of the Inertia of a Sphere moving in a Fluid. 351 



by the writer for the study of oscillatory motions under 

 water, a light cord attached to the mine-case passing round 

 the drum of the instrument, and equal intervals of time being 

 indicated by a small lateral movement given to the recording- 

 pen electrically from a clock. From the record thus obtained 

 the velocity and acceleration at any instant could be measured. 

 The friction of the instrument was negligible, but a counter- 

 poise applied for the purpose of maintaining a small tension 

 in the cord reduced the downward force on the mine-case bv 

 0-OG lb. 



The equation of motion may be written : — 



at 7 



where M' is the inertia of the body, v the velocity, F the 

 vertical force due to gravity (corrected for counterpoise of 

 the recording instrument), and kv n a term expressing the 

 frictional resistance to the motion of the body through the 

 fluid. 



The correct value of n will be such as to make the relation 



between -- and v n linear. As the frictional resistance is 

 at 



mainly that due to skin friction and eddy formation, it might 



be anticipated that n w T ould have a value approximating to 2. 



The values of the velocity, acceleration, and square of 



velocity are given in the following table :■ 



V J ** A V fe* 





o """^^ • 









dv 





Time 



v. 



di 





(sees.). 



(ft. sees.). 



(ft. sees. 2 ). 



v 2 . 



2-5 



0-1333 



0-01814 



0-0178 



5 



0-1768 



0-01667 



00312 



7-5 



0-2195 



0-01745 



0-0482 



10 



0-2631 



0-01747 



0-0691 



12-5 



0-3026 



0-01412 



00916 



15 



0-3383 



0-01440 



0-1145 



17-5 



0-3711 



0-01187 



01378 



20 



0-3988 



0-01024 



0-1592 



22-5 



0-4233 



0-00936 



0-1792 



25 



0-4458 



0-00867 



01990 



27-5 



0-4683 



0-00932 



0-2193 



30 



0-4895 



0-00760 



0-2395 



32-5 



0-5075 



0-00680 



0-2575 



35 



0-5238 



0-00627 



0-2748 



The relation between -=- and v 2 is plotted in fig. 1. It will 



be seen that the plotted points lie close to the straight line 

 y = 0-0193 -0-0494 ^. 



