86 Proceedings of the Royal Irish Academy. 
There remain nine points not accounted for, viz. : — 
Li I Ee I B I P I I Al I P I S I CI. 
These nine points are found to lie upon a simple serpentine cubic 
with one real asymptote, which I have plotted in Plate vi. 
Taking the point 20 for origin, the co-ordinates of the nine points 
are as follows : — 
y 
1. 
Lithium. 
- 13 
- 1 
2. 
Beryllium. 
- 11 
- 2 
3. 
Boron. 
- 9 
- 3 
4. 
Fluorine. 
- 1 
- 1 
5. 
Sodium. 
+ 3 
+ 1 
6. 
Aluminium. 
+ 7 
+ 3 
7. 
Phosphorus. 
+ 11 
+ 3 
8. 
Sulphur. 
+ 12 
+ 2 
9. 
Chlorine. 
+ 15i 
+ 1 
By means of this Tahle, the nine unknown co-efficients of the cuhic 
can be found, and the curve plotted, with its asymptote, as I have 
done in Plate vi. 
The total curve consists of — 
a. the lineal branch ; 
I, the cubic branch ; 
and there is a possibility of forming an element wherever the monad, 
dyad, triad, or tetrad lines intersect the curve. 
The first three elements, viz. — Li | Be | B group themselves upon ] 
the cubic branch, and also the last three elements, viz. P | S | CI arej 
found upon the cubic branch. 
The fourth element, carbon, is found upon the lineal branch, and 
could not occur upon the cubic branch, which lies altogether inside the j 
