849 



have not come across the fictitious addition to tlie moment of inertia 

 which usually occurs in problems of this kind. This addition does 

 not show itself, until the real part is extracted from equation (24). 

 This real part is equal to 



d^CL , dd ^„d(i' ,, , ,„^. 



K + L' L" — + iV/«' = , . . 29) 



df dt dt 



having put a t= <t' -\- a" i ; and as is easily found from (8') 



dn" 1 d'-a' k' da' 



dt k" dt'' k" (It ' 



so that 



V k" J dt' ^ y k") dt ^ 



which means an apparent increase of the moment of inertia by the 



amount K'^ --. ') 



k 



Substituting the expression (2) in (29) and asain expressing tlie 

 fact that for all values of t the equation must be satisfied, by 

 equating to zero the coefficients of cos and iin, the same equations 

 (26') are arrived at. 



11. The separation of the general expression (24') into its real 

 and imaginary parts is a troublesome performance, which is of no 

 practical value; the general expressions for L' and L" are so involved, 

 that they are practically useless for the computation of i] from the 

 observed values of T and rf by means of the equations (28). As a 

 matter of fact it is only under simplified conditions, that the deter- 

 mination of »j by observation of tlie oscillations of a spiiere is 

 practically possible. Now Hie whole problem becomes most simple, 

 when the liquid may be considered as unbounded ; in that case 

 it follows from (25) which may also be written as 



L — 4 jr/i")i ( bR f 2 H 



') From (29') it also follows, that even in tlie case of friction in a liquid the 

 well-known equation 



T' - IV d-' 



7V 4.-»= 



still holds, on condition that for T„ is taken tlie fictitious periodic time T^ given by 



T„ = -- . , 



