of Edinburgh, Session 1875-76. 
73 
29. Consider now the actual vortex made up of an infinite 
number of infinitely small vortex filaments. If these be of 
volumes inversely proportional to their vortex densities (§ 25), so 
that their circulations are equal, we now see from the constancy 
of the impulse that the sum of the resultant areas of all the 
vortex filaments remains constant ; and so does the sum of their 
rotational moments: and the resultant areal axis of them all 
regarded as one system is a fixed line in space. Hence, as in the 
case of a vortex filament, the translation, if any, through space is 
on the average along its resultant axis. All this, of course, is on 
the supposition that there is no other vortex, and no solid 
immersed in the liquid, and no bounding surface of the liquid near 
enough to produce any sensible influence on the given vortex. 
2. Experiments illustrating Rigidity produced by Centrifugal 
Force. By John Aitken, Esq. 
If an endless chain is hung over a pulley and the pulley driven 
at a great velocity, it is well known that the motion so communi- 
cated to the chain has almost no tendency to change the form of 
the curve in which the chain hangs, and that the principal effect 
of the motion is to confer on the chain a quasi-rigidity which 
enables it to resist any force tending to alter its curvature. 
This is only true in a general sense, and possibly may be true of 
some ideal form of chain ; but in all chains we can experiment on 
there are forces in action in the moving chain which tend to cause 
the chain to depart from the form which it has while at rest. 
I shall refer to these disturbing forces later on. As the disturb- 
ing forces in most chains are very small, we shall neglect them, 
and for the present suppose the centrifugal force just balances the 
tension at all points. The following experiments were made to 
illustrate the balance of these forces, to show that into whatever 
curves we may bend the chain when in motion, the centrifugal force 
has no tendency to alter these curves: that all forms are forms of 
stability, as far as the centrifugal force is concerned. 
The first experiments were to show the effect of destroying the 
balance between the tension and the centrifugal force. In these 
experiments the links on the descending side of the loop were 
