242 Mr. L. F. Richardson on a Freehand Graphic way 
It remains to be shown what accuracy may be expected 
from the freehand method. This is of course largely a 
personal matter. I exhibit my own handiwork. Others will 
doubtless obtain greater precision. Throughout this paper I 
have chosen test cases in which the analytical verification 
should not be too difficult. Hence the diagrams look rather 
stiff and formal and do not in any way do justice to the 
freedom of this graphic method. 
Fig. 2. 
Ik 
< 
\^\ S ' 
X \>\ 
- "T " 
V \ 
Example of the solution 
d 2 V 
^— 2 =0. — Along one 
pair of opposite edges of a square V = 1, along the other pair 
V = 0. Find Y at all points inside. By symmetry V will be 
equal to -J along the diagonals. And again by symmetry, 
the lines joining mid-points of opposite sides will be normal 
to the contours of V. So that it is only necessary to find V 
in half one-quarter of the square. Further, by symmetry, at a 
