854 



16. As an example of a calculation the results of a preliminarj- 

 experiment made by Mr. Ch. Nicaise in water of 20° C. may be 

 given here. A brass sphere of 1,927 cm. radius and weighing 

 250,8 grms. was suspended from a wire of phospiiorbronze, such 

 that in air the time of swing was 12,05 sec; immersed in a large 

 vessel with pure Avater the sphere had a periodic time of 12,24 sec. 

 the amplitude of the oscillations diminishing per time of swing in 

 a constant ratio, the natural logarithm of which was 0,1148 fit was 

 found that this did not increase appreciably, until much narrower 

 vessels were used, which shows that the liquid could be considered 

 as being practically unbounded). For this experiment we have 

 therefore 7^ = 1,927, /v = 372,5, ?'„ = 12,05 (properly speaking the 

 time of swing ought to have been measured in vacuo, but this 

 would not have made a difference within the limits of accuracy of 

 the observation) T=r 12,24, d=r 0,1145 (freed from the internal 

 friction of the wire) ') and ft = 0,998. 



This gives — = 0,0091 and i|) = ^^-- = 0,016, and therefore 



within the limits of accuracy of the obsei'vation 



L' = =: 7,08 , L" = — ^— = 6 . 



T„ ' ' T„ _ 



A first approximation with ij = 0,01, gives b' :=zb" =\y^ li*^5^ 



therefore b'R = b"R = 10, so that yj = 0,05, </ = 0,004. The visco- 

 sity is now given hj 



2,05ji + 0,966 i/»j = 0,118L 

 hence : 



1,,, = 0,01014, 



a value which agrees very well with the known data. The equation 

 with L" gives as a very rough verification ?/ = 0,010. 



17. The formulae become even simpler, if b'R and b"R are large 

 numbers (say of the order 1000); in that case we have: 



« = « — <;-*''—■«) , (32) 



r' 



L' — ^-jiR'b'ii , L" = ^.-rR'b"ii (33) 



1) Observation gave 5 = 0,1148; in air J = 0,0011, of which, according to a 



calculation of L' with n = 0,0002 and ^ = 0,0012, the fraction 0,0008 is due 



to the friction of the air, so that 0,0003 is left for the internal friction of the 

 suspension. 



