(Excerpt from the Proceedings of the 
University of Durham Philosophical Society, 
Vol. IV., Part 2.) 
Tur DISPLACEMENT OF THE ParricLes IN A CASE 
A eeu cates eae creat eae Dafa 
or Fium Morton. 
By '[. H. Havecock, M.A., D.Se. 
[Read March 3rd, 1911.] 
The leading features of the motion induced by the passage 
of a cylinder through a perfect fluid are well known, but 
certain aspects of the permanent displacement of the fluid 
particles are less familiar. The following notes on these 
were suggested by an unexplained paradox which is men- 
tioned in recent treatises, such’as Lanchester’s Aero-dynamics 
and Taylor’s Speed and Power of Ships; it was found later 
that the same difficulty is mentioned by Maxwell in a paper 
on the paths of the particles. The present remarks are 
arranged as follows: 
1. From the ordinary theory of the fluid motion is 
deduced a simple proof of Rankine’s formula for the 
radius of curvature of the path of a particle, and the 
solution is then completed in terms of elliptic 
functions. 
2. After drawing paths of particles, curves are obtained 
for the subsequent positions of lines of particles 
which were abreast of the cylinder at certain times. 
3. A graphical study of the deformation of a group of 
particles as it passes near the cylinder suggests a 
difference between the behaviour of an ideally con- 
tinuous fluid and one which is molecular. 
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