297 
of Edinburgh, Session 1876 - 77 . 
arrangement just described, the loop passes symmetrically through 
the simple knot, we have another six- crossing form, very much 
resembling the last, but which is essentially not amphicheiral. 
It is figured below in one of its forms — the others may be got by 
deformation — and the schemes of the two kinds are appended for 
comparison. 
Figs. 3 and 4 A. D¥> E G AD F CH? B \ A.. 
Fig. 5 ADBFCFDiECF.BI A. 
It will be seen that the sole difference between the amphicheiral 
knot and that last figured, lies in the inversion of the positions 
of A and F in their even places in the scheme. 
It appears, then, that none of these abbreviated methods, how- 
ever useful as temporary aids to classification, can take the place 
of the scheme in fully describing the form of a knot and in 
measuring the amount of beknottedness in general. Especially is 
the scheme required in order to calculate the beknottedness in 
terms of the electromagnetic work. And this conclusion might, I 
think, have been inferred from the prominent part which the 
arrangement of the letters in the even places plays in determining 
the form of a knot; an arrangement of which only traces are left 
when we substitute the sign of the work at each junction for the 
letter attached to it, thus losing all control of the amount to be 
added or subtracted on account of the mere number of coils. 
[ Added Jan. 27th .'] — Professor Clerk-Maxwell, to whom I sent 
some of the above results (and to whom, as well as to Sir W. 
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. 
