935 
XXIX. An Experimental Investigation of the Circumstances winch determine 
whether the Motion of Water shall he Direct or Sinuous, and of the Law of 
Resistance in Parallel Channels. 
By Osborne Reynolds, F.R.S. 
Received and Read March 15, 1883. 
[Plates 72-74.] 
Section I. 
Introductory. 
1. Objects and results of the investigation. —The results of this investigation have 
both a practical and a philosophical aspect. 
In their practical aspect they relate to the law of resistance to the motion of water 
in pipes, which appears in a new form, the law for all velocities and all diameters 
being represented by an equation of two terms. 
In their philosophical aspect these results relate to the fundamental principles of 
fluid motion; inasmuch as they afford for the case of pipes a definite verification of 
two principles, which are— that the general character of the motion of fluids in contact 
with solid surfaces depends on the relation between a physical constant of the fluid and 
the product of the linear dimensions of the space occupied by the fluid and the velocity. 
The results as viewed in their philosophical aspect were the primary object of the 
investigation. 
As regards the practical aspect of the results it is not necessary to say anything by 
way of introduction ; but in order to render the philosophical scope and purpose of the 
investigation intelligible it is necessary to describe shortly the line of reasoning which 
determined the order of investigation. 
2. The leading feat ures of the motion of actual fluids. —Although in most ways the 
exact manner in which water moves is difficult to perceive and still more difficult to 
define, as are also the forces attending such motion, certain general features both of 
the forces and motions stand prominently forth, as if to invite or to defy theoretical 
treatment. 
The relations between the resistance encountered by, and the velocity of, a solid 
body moving steadily through a fluid in which it is completely immersed, or of water 
6 D 2 
