of Edinburgh, Session 1871-72. 
681* 
from being (as we might erroneously at first sight expect it to be) 
carried sideways with the augmented stream. A properly trained 
dynamical intelligence would at once perceive that the constancy 
of moment of momentum round the axis requires the globule to 
move directly towards it. 
15. Suppose now the globule to be of the same density as the 
liquid. If (being infinitely small) it is projected in the direc- 
tion and with the velocity of the liquid’s motion, it will move 
round the axis in the same circle with the liquid ; but this motion 
would be unstable [and the neglected term w (39) adds to the in- 
stability]. Compare Tait and Steele’s “ Dynamics of a Particle,” 
§ 149 (15), Species IV., case A = 0 and AB finite ; also limiting 
variety between Species I. and Species V. The globule will 
describe the same circle in the opposite direction if projected with 
the same velocity opposite to that of the fluid. If the globule 
be projected either in the direction of the liquid’s motion or 
opposite to it, with a velocity less than that of the liquid, it will 
move along the Cotesian spiral (Species I. of Tait and Steele), 
from apse to centre in a finite time, with an infinite number of 
turns. If it be projected in either of those directions with a velo- 
city greater by v than that of the liquid, it will move along the 
Cotesian spiral (Species V. of Tait and Steele), from apse to asymp- 
tote. Its velocity along the asymptote, at an infinite distance from 
the axis, will be 
where a denotes the distance of the apse from the axis, and - K — the 
velocity of the liquid at that distance from the axis. If the globule 
be projected from any point in the direction of any straight line 
whose shortest distance from the axis is p, it will be drawn into 
the vortex or escape from it, according as the component velo- 
and the distance of the asymptote from the axis will be 
a 
Sira 
