295 
of Edinburgh, Session 1876 - 77 . 
copper crossings, or when the uncorrected expression for the electro- 
magnetic work vanishes. Thinking of this in connection with the 
fact that a change from right-handed to left-handed in a knot simply 
changes silver to copper, or vice versa, i.e., reverses the sign of the 
electro-magnetic work, 1 was led to see that there is a class of knots 
which are capable of being changed from right to left-handed , without 
* 
change of form , by the ordinary processes of deformation. Of course 
this implies that there is a mode of interchanging the letters, two 
and two, in the scheme, so that their order remains unaltered ; or, 
what comes to the same thing, that we shall get exactly the same 
scheme (signs not included) by taking either of two different 
crossings as A, and lettering as usual from it in the same direction 
round the curve. 
It will be readily found by trial that this can be done with the 
only forms which have four valid intersections — as they are figured 
in my former paper — if only the wire or cord be so twisted about 
that, w T hile the form is preserved, the junctions B, D be brought into 
the positions relative to the figure which were formerly occupied 
by A, C. For the scheme 
+ + + + 
ADB ACBDC | A 
— + — I 1 — + 
remains the same, so far as the letters are concerned, if we keep 
the same cyclical order of letters, but write A for B, B for C, &c. 
In estimating the electromagnetic work, by the rule above, w ? e find 
we may leave out either A, C, or B, D. So that the work is ± 8?r, 
i.e., one degree of beknottedness. 
The following case, with six intersections, is very instructive. 
Either figure is formed from the other by throwing the lower coil 
over the top of the whole. 
3 4 
It will be seen that each of these forms may be regarded as a 
