289 
of Edinburgh, Session 1876-77. 
C is the Mn0 2 equivalent to the available oxygen. 
D is the MnO found by weighing as Mn 3 0 4 . 
E is the Fe 2 0 3 found by titration with SnCl 2 . 
F is the alumina found by subtracting the Fe 2 0 3 found in E 
from the weight of the precipitate with acetate of soda. 
G-is the water expelled on ignition; it is obtained by deducting two- 
thirds of the oxygen found in B from the loss of weight by ignition. 
It will be seen from the results given in the above table that the 
nodules from different localities vary greatly in composition, though 
in the same locality they have similar composition, irrespectively 
of the nature of the nodules. The insoluble residue contains, 
besides silica and clay, sand of the same mineral nature as is found 
in the bottom at the same locality. The manganese is present 
wholly as Mn0 2 , and the iron as Fe 2 0 3 . In No. 6 there is 3 per 
cent, of cobalt ; this metal, along with copper and a little nickel, 
is present in all of them. Zinc was not found in any of the above 
specimens. 
2. Note on the Measure of Beknottedness. By Prof. Tait. 
In drawing the various closed curves which have a given number 
of double points, I found it desirable to have some simple mode of 
ascertaining whether a particular form was a new one, or only a 
deformation of one of those I had already obtained. Of course 
the schemes (as described in my former paper) contain the desired 
information, but it may sometimes be difficult to obtain in this 
way; for, when the number of intersections is large, we may have 
to change the crossing which is taken as the initial one several 
times before we hit upon the same notation for like crossings (if 
such exist) in the two schemes compared. And the methods of 
deformation already given often present their results in forms so 
distorted that it is not easy at once to recognise their identity with 
other drawings of the very same curves. 
The method of treatment described in my paper, which depends 
upon the study of the plait , supplies (by the + and - signs over 
the various crossings) exactly the sort of information we require, 
though it may leave ambiguities. But some simple mode of apply- 
ing it is requisite. 
I first tried a modification of the process (formerly described) of 
