﻿396 Royal Society :— 



Where in the formula which thus represents the discharge from 

 a pipe of given radius, in terms of the velocity of the central filament, 

 the radius is made infinite, an expression is obtained for the volume 

 of liquid of a cylindrical form, but of infinite dimensions (laterally), 

 which would be put in motion by a single filament of liquid which 

 traversed its axis ; and, conversely, it gives the volume of such a 

 liquid in motion which would be held back by a filament of liquid 

 kept at rest along its axis. Thus it explains the well-known retard- 

 ing effect of filaments of grass and roots in retarding the velocities of 

 streams. 



It is the relation of the velocity of any film to that of the central 

 filament which the author establishes in the above formula. To the 

 complete solution of the problem it is necessary that he should further 

 determine the actual velocity v of the central filament. This is the 

 object of the second part of his paper. This velocity being known, 

 the actual discharge per 1" is known. The following is the formula 

 finally arrived at : — 



i- 250 E 950 H "Ills 



where L * J 



Q=discharge per 1" in cubic metres. 



R=radius of pipe in metres. 



I = length of ditto. 



h =head of water. 



C =a constant dependent on the state of the internal surface of 

 the pipe. 



The values of this constant C, as deduced from the experiments 

 of M. Darcy are given, 



1 st, for new cast-iron pipes ; 



2nd, for the same covered with deposit ; 



3rd, for the above cleaned ; 



4th, for iron pipes coated internally with bitumen ; 



5th, for new leaden pipes ; 



6th, for glass pipes. 



The author compares this formula with sixty-two of M. Darcy's 

 experiments, and records the results of this comparison in the last 

 three Tables of his paper. 



The paper concludes with an investigation of the rise in the tem- 

 perature of a liquid flowing through a pipe caused by the resist- 

 ances which its coaxial films oppose to their motions on one another 

 (or, as it is termed, their frictions on one another) and on the in- 

 ternal surface of the pipe. The pipe is in this investigation supposed 

 to be of a perfectly non-conducting substance. 



February 9.— General Sir Edward Sabine, K.C.B., President, in the 



Chair. 



The following communication was read : — 



" Observations of the Eclipse at Oxford, December 22 1870 " Bv 

 John Phillips, M.A., D.C.L., F.R.S. * 



At my observatory, situated about one third of a mile eastward from 

 the great establishment founded in the name of Dr. Radcliffe the 



