Viscosity of Water. 505 



In this formula L is the length and E, the radius o£ the 

 capillary, and T the time taken for volume V of the liquid 

 of density & to flow through the capillary under a pressure 

 gph ; iiR is a small length of tube producing a loss of 

 pressure equivalent to that arising from the friction at the 

 ends, its value must be calculated for each series of experi- 

 ments ; m is the numerical factor in the kinetic energy 

 correction, which has a theoretical value of 1*12^ but which 

 has a practical value which must be determined. The factor 

 m has been neglected in so many recent determinations of 

 viscosity, that it is worth the while to repeat the information 

 given by Knibbs respecting it. In 1860 Neumann deduced 

 the value m = 1, and Jacobsen used it in his ' Introduction 

 to Hemodynamics ' (1860). Hagenbach deduced the value 

 m = l in the same year. Reynolds (following Bernoulli) in 

 1883 used the value m = \. Couette in 1890 independently 

 obtaiced the value m = l. Boussinesq (1891) obtained a 

 more accurate value m = l'12. Gartenmeister stated (1890) 

 that Finkener had in an unpublished treatise shown that 

 Couette's value was the correct (?) one. TVilberforce (1891) 

 pointed out the defect in Hagenbach's reasoning, and he 

 used the value m=l. Knibbs has shown that theoretically 

 Neumann's correction as deduced by Boussinesq is correct, 

 and that experimentally its value varies considerably. Knibbs 

 has deduced values of m from Jacobsen's results, and stated 

 that individual results show how, even under circumstances 

 in which uniformity might be expected, it is not realized ; and 

 that if the correction be of sensible magnitude, the deduced 

 viscosity is, to the extent of this uncertainty, unreliable. 



Determination of m and n. — Preliminary experiments were 

 made in order to obtain correct (experimental) values for the 

 constants m and n. The temperatures were kept as close to 

 50° C. as possible, and, under different pressures, the times 

 of flow were recorded. The pressures were reduced to equi- 

 valent pressures at 50° C. Knibbs has shown that the re- 

 duction formula, for experiments carried out at a certain 

 temperature, may be expressed in the form 



C + c/T=pAT, (2) 



where 0=^(1 + nB/L)j^, .... (3) 



j mS V 2 .., ^ 7 , 

 and C= ^W (1 + 2kt) ' W 



Equation (2) is that of a straight line such that if 1/T be 

 taken as abscissae, and corresponding values of phT as 

 ordinates, the line passing through the points so determined 



