336 Mr. H, S. Allen on the Motion of 



6. Terminal Velocities attained by Solid Spheres. 



As long as we are restricted to comparatively small 

 velocities, less for instance than 10 centim. per second, it is 

 necessary to employ spheres of small radius, unless the density 

 of the sphere is very nearly the same as that of the liquid. 

 In the latter case great precautions must be taken to ensure 

 the temperature remaining constant from place to place, and 

 from time to time. 



A series of experiments were made with spheres of pure 

 paraffin, of specific gravity 0U07. The spheres were formed 

 by melting a small piece of paraffin in a mixture of alcohol 

 and water whose density was adjusted so as to be the same 

 as that of the melted paraffin. On shaking the warm mix- 

 ture the paraffin broke up into a large number of small 

 globules which solidified without losing their spherical form. 

 The most perfect spheres were selected for the experiments, 

 and their diameters were measured under the microscope. 



These spheres were allowed to rise in a wide tube inverted 

 in a basin of liquid and filled by suction at the upper end. 



The first experiments were made on paraffin spheres rising 

 through water. As the water did not wet the spheres it was 

 found impossible to avoid small air-bubbles clinging to them 

 and travelling with them up the tube. Irregularities were 

 thus introduced into the result which prevent great importnnce 

 being attached to them. However, the observations when 

 plotted are found to cluster round the line represented by the 

 empirical formula. 



Better results were obtained from experiments on the 

 ascent of paraffin spheres in aniline, although in this case also 

 care had to be exercised to prevent the presence of air- 

 bubbles. The results are given in Table IV. The critical 

 radius is about '051 centim. 



In order still further to test the applicability of the formula 

 six small amber spheres were turned for me by a working- 

 jeweller, with what success is shown by the maximum varia- 

 tions from the mean radius given in Table V- Amber was 

 selected for these spheres because its density is slightly 

 greater than that of water. The density was determined by 

 finding that of a saline solution in which the spheres would 

 neither rise nor sink. The observed velocities and those 

 calculated from the empirical formula are given in the last 

 two columns. Although the agreement in some cases is far 

 from good, it is still sufficiently striking when we consider 

 that the formula was derived from observations on air-bubbles 

 ascending in water. 



