851 



12. In our experiments we intend to choose the conditions such 

 that the liquid may, at least approximately, be considered as unbounded; 

 moreover we shall arrange to make ö small. It is easily found, what 

 conditions these simplifications are subject to. 



Clearly it is necessary that the factor (>y'^^'—^) obtains so high a 

 value, that the terms containing this factor are sufficiently prepon- 

 derant; this condition does not necessarily involve a, specially high 

 value of h' , for if e.g. R'—R = l i.e. if the distance of the two 

 spherical surfaces is only 1 cm. (and this will be about the case 

 in our experiments) still even for b' =^ 10, the value of t;'"'^^^' 

 will be as high as 10000 about. For water in C. G. S. units ?i =r 0,01 

 and ;x = l, so that even with 7'= 3, i.e. a time of swing of 3 

 second, b' will reach the value JO, so that even in that case the 

 desired condition will be fulfilled of the wave-motion, which starts 

 from the oscillating sphere, when arriving at the external sphere, 

 being practically completely damped out (§7). If it is further taken 

 into account, that the oscillating sphere can only undergo an influence 

 from the bounding wall by the waves reflected on the wall returning 

 to the sphere and that the returning waves again undergo a damping- 

 process, it becomes clear, that the damping on the way from the 

 inner sphere to the outer wall does not need to be so very complete, 

 in order to be able to consider the liquid as • being practically 

 unbounded. 



This fact is also expressed in our equations (24") and (31). Prac- 

 tically (24") is identical with (25), or Li = 0, when e^-^*'uK --«) is 

 sufficiently small, i.e. when the damping over a distance 2{R'—R) 

 is sufficiently strong; in order that (;-2*'(iï'-/J) uiay be say xgVo 

 with R' — /? = !, even 6' = 3 would be sufficient and this would 

 still be the case for water with T as high as 30. A somewhat 

 large time of swing of about that magnitude is favourable to the 

 readings from which the logarithmic decrement must be determined 

 and it is accordingly intended in our experiments to make the 

 periodic time about that size. 



With R' — 7^ = 1 and T=:30 even when working with water 

 the liquid can thus approximately be considered as unbounded. But, 

 moreover, it appears from (20) that with a given time of swing b' 

 and b" become greater, and therefore the conditions more favourable, 



ij 



according as the ratio - is smaller; for very mobile liquids, like 

 H 



ether and benzene, they would therefore be even more favourable 

 than with water, and, as the available data show, most favourable 



