HALL. AIR RESISTANCE TO FALLING INCH SPHERES. 383 



We have further, if s is the distance fallen, from (2) 



ds = vat = -„ • (4) 



>vr 



Integrating this equation for s between the limits and 2285 (the ob- 

 served value) and for v between and v, we get 



• = 2285 = - | [log (* 2 - gc)j V Q = - *log ( 1 - £\ (5) 



Writing now (3) in the form 



Vfc+JO =f 4.S52\fc (6) 



gc — v 

 and (5) in the form 



/ ( 4570 \ 



v =y gc \l-e c ), 

 and substituting for v in (6), we get 



Vgc (l +yi- e-^) 4 . 352 v/i 



or 



or 



0) 



(8) 



The value of c which satisfies this equation I find to be about 48000. 

 The value of k, the coefficient in question, is on, the mass of the ball, 

 which is about 73.8 gm., divided by c. 



h = 73.S -f- 48000 = 0.00154. 



