14 ON THE V18O08ITY OR INTERNAL FRICTION 



The tangential force on the upper surface will be 



<F0 



and the mass of the stratum per unit of surface is pdy, so that the equation 



of motion of each stratum is 



<P0 #0 .. 



which is independent of r, shewing that the stratum moves as a whole. 



The conditions to be satisfied are, that when y = 0, 8 = ; and that when 

 y*&, 0=Ce- u coa(nt + a) .............................. (3). 



The disk is suspended by a wire whose elasticity of torsion is such that 

 the moment of torsion due to a torsion 6 is Itfd, where / is the moment 

 of inertia of the disks. The viscosity of the wire is such that an angular 



tlft dfl 



velocity -*- is resisted by a moment 2lk -y-. The equation of motion of the 



disks is then 



where A=\ s Ltn*dr = \irt*, the moment of inertia of each surface, and N is the 

 number of surfaces exposed to friction of air. 



The equation for the motion of the air may be satisfied by the solution 

 = e- u {e? v cos (nt + qy) -e' 1 * cos(nt-qy)} .................. (5), 



provided 2pq = <- ..................................... (6), 



and <f~P' = P * .................................. (7); 



and in order to fulfil the conditions (3) and (4), 



2ln(l - )(** + e-* - 2cos 2qb) = NAp{(pn - lq)(tf* - e~+) + (qn + Ip) 2sm2qb} . . .(8). 

 Expanding the exponential and circular functions, we find 



where c = 



F 



/ = observed Napierian logarithmic decrement of the amplitude in unit of 

 time, 



= the part of the decrement due to the viscosity of the wire. 



