532 Mr. H. S. Allen on the Motion of 



constant k in the relation 



R=fyoa 2 V 2 ; 

 for if W is the actual weight of a sphere, 



R = S=£w, 

 fl- 

 an d so 



log & = log W + log (-—-)— 2 log aV. 



The mean density of the steel balls was found to be 7*731. 



The values of k for the spheres, excepting the largest, are 

 the following : — 



II. 5-61 x lO" 4 . 



III. 5-42 x 10~ 4 . 



IV. 5-49 x 10" 4 . 

 V. 5-52 x 10- 4 . 



VI. 5-48 xlO- 4 . 



Mean 5-50 x 10~ 4 . 

 The formula giving the terminal velocity will be 

 kpa? V 2 = §7T# (a — p) a 3 



v 2 =; 



1 A_„°"-P 



1^9 



k " " p 



E. S. Woodward * has made a preliminary series of ex- 

 periments on metallic spheres falling in water. Spheres of 

 steel, silver, aluminium, and platinum were dropped in a 

 tube of water 16 feet long and 1 foot in diameter. The 

 spheres varied in diameter from one inch to two inches. 

 All the spheres acquired a constant velocity inside of the first 

 metre. Newton's law t that resistance to motion is propor- 

 tional to the square of velocity seemed to be verified. The 

 times of falling were determined with a chronoscope. 



No further details have yet been published. 



* Trans. New York Acad. Sci. xv. p. 2 (1896). 



t " But, yet, that the resistance of hodies is in the ratio of the velocity, 

 is more a mathematical hypothesis than a physical one. In mediums 

 void of all tenacitj r , the resistances made to hodies are in the duplicate 

 ratio of the velocities. For hy the action of a swifter hody, a greater 

 motion in proportion to a greater velocity is communicated to the same 

 quantity of the medium in a less time ; and in an equal time, by reason 

 of a greater quantity of the disturbed medium, a motion is communicated 

 in the duplicate ratio greater ; and the resistance is as the motion com- 

 municated." — Newton, ' Mathematical Principles of Natural Philosophy,' 

 Book IT. Scholium. 



Newton's own experiments on the resistance experienced by falling 

 spheres are described in Sect. VII. of the same Book. 



