48 
Proceedings of the Royal Society 
circuit. By gradually raising or lowering the upper vessel, a longer 
or shorter column of liquid can he made part of the circuit. On 
listening in the telephone, so long as the liquid vein is short and 
limpid, no sound whatever is heard. This shows that the electric 
current has uninterrupted circulation. On gradually lengthening the 
liquid vein, a point is reached when a rattling noise is heard in the 
telephone. This arises from the altered resistance caused by the 
liquid vein beginning to break up into globules. On still farther 
lengthening the vein, a point is very soon reached when all sound 
in the telephone again ceases. This corresponds to the stage when 
the liquid vein has actually separated into detached drops, and so 
broken entirely the electric circuit. 
2. On the Measurement of Beknottedness. By Professor Tait. 
(Abstract.) 
In my former papers on the subject of Knots, I have provisionally 
measured Beknottedness by the smallest number of changes of sign 
at the crossings, which will render all the crossings nugatory. 
Though I have not seen occasion to doubt the accuracy of this 
mode of measurement, there are two objections to it — (1) It is very 
difficult of application in complex cases ; (2) It suggests no direct 
relation to the electrodynamic method which, except in the case of 
knots wholly or partially amphicheiral, gives results quite in accord- 
ance with it. 
The object of the present paper is to describe a method which, 
while at least partially meeting these objections, very considerably 
simplifies some of the more important processes for the treatment of 
knots, which I have already given. 
In this abstract a very simple example will suffice to indicate the 
method. Take the following six-fold knot 
and modify the sketch, as on next page, the dotted line being traced 
always on the right-hand side of the full line as we go round the curve. 
