Measurement of Absolute Viscosity. o55 



rapidly approaches the mean head 



The factoi 



log H/F 



J(H + F) as the initial and final heads become large as 



compared with their difference ; and as long as this fact is 



not lost sight of, there is no reason why the more cumbersome 



calculation should be necessary. The subjoined table shows 



at a glance the extent of the error involved. 



Ratio of mean Ratio of 



head to differ- initial to 



•encein heads. final head. 



H-F 



H 



F 



2»+l 

 2n-l 



GO 



9 



5 



3f 

 3 



Ratio of 



mean head to 



corrected head. 



i(H+F) '*=£ 



Percent, error, 



nlog 



2»fl 



2n-l 



• 



lOOlnlocr 



H 



3 



4 



10 



20 



30 



00 



3733 



2071 

 1369 



0397 

 0186 

 0094 

 0052 

 0008 

 0002 

 00015 



~e-2n-l 



X> 



3733 

 20-71 

 13*69 



9-86 



3-97 



1-86 



094 



0-52 



o-os 



002 

 0015 



The formulae which have been advanced to correct for the 

 kinetic energy of the liquid are almost as numerous as 

 the factors they contain. 



It might, therefore, be not out of place to work it oat 

 once again from first principles. 



If: W is taken as the total work done in the system, and 

 We: as that expended on kinetic energy, then we can write 



v = v (found) x(l-~^). 



The total work W is equal to V. d.#.|(H + F), where V 

 is the volume which passes any fixed point in the system • 

 d the density ; H the initial, and F the final head. 



The allowance to be made for the work expended on 

 kinetic energy is rather more elusive than it appears at 

 first sight. 



2 A2 



