﻿Valuable Head in Viscosity Determinations. 955 



Re-calculating with this value we get r} 2) which gives us 



- 3 ~ -y ' 



from which ^ 3 is calculated, and so on. The first value 

 for C or Oi being too large, r/i will be too small. Simi- 

 larly, r)2 will be too large and rj z again too small. Thus 

 V1V2V3 •••• form a series in which the even terms and the odd 

 terms respectively converge asymptotically to the true 

 value for rj. The rapid convergence of the series con- 

 siderably shortens what would otherwise be a rather 

 laborious calculation ; three or four terms are sufficient to 

 fix the final value. 



As an example, we take one of the standard runnings of 

 •water at 20° 0., and select in particular that one as set 

 forth in detail in Archbutt and Deeley's ' Lubrication and 

 Lubricants,' 3rd edition, p. 157. This example is chosen 

 as there is a considerable fall in the head, although, on the 

 other hand, the kinetic energy term is small. We quote 

 •the data of the experiment in full : — 



H = 23-56 g = 980-51 



F= 11-60 p= 0-99826 



r= 0-0309 V= 4-00756 



*= 136-0 1= 21-991; 



From these figures we get as the first value for C or 

 C, = 890-52 giving Vl = -0100609, 

 from which C 2 = 897-24 „ rf 2 = '0100692 

 C 3 = 880-69 „ rj 3 = -0100680 

 C 4 = 880-49 „ ij 4 = -0100682, 

 from which we can write down the final value of 77 as 

 •01006818. The value of n calculated from the same data, 

 using the equation 



_ ^^(H-F) _ Vp(H'-F') log. H/F 

 v ~ SV/log/H/F 127r/*(H-F) 2 (H + F) ' ' ' {) 

 re -0100721. 



The difference between this and the correctly calculated 

 value '01006818 is not very striking, but when one con- 

 siders that here the kinetic energy term is small (only 

 '5 per cent, of the total) this is not surprising. In order 

 adequately to demonstrate the shortcomings of the ordinary 

 formulae, it would be necessary to make a running under a 

 considerably increased initial head, in order that the K.E. 

 -correction should become appreciable, and to continue the 

 Tunning until the final head w;is relatively small. 



3Q2 



