Experiments with Rotating Viscous Liquids. 253 



and <o to raise again the load at the end o£ the cord until it 

 come< to rest. 

 Lot us put : — 

 I = average moment of inertia of the rotating mass ; 



\V = mass of the load in grammes hung on the cord ; 

 ct = angular velocity; 



r = linear velocity of the falling mass ; 

 g = acceleration of gravity: 

 H = total descent of the load ; 

 h = greatest height to which the load is raised; 

 t — time of descent ; 



f = total retardation due to friction in grammes weight; 

 = friction at axle -f- fluid friction. 

 For the descent we have 



(W-/)^H=i I«* + i Wv 2 (1) 



For the upward motion, 



U^=(W+/\gh (2) 



By elimination of ^Its 2 between (1) and (2), and by putting 



2fl 



<•= . we get, alter rearranging, 



W /„ , 2H 2 > 



It will be observed that the assumption is made in 

 equation (2) that the kinetic energy of the falling load W 

 has been absorbed by the viscosity of the cord before the 

 upward motion begins — an assumption which cannot be far 

 from the truth : and in any case does not affect the value 

 of / to any great extent. The cord used was chosen so as 

 to show as little " spring " as possible. It is worth noticing 

 that the kinetic energy of the load, when at the bottom of 

 the descent, was not expended in reducing the speed of the 

 rotating mass, because at this stage of the motion the cord 

 was all run off, and consequently its point of attachment, 

 to the axle was vertically under the axis of rotation. The 

 cord wound itself on the axle, and unwound, quite evenly. 



Methods oj Observation. 



The quantities in the right-hand member of (3) above 

 which offer most difficulty in measuring are t and h. 



The time of fall from rest of the loud was measured by help 

 of an electrical device of a well-known type. On a moving 

 strip of paper two pens placed side by side drew continuous 

 traces. Each pen was attached to the armature of a small 



/^C-'-v) « 



