863 



5. In the above discussion we assnmed the liquid to he unbounded, 

 but it is evident, that everything remains valid, wheu tlie liquid 

 is externally bounded by a sphere; the only additional condition 

 is that R' must have the same reduced value in both systems. 



By varying the ratio in all possible ways (from to go) an infi- 

 nite series of similar cases is again obtained. 



It is obvious that similarity may still exist, if the bounding sur- 

 faces were arbitrary, if only similar; the vibrating body would not 

 even have to be a sphere '). For this reason it would be possible to 

 make relative measurements of viscosities with "similar" apparatus 

 (in the simplest case with one apparatus); this might be done by 

 first determining the undamped time of vibration and the decrement 

 in a standard liquid (e. g. water}, then for the experiment in the 

 liquid which is to be examined first modifying the moment of 

 inertia of the vibrating system until condition (II) is satisfied, that 

 is: for the same apparatus increasing or diminishing K proportion- 

 ally to ;t and finally changing the rotational couple until the 

 logarithmic decrement becomes the same as in the first liquid: 

 according to (1) the times of vibration of the undamped oscillations 



fi 



for one and the same apparatus would then be proportional to - 



n 



and in this manner it would be possible to calculate rj. 



It is obvious, however, that relative measurements of that nature 

 would be much more elaborate than absolute measurements by 

 direct calculation of ^i from experimental data obtained in the simple 

 cases, which were dealt with in the previous paper. 



6. Returning to the case of a sphere oscillating in an externally 

 unbounded liquid, it was shown that all possible cases which can 

 occur can be realized by giving A' and M, or K and 1\ all possible 

 values between and oo. In order to give a general survey of the 

 different cases 1 have calculated for special values of ft, jj and R 

 a few systems of values of K and 7', (or K and M) corresponding 

 to definite values of ó and T. To simplify the calciUations I have 

 taken fx = 1. tj = 1 and R =^ I (C. G. S. units), representing a 

 fictitious liquid which might, however, be realized at a special 

 temperature by mixing special real liquids. In that case, d and 1' 

 being given, K and T„ are determined by the equations (comp. 

 equations 18, 28 and 30) 



1) This, of course, does not follow from the foregoing discussion but may be 

 proved in a more geiicral way. (Note added in the translation.) 



