853 



14. In all the above calculations it is assumed that the oscillations 

 of the sphere are onl^' weakly damped ; this condition can in any 

 case be satisfied, independently of the S|)ecific properties of the li(iuid. 

 For, even when L' obtains a high value, the logaritlunic decrement, 

 by formula (28j can be made as small as desired by giving the 

 oscillating system a high moment of inertia; tiiis does not necessarily 

 involve a corresponding increase of' the time of swing, because the 

 rotational moment M may still be chosen at will. 



It is, moreover, easily seen, that for substances with a small value 



1] 



of - the circumstances must again be the most favourable : according 



ft , 



to (28) and (31)) it is exactly for these substances, that under other- 

 wise equal circumstances the oscillations of the s|)here will be least 

 damped. 



15. When ecpiation ('25) holds, the calculation of ?;, the quantities 

 fj, A^ K, T„, T and ó being known from the experiment, can be made 

 in a fairly simple manner. First L' and L" are calculated with the 

 aid of equations (28) or, as the case may be, (28'). An a})proximate 

 value of 1] having been found, // and //' can be obtained in first 

 approximation by means of (20) and using these values a suffi- 

 ciently accurate value can in general be calculated from the terms 



b'R + 1 1 

 »= and (/ == — 7 in eciuations (30V 



Finally it only remains to solve the following quadratic ecpiation 

 in [/-^i : 



(2 + p) 11 4- y'R l/,ni == ^^ (a) 



An alternative method of calculation woidd be from 



_ SL" 

 ^' ~ 8jtR'y'y^{l-q} ^''^ 



but in general this will yield a much less accurate value owing to 



T—7\ 

 the smaller accuracy with which il' =: —;- — is determined as coni- 







pared with <i. Equation (A) ought rather to be looked upon as a 

 kind of check on the result obtained; but it may also render excel- 

 lent ser\ice for the purpose of obtaining an approximate value for 

 rj, if this should not be known; in that case it is even sufficient to 

 neglect q with respect to 1. 



