a Sphere in a Viscous Fluid. 529 



also made 4" 5 centim. in diameter. The vessel was connected 

 by a siphon with a large vessel of water, so as to keep the 

 water-level nearly unaltered when this tube was filled by 

 suction. 



Table VIII. 

 Steel Balls in Water. — Large Vessel. 





Weight W. 



logW. 



Radius a. 



log a. 



Velocity V. 



logV. 

 21245 



log «V. 



Temp. 

 10°-8C. 



I.... 



gin. 

 2010 



•3034 



cm. 



•3961 



1-5978 



cm ./sec. 

 133-2 



1-7223 



II.... 



1-036 



•0153 



•3173 



F5015 



126-3 



2-1016 



1-6031 



ll°-7 0. 



III.... 



0-7006 



1-8455 



•2786 



T4449 



1205 



2-0808 



1-5257 



12°6 C. 



IV.... 



0-4354 



T-6389 



•2379 



T3764 



110-5 



20432 



1-4196 



12°4 O. 



v.... 



02542 



T-4051 



•1993 



P2996 



100-5 



20020 



1-3016 



11°-4C. 



VI.... 



0-1316 



1-1192 



•1590 



F-2014 



909 



1-9586 



1-1600 



ll°-5 0. 



1 



The observed velocities are given in Table VIII., which 

 also contains the radius and weight of each ball. 



These velocities were all obtained from a fall of more than 

 34 centim. 



A. comparison of these results with those already given in 

 Table VII. for the same balls falling in a smaller vessel, shows 

 that the effect of increasing the width of the vessel from 

 3 centim. to 6 centim. is to increase the velocity by only 

 about 4 per cent. Hence we may fairly conclude that in the 

 larger vessel the circumstances attending the fall do not 

 differ in any material respect from those in an infinite fluid 

 for a corresponding fall, and that even if the velocities could 

 be still further increased by increasing the size of the vessel, 

 the manner in which the velocity depends on the size of the 

 sphere would not be affected. 



11. Law of Resistance. 



In order to determine from these results the relation 

 between the resistance and the velocity of the sphere, re- 

 course was had to the method of logarithmic coordinates. 

 It has been shown that if the resistance can be represented 

 by a single term, it must be proportional to (aV)". 



The values of log aV were calculated and employed as 

 ordinates, while the abscissae were given by the values of 

 log W, since for spheres of the same density the resistance is 



