in Moving Viscous Liquids, 475 



equation (7) 



dq q _ 2sah 



dr r r*[h* — or) ' 



(8) 



i^tr^ (9) 



§ 7. Let N stand for the number of revolutions of the 

 cylinder per unit of time. Lei R be an optical coefficient. 

 A the double retraction referred to unit length. Let further 

 Aira?b 2 1:;ttV(//-'-/-7 



r2(6*-a')~~ A; +{¥-(*)* ' ' ' { } 



Using the relations (8) and (9) of the preceding paragraph, 

 we find from equation (2), § 5, 



ANRT 

 AaB I+BJPF « 



According to this equation, the quantity A/X should not be 

 constant, as was at one time supposed : it should decrease as 

 N increases. 



§ 8. The numerical results given by Umlaut in the paper 

 quoted above are probably among the most exact hitherto 

 published on accidental double retraction in liquids. But 

 the accuracy of the results is not the same for the various 

 substances studied. On close examination it is easy to see 

 that the most reliable data arc those obtained with gum 

 tragacanth — a tact which is also confirmed by Umlauf 

 (p. 311 of the cited volume of the Annalen). The following 

 are the results of the corresponding series of experiments ; 

 we have supplemented them by the numbers contained in 

 the last column of the table. In order to calculate this 

 column, we have assumed T=0'0014 sec. for this series ; as 

 regards the coefficient I>, we have calculated its value by 

 means of formula (1), § 7, making use of the data supplied 

 by Umlauf regarding the dimensions of his apparatus. 



N. 



-i. 





.A X. 





A(l+BN a T 2 )/N. 



26-0 



74. 



10-4 



285. 



io- 6 



300 . io-* 



3<H> 



1)7 





265 





309 



43-5 



in:} 





237 





203 



54-0 



114 





211 





288 



58- 1 



120 





207 





295 



65-2 



1132 





202 





309 



The way in Which the values of A/N" and A(1 + BN 2 P)/X 

 vary according to these experiments is in perfect agreement 

 with our predictions. It is to he noted that the temperature 

 of the liquid was never strictly constant in these experiments; 

 it varied from 13 a 2 C. to 15° : 7 C. 



It is a matter of doubt as to whether the results obtained 



