436 
MESSRS. T. E. THORPE AND J. W. RODGER ON THE RELATIONS 
- pYj^irl 
is the true value of the kinetic energy correction. This value is greater than that 
given by Hagenbach in the ratio of ^2 to 1 . 
Simultaneously with the publication of Couette’s paper, Gartenmeister (‘Zeit. fur 
physik. Chera.,’ 6 , 524, December, 1890), stated that, from considerations not then 
published. Professor Finkener, of Berlin, had arrived at a correction which is identical 
with that given by Couette, and, more recently, Wilberforce (‘Phil. Mag.,’ 5, 31, 
407, 1891) has shown that, from Hagenbach’s assumptions, the value of the 
correction, as given by Couette and Finkener is correct, as there is a slip in the 
reasoning employed by Hagenbach. What may be termed the Couette-Finkener 
value of the correction is the one adopted in this paper. It is shown by Couette to 
give much better results than that of Hagenbach when applied to observations 
made with two of the shortest tubes used by Poiseuille, in which the velocity of 
efflux was large and varied considerably. 
’Jdie formula corrected for kinetic energy is therefore 
7} — 7rlHp/8V/ — pY187 tL 
(2.) Couette alone seems to have attempted to obtain a measure of the friction 
near tlie ends of the tube. What actually takes place in this region is not suffi¬ 
ciently known to admit of the magnitude of the effect being theoretically deduced. 
Couette concludes, however, that in order to assess its value experimentally, it may 
be regarded as the same as that of a slight alteration in the length of the tube 
employed, and the formula for a finite tube containing the corrections for kinetic 
energy and the influence of the ends, he gives as 
— \ ^ 
\ SVl Stt/J I 4- L' 
H ere, L is the length wliich must be taken in a tube indefinitely long and of the 
same radius as the finite tube in order that when V volumes of liquid flow per unit 
time through the tube the work spent in friction per unit time for the length L will 
be the same as that dissipated by the influence of the ends. The magnitude of L 
which takes note of this friction effect he attempted to deduce from such experi¬ 
mental data as were available. Two sets of observations were made bv Poiseehlle 
•/ 
with short tubes (say A and B) of the same radius but of difterent lengths. From 
observations made with these short tubes at a uniform temperature of 10 °, the values 
of Tj calculated by the formula for an indefinitely long tube vary with the velocity of 
efflux. On introducing the Couette-Finkener correction for kinetic energy, unless 
in the case of the highest velocities, the value of 77 is constant for either tube, but is 
different in the case of tube A from that in the tube B, and in both cases it differs 
