331 
of Edinburgh, Session 1876 - 77 . 
subject of change of scheme of a given knotting which was dis 
cussed in my last paper. To give only a very simple instance, 
notice that the first of the changes there mentioned is merely that 
from 
/ 2 \ 
m - n 
ii ii 
to 
m — n 
ll X 2/|| 
where the double lines may stand for any numbers of connection 
whatever. 
I conclude by stating, in illustration of the remarks made at 
the end of my last paper, that I have hastily (though I hope cor- 
rectly) investigated the nature of all the valid combinations among 
720 which are possible in the even places of a scheme correspond- 
ing to 6 intersections (only 80 of these are not obviously nugatory) 
— and that'I find only four really distinct forms . They are 
1. Two separate trefoil knots. Here there are two degrees of 
beknottedness. 
2. The amphicheiral form. (Figured on p. 295 of my Note on Be- 
knottedness . Also in a clear form in the last cut of my first paper.) 
3. Fig. p. 297 of the same paper. These two forms are essen- 
tially made up of a trefoil knot and a loop intersecting it. 
4. The following knot, which belongs to a species found with 
every possible number of crossings from 3 upwards. This species 
furnishes the unique knots with 3 and with 4 crossings, and one of 
the only two kinds possible with 5. 
