6 
The cross-marks on the curves indicate the spaces covered in 
successive equal intervals of time by particles which were 
simultaneously at similar points (B) of their paths. 
2.—With the help of these curves we can trace the 
changes in any line containing always the same particles. 
For this purpose we draw the relative stream lines given by 
(1), for the same values of }/a as are shown in Fig. 2. We 
superpose this diagram on 
Fig. 2, with the axes of «x 
coinciding, and draw a curve 
through the intersections of 
corresponding actual and rela- 
tive paths; displacing one 
diagram parallel to the direc- 
tion of motion, we mark again 
the intersections and obtain 
the displaced position of the 
same set of particles. For 
instance, with the actual 
paths as in Fig. 2, we obtain 
by this method the successive 
positions of a line of par- 
ticles which at some instant 
Figure 2 formed a straight line abreast 
of the cylinder; these curves are shown for one quadrant in 
Fig. 3. 
The diagram can also be described in another manner. 
The cylinder moves from left to right. At the instant repre- 
sented in Fig. 3, AB is a line of particles abreast of the 
cylinder; the successive curves to the left are the present 
positions of particles which were abreast of the cylinder at 
certain equal intervals of time previously. The unit of time 
T is that taken by the cylinder to move through one-quarter 
of its diameter. Thus the curve C!D)!E! represents the 
present position of particles which were abreast of the 
cylinder at CDE at a time 5T previously. It_may be 
noticed that the circumference of the cylinder forms part, 
85 
