page 296 note * Feb. 19.—This is not correct. There is but one degree of beknottedness, for the two knots are not “virtually separate,” as they have a part in common, while one is right-handed and the other left-handed. In fact, the figures above are mere transformations of the last cut in my former paper—which is shown to be capable of being opened iip by a single change of sign. This can be done in the figures above, at either end of the lower coil where it forms part of the external boundary. But if, without altering the outline of the figure, we change all the signs in either of the two component knots, so as to make them both right-handed, or both left-handed, the whole acquires the double degree of beknottedness wrongly assigned to it in the text. But it has now continuations of sign, and in virtue of these it happens to be reducible. In fact, when we make it into a clear coil after these changes of sign it becomes the pentacle (fig. 1 above), the only knot with fewer than six crossings which possesses, as we have seen, two degrees of beknottedness. I stated in my first paper, that when the signs in any non-nugatory arrangement are alternately + and − the cord “is obviously as completely knotted as its scheme will admit of.” This completeness must be understood of what may be called Knottiness, not of Beknottedness. For it has just been shown by a particular case that we can occasionally increase the degree of beknottedness, while diminishing knottiness, i.e., losing crossings by so altering their signs as to make some of them nugatory. The point thus raised, i.e., the distinction between Knottiness and Beknottedness, is a very troublesome and delicate one, and is obviously related to several of the difficulties pointed out in the present paper.