Resistance of the Air to Falling Spheres. 733 



In these last experiments the violence of impact of the 

 spheres on the catcher caused slight deformations, and these 

 results are consequently of a less degree of accuracy than 

 the previous ones. 



It was thought well to test whether two spheres of 

 different diameters, loaded so as to fall in the same time 

 through a certain height, would also fall in equal times 

 through other heights. This was tested in the tower for 

 different weights, and consequently for different ranges of 

 velocity ; hut no difference in behaviour could be detected 

 with certainty. Experiments in which the balls fell a 

 distance of about 7300 cm. outside the tower, appeared to 

 show that, in some cases, one sphere might fall more rapidly 

 than the other in part of the fall and less rapidly in another 

 part, but the air was never sufficiently still for one to be 

 sure that the observed effect might not be ascribed to 

 differential motion of the air itself. 



In the light of Eiffel's results (Comptes Rendus, 

 Dec. 1912), it would appear that there was some ground for 

 expecting some such effect as that observed. For Eiffel 

 found that the law expressing the relation between resistance 

 and velocity undergoes a somewhat sudden change in the 

 neighbourhood of a certain critical velocit}-, the resistance 

 suddenly decreasing. He found that the critical velocity 

 was higher for spheres of smaller diameters : e.g. for 

 spheres 33 cm. and 1 6'2 cm. in diameter respectively, the 

 critical velocities were 400 and 1200 cm. /sec. Hence the 

 critical velocities for the spheres used in the present experi- 

 ments were probably not attained, at least in the experiments 

 made inside the tower. 



In Eiffel's curves (loc. cit.) for resistance and velocity, a 

 marked discontinuity is shown for the sphere of 24 cm. 

 diameter, and a still more marked discontinuity for the 

 sphere of 16 cm. diameter, and he showed that these dis- 

 continuities were associated with a change in the type of 

 air-flow, but his spheres appear to have been held on rods in 

 the current of air. The disturbing effect of the rod might 

 be expected to be more marked for the small sphere than for 

 the large one ; and further experiments are required to test 

 whether the discontinuities would be observed in the case of 

 true spheres without any projecting attachment, or, if they 

 do occur, whether they occur at the same velocities as he 

 observed. 



The celluloid spheres used were the smoothest and truest 

 that could be procured, but in each there was a very 

 perceptible rim round the circumference where the two 



