Coefficient of Viscosity of a Liquid. 411 



per unit length is easily proved to be 87t/jlv 2 , and the rate at 

 which energy is supplied is gphv —r- . Hence we obtain, if I 

 is the length of the tube, 



^^f= 8 -4 ? - D f^('f) + 4 , f)}] + - 2DF (f> 



which may be written 



or 



gpD^ ypD T \ fju ) 

 _ 32filv v 2 A (rp& 



II — 1 v v "T" 



9PW 9 



*m 



If the walls of the vessels are everywhere at a distance from 

 the ends of the tube which is great compared with the dia- 

 meter of the tube, it may be expected that the function <f> will 

 be practically independent of the shapes of the vessels. In 

 any case, from the results of two experiments made with 

 vessels proportioned to the diameters of the tubes, and with 

 pressures so chosen that vD is the same in both, we can elimi- 

 nate the correction. In particular, using the same vessels in 

 the two experiments and tubes of the same diameter but of 

 lengths 1 1 and l 2 , if the heads corresponding to a mean 

 velocity v be A] and h 2 , we have 



gpW^-h) 

 ^~ 32^(/ 1 -/o) ' 



The large number of observations made by Poiseuille upon 

 water at a constant temperature, and the close agreement 

 which, according to his method of exhibiting the results, 

 appeared to exist between those of his first series of experi- 

 ments, led me to apply the above methods of calculation to 

 most of the data which his second series of experiments fur- 

 nish. It would be wearisome to tabulate the issues of the 

 calculations at length ; the various results obtained with the 

 same piece of tube seemed on the whole to point to the simple 



v 

 correction of h by — as being appropriate for a considerable 



range of velocity ; but they were not very consistent, and the 

 results obtained with different portions of tube, even those 

 which were cut from the same piece, and about the ratio of 



