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—(I) 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 accordance 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.