848 



D being the form given in (17'). L is again a complex quantity. ') 

 When the liquid is (practicallyj unbounded and the motion periodic 

 (i.e. Q = 0), we have simply : 



, b^R'' -H 36/!; + 3 

 L = ^:iR^ii 1^— (25) 



9. The expression (8') actually satisfies the equation (24), when 

 k satisfies the equation 



Kk" 4- Lk ^- J/ -J (26) 



If we put again L ^ L' -\- L"l, we find: 



K{k'--k"-') -f L'k' — L'fi' + J/= and 'IKk'k" + IJk" + L"k' = 0, (26') 



oi' according to (9') and (1), 



LT L"T T' L'T L"T 

 d-' — 4jr'' - ff 2.T -f 4.V =:Oancl 47rrf=2.-r ó (27) 



These are therefore the equations which determine k' and k", 

 and thus also é and T, under the given experimental conditions; 

 conversely they enable us to conqiute L' and L" from the experi- 

 mental values of T and 6 and thereby by the aid of (24) to 

 calculate t;. 



From (27) it follows that: 



j2 



7V^ 4.^^ t 0^ 



L" 

 K 



T- 4.-t-^ 



7V4V + d^ 



(28) 



When ff is a small number, as also «f^ 



T— r„ 



fas is usually the 



case), we may write : 

 L' 2d 



K = l:^' 



L" 



4jt 



K T ^ 



1 4 



i|' + A (if-' 



7.^) ^ ■••] 



^ [1 + i i^p'-t) + ■ -1 



If' 



+ ... 



4jr 



I — 



2if) 



(28') 



10. As we have been using complex quantities all along, we 



1) The meaning of this is as follows : the real angle k satisfies equation (23), 

 where everything is real, even C, the moment of the frictional forces, which is 

 determined by (28') with w still real. If, however, a complex angle a is introduced, 

 the real part of which is the real ce, C will be the real part of (23'), where u must 

 be taken as a complex quantity, and this is at the same time the real part of 



an expression of the form / — -, where L is then similarly a complex quantity. 



