HYDBODYNAMICS. 



CHAPTER I. 



THE EQUATIONS OF MOTION. 



1. THE following investigations proceed on the assumption 

 that the matter with which we deal may be treated as practically 

 continuous and homogeneous in structure ; i. e. we assume that 

 the properties of the smallest portions into which we can conceive 

 it to be divided are the same as those of the substance in bulk. 



The fundamental property of a fluid is that it cannot be in 

 equilibrium in a state of stress such that the mutual action 

 between two adjacent parts is oblique to the common surface. 

 This property is the basis of Hydrostatics, and is verified by the 

 complete agreement of the deductions of that science with ex 

 periment. Very slight observation is enough, however, to convince 

 us that oblique stresses may exist in fluids in motion. Let us 

 suppose for instance that a vessel in the form of a circular 

 cylinder, containing water (or other liquid), is made to rotate 

 about its axis, which is vertical. If the motion of the vessel be 

 uniform, the fluid is soon found to be rotating with the vessel as 

 one solid body. If the vessel be now brought to rest, the motion 

 of the fluid continues for some time, but gradually subsides, and 

 at length ceases altogether ; and it is found that during this 

 process the portions of fluid which are further from the axis lag 

 behind those which are nearer, and have their motion more 

 rapidly checked. These phenomena point to the existence of 

 mutual actions between contiguous elements which are partly 

 tangential to the common surface. For if the mutual action were 

 everywhere wholly normal, it is obvious that the moment of 

 momentum, about the axis of the vessel, of any portion of fluid 



L. 1 



