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XLVIII. On the Calculation of the Coefficient of Viscosity of a 

 Liquid from its Rate of Flow through a Capillary Tube. By 

 L. B. Wilberforce, M.A., Demonstrator in Physics at the 

 Cavendish Laboratory, Cambridge* . 



IN the method ordinarily employed for calculating the 

 coefficient of viscosity of a liquid from observations upon 

 its rate of transpiration under a known pressure through a 

 capillary tube of known dimensions, it is assumed as a first 

 approximation that the character of the motion at all sections 

 of the tube is the same, and that the motion of the fluid 

 outside the tube can be neglected. Thus, to this approxi- 

 mation, all the energy supplied to the liquid is supposed to be 

 converted into heat within the tube. 



If greater accuracy is aimed at, it will therefore be neces- 

 sary to apply corrections on account of (1) the motion of the 

 fluid outside the tube, and (2) the difference of character of 

 the motion within the tube at points near its ends from that 

 at points remote from them. 



The second of these causes seems hitherto not to have been 

 considered ; but a value for the correction necessitated by the 

 first cause was investigated by Hagenbach (Pogg. Ann. cix. 

 1860), who noticed that a part of the energy supplied still 

 existed in the issuing fluid as kinetic energy, and that a de- 

 duction on this account must be made from the whole energy 

 given to the liquid before it could be equated to the energy 

 expended within the tube. The validity of the assumption 

 upon which he proceeds is, however, very doubtful ; but 

 before discussing this I wish to point out an error in the 

 method which he has employed in calculating his correction. 



Let p be the density of the liquid, r the radius of the tube, 

 z the distance of a point from the axis of the tube, and f the 

 velocity at that point ; then we shall begin by assuming that 

 everywhere in the tube, even at the end from which the fluid 

 issues, 



fee (rW) ; 



or, if v denotes the mean velocity of the fluid, 

 * Communicated by the Author. 



