314 REPORT — 1869. 



which take account of their lateral distance from it : these conditions constitute the 

 angle (f), and are fully represented by it. 



The best experiments seem to show generally that the force of fluid friction is 

 as the square of the velocity ; and as it is probable that for any given plane moved 

 with various velocities the integral value of ^p throughout the area will in each 

 case be as the velocity, it woidd seem that we may substitute for the ordinary ex- 

 pression F=kv'^a (in which F is the force per square foot at every point in the area, 

 V the absolute velocity of the plane in relation to the wholly undisturbed fluid, 



and a the area) F—Jkcj)'^ da, where ^ is the value of filamental angle which the 

 existing conditions have called into play at each particidar point in the area. 



If to an infinitely extended plane, immersed in an infinitely extended fluid, we 

 suddenly assign a definite velocity and maintain it, motion will gradually spread 

 itself into the fluid from the plane, the layers nearest the plane having always the 

 greater A'elocity, and each experiencing an acceleration depending on the differ- 

 ence of frictional force measured at its two faces. If the thickness of any layer 



be represented by dh, then ^ will be the difference of iilaniental angle, and 



2k(j) li the difference of force. 

 dh 

 On this basis a differential equation might be constructed .sho■^^'ing the rate at 

 which the velocity would penetrate the fluid in the case supposed, and this might 

 be extended to the case of a finite plane penetrating an undisturbed mass of fluid 

 with a definite velocity. 



On Heads and Ilailways in Northern India, as affected hy the Ahradiny and 



Transportinq Power of Water. 



By TnoMAs Login, C.E., F.E.S.E.', and Memh. C.E. Inst. 



[A communication ordered to be printed in c.rtcnso in the Proceedings.] 



At the last Meeting of this Association the author drew attention to the 



" Abrading and Transporting Power of Water," when he ventured to bring fonvard 



his views regarding this important subject. Since that time he has studied the 



subject still more, ami in the theory then brought forward he has been more and 



more coniirmed. 



As many of those present may not have seen or heard what these Aiews are, 

 he briefly recapitulated the most prominent points before entering on the question 

 of their practical application to engineering works. 



1. All silt-bearing streams when in train only transport a given proportion of 

 earthy matter, 



2. That the proportion depends on the velocity, and the nature of the materials 

 transported. 



3. Any increase of the velocity must cause a tendency to cutting, and any decrease 

 to deposit. 



4. That a silt-bearing stream is retarded by having to exert a force sufficient to 

 transport certain proportions of certain descriptions of earthy matter, consequently 

 the slope required for a given velocity under such circumstances must be gi-eater 

 somewhat than if the water was pm-e. 



From those conclusions he amved at certain deductions regarding the flow of 

 water down irrigation canals, which at present it is not necessary to dwell on, and 

 he went on to state that, so far as his personal observations extended, they went 

 to show that, though the transporting power of water increased with the velocity, 

 yet it diminished as the depth increased, and suggested that this was possibly owing 

 to the rotatory motion of liiiids, wliich are supposed to follow some figure more of 

 the nature of the involutes of circles rather than straight lines. 



Having got so far, he stated his belief that it signified little what may be the 

 cross section or velocity of a stream while passing over or through a work, 

 •so long as it could again resume its natural section and velocity immediately on 

 leaving it. 



The main object of his former paper was to show how the above-mentioned 

 conclusions affected the question as to the ]n'oper velocity to give to artificial 



