main source of error. 



The square of the radius of the bubble was found to 

 diminish uniformly as the total distance traversed increased, 

 the rate of decrease being independent of the velocity, that 

 is, of the time. That this diminution is due to a surface 

 erosion similar to that observed in the passage of the drop of 

 alcohol through olive oil seems obvious, since a bubble would 

 sometimes remain for several hours at rest and show no 

 decrease in size, while one trip along the tube would result 

 in a very marked decrease. The rate of decrease is quite 

 different in different oils, but does not seem to depend 

 primarily on the amount of air contained in the oil. 



By plotting the squares of the radii as ordinates and the 

 number of trips, or the total distance traversed, as abscissae, 

 we obtain a curve from which may be determined the pro- 

 bable radius at the time when the velocity was recorded. 

 For most cases it is sufficient to take the radius as that given 

 by the curve for the point half-way between the lines of 

 transit. But with very small bubbles where the fractional 

 decrease in radius is large for a single trip, a closer approxi- 

 mation is obtained by assuming the relation di' 2 /dx=- constant, 

 and thus computing the probable radius. If a and b are the 

 radii obtained from the curve for the first and second transits 

 respectively, in any one observation, and if the ratio b 2 /a 2 is 



