the Motion of Spheres through Liquids. 759 



Method and Apparatus. 



If from the observed times of fall of spheres of various 

 sizes we compute the apparent viscosity coefficient of the 

 liquid by Stokes's law, and if we plot these values as functions 

 of the radii, we should be able to determine the radius 

 at which the computed values begin to depart from the 

 actual value as determined directly by the capillary tube 

 method. 



Spheres. — Among the kinds of spheres used may be men- 

 tioned mercury, platinum, iron, Rose metal, wax, spheres of 

 oil in water, and spheres of water in oils. Mercury proved 

 unsatisfactory for several reasons, especially because of the 

 difficulty in diameter measurements. Iron and platinum 

 spheres could be obtained only in large sizes, and were used 

 merely to check other observations. The most satisfactory 

 results were obtained witli spheres of wax and of Rose metal. 

 The method of making these spheres will be referred to 

 later. 



Temperature.— As the change of viscosity with temperature 

 is very rapid in the more viscous oils, it is important that 

 the temperature be maintained constant to within at lea>t 

 one-tenth of a degree during the experiments. This was 

 done by means of an electric heater and a fan for maintain- 

 ing the circulation of the air. With this arrangement the 

 temperature as shown by a thermometer strapped to the fall 

 tube could be maintained with the desired degree of accuracy 

 for indefinite periods, providing that the room was always 

 slightly warmer than the outdoor air. 



The Fall Tubes. — Three glass tubes were used of lengths 

 about TO cm., and of internal radii A = 022 cm., B = 0*547 cm., 

 C = l*63 cm. These were etched with fine lines as nearly as 

 possible at right angles to their axes, and were mounted 

 vertically in adjustable supports. With the adjustment 

 properly made the spheres fell very accurately along the 

 axes of the tubes, but check experiments showed that even a 

 very considerable deviation from an axial course produced 

 no noticeable change in velocity. 



Velocity. — To comply with condition (5) it is necessary to 

 work with small velocities. There are three factors by which 

 this may be brought about ; a liquid may be chosen with a 

 very high coefficient of viscosity ; the spheres used may be 

 of nearly the same density as the liquid ; or spheres may be 

 used of extremely small radii. In practice these three 

 factors must be so balanced as to minimize the total error 

 introduced in the three measurements. In timing a stop- 



