ON FLUID MOTION. 



CHAPTER I. 



THE EQUATIONS OF MOTION. 



1. THE following investigations proceed on the assumption 

 that the fluids 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 

 them to be divided are the same as those of the substance in 

 bulk. It is shewn in note (A), at the end of the book, that the 

 fundamental equations arrived at on this supposition, with proper 

 modifications of the meanings of the symbols, still hold when we 

 take account of the heterogeneous or molecular structure which is 

 most probably possessed by all ordinary matter. 



2. 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 veri 

 fied by the complete agreement of the deductions of that science 

 with experiment. 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 



L. 1 



