(530 3 
The sectioning of two roots (in this case the 10th and 11th) 
entails here the same consequences as the sectioning of one root for 
the lower trunk-dermatomata. Towards the mid-dorsal line sensibility 
is preserved, towards the mid-ventral line an insensible triangle is 
formed. Even by sectioning three roots in this region, as has 
been done in fig. 26 (10th, 11th and 12th), we only succeed in 
achieving here what is achieved for the lower dermatomata by the 
sectioning of two roots, i.e.: an upper ventral insensible triangle 
with broad basis, and, separated from this by a sensible lateral band, 
a lower ventral insensible triangle with narrow basis. Therefore the 
statement does hold no longer good here, that the insensible band 
of two sectioned roots cannot be smaller at the mid-dorsal line than 
half of the isolated central area. Even on the 11th and 12th this 
influence of the extremities is still exerted (see Fig. 26). The insen- 
sible dorsal triangle, dependent on the section of these two roots, 
is very narrow there. 
Meanwhile we are enabled also to survey in a simple manner 
the different relations, existing at the mid-dorsal line, in the lateral 
part (largest breadth of central area), and at the mid-ventral line. 
When we conceive a ranging of successive central areas, twhether 
overlapping one another or not, supposing them (in as far as the 
middle trunk-dermatomata are concerned) to be all of the same size, 
and, if overlapping one another, to do so to the same extent, then 
the differences in these relations may be expressed by a formula in 
the following manner. 
Starting from a lower central area, we will call the distance 
between its cranial end and the caudal end of the next central area 
y, and the distance between its cranial end and the caudal end of 
the second following central area x. Then it will follow clearly (for 
at the mid-dorsal line only a transposition was performed, as y 
represents in that case the overlapping of the central area, z the part 
of the central area not overlapped by central areas, that the breadth 
of the central area = 2+ 2y.1). The breadth of two central areas 
lying adjacent to one another, is thus represented by 2e + 3y, 
three by 32+ 4y etc. In the same manner the breadth of the 
analgetic bands will be represented: for one sectioned root by a, for 
two roots by 2e Jy, for three roots by 2e + 3y ete. 
But this formula is a general one, in as much as it holds good 
not only here, but also for the mid-ventral line and the lateral parts- 
') See: Proceedings of the Roy. Acad. of Sciences. Meeting of Dec. 28th 1901, p. 360, 
