138 WORK OF M. R. SCHMIDT. 



The measurement of viscosity, for some reason, seems to be beset with much 

 greater experimental error than would be expected, considering the simple nature of 

 the operation. The values given in Landolt-Boernstein's "Tabellen" often show 

 differences of more than 1 per cent in the results of various observers. During the 

 present work it was found to be difficult to get results that would agree closely in 

 duplicate determinations. It may at first sight be supposed that by taking three 

 "steps" to determine the viscosities of the thicker solutions, as was done in this 

 work, experimental error is introduced at each step, so that the values found by 

 means of instruments with wide capillaries would necessarily be of doubtful accuracy. 

 As a matter of fact, though experimental error is introduced, the departure of the 

 values found from the true values is influenced much less by this fact than by an 

 inherent difficulty in the method. 



The Poisseuille formula for determining viscosity is v = , where v is the 



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volume of liquid whose viscosity coefficient is 17, which, under a pressure p, will 

 flow in the time t through tube of length I and radius r. In deriving this formula, 

 the liquid is considered as leaving the tube with a kinetic energy of zero, which, mani- 

 festly, is an impossible condition in practice. If the liquid flows out of the tube with 

 a positive kinetic energy, a correction must be introduced. On rearranging the 

 formula, with the correction it becomes 



*r*pt vd 



v = 



Svl Sirtl 



where d is the density of the liquid. In determining viscosities by the relative 

 method that is, by means of the Ostwald viscosimeter the corrected formula is 

 rarely used. For two liquids flowing by their own weight through the same instru- 

 ment, between the same differences in level, 



But, 



whence = , which is the ordinary formula. 



7?2 Pitt 



It is evident from the corrected formula that when t is smallest the correction is 

 greatest. Hence, a greater error is introduced by measuring the viscosity of a 

 liquid whose time of flow is much greater than that of the standard than in the case 

 of one with nearly the same viscosity as the standard. In other words, the error 

 would be a minimum if t could be kept constant. Therefore, the error is kept lowest 

 by using in each instrument liquids whose times of flow do not differ too greatly 

 from t . As the correction is always negative, the viscosity of a liquid determined 

 without using intermediate steps should be greater than if several viscosimeters are 

 used. This is illustrated in the case of 75 per cent glycerol and methyl alcohol 

 at 25. T is the time of flow. 



