8 
into parts retaining the characteristie properties of a fluid. 
We introduce other limitations when we regard the fluid as 
made up of a large, but finite, number of particles or mole- 
cules which retain their identity during the motion. For 
such a molecular fluid, it is known that solutions obtained 
by continuous analysis imply that the molecules move in 
such a way that their order of arrangement does not alter. 
Also if we consider a group of molecules forming an element 
of volume round some point at any time, the same molecules 
will form an element of volume in the neighbourhood of some 
other point at any subsequent time; that is, the deformation 
of an element of volume must be infinitesimal. An inspec- 
tion of Fig. 4 shows that this condition is not fulfilled in the 
a 
vicinity of the cylinder. One can imagine a curve drawn 
round the cylinder, not symmetrical fore and aft, within 
which the conditions are certainly not satisfied. These 
FIGURE 4. 
considerations may help to remove an apparent absurdity. 
If we examine curves, as Maxwell’s, showing the successive 
forms of lines of particles originally straight in advance of 
the cylinder, we notice that the cylinder never penetrates 
through any such line, all of them being looped always round 
the cylinder. Quite apart from other considerations which 
enter in the case of an actual fluid, we are relieved from this 
conclusion by remembering that, on account of molecular 
constitution alone, there is a region round the cylinder 
within which the solution obtained by continuous analysis 
does not represent the true state of motion. 
87 
