26S Mr. L. F. Richardson on a Freehand Graphic way 
the surfaces V = const., and that the magnitude of the vector 
is equal to the space-rate of V along the said normal, 
multiplied by a scalar function of position ; which according 
to the particular application will be the conductivity, perme- 
ability or some other specific constant. Then we may require 
the conditions which must hold at a boundary where the 
specific constant has a discontinuity while V is continuous — as, 
for example, where magnetic flux passes from air into mild 
steel. These conditions, which I take from Prof. J. J. 
Thomson's ' Elements of Electricity and Magnetism,' may be 
stated thus : — If K 2 , K 2 are the aforesaid specific constants 
on the two sides of the boundary, and 1 and 2 are the 
corresponding angles which the direction of the vector makes 
with the bounding surface, then 
^ tan 1 — ^ tan # 9 . 
Now if the graph be drawn on a surface which is normal 
to the guiding lines, the direction of the vector lies in the 
graph, and X and 2 are the actual angles which one sees. 
The same is true of the Mercator's map of a spherical surface 
distribution, since the angles are unchanged by projection. 
But with our method for screw symmetry, the angles X and 
2 do not immediately appear, and comparison must be made 
with the angles of the slant sections of the rectangular tubes 
given on the standard chart. 
VII. Miscellaneous ^Xotes on Draughtsmanship. 
(a) Since with the exception of given boundaries and lines 
deduced from symmetry no part of the field can be said to be 
correct until the whole field is correct, it is advisable to begin 
by covering the whole field with intersecting lines, however 
erroneous they may be, and then to carry out amendments 
over wide areas at one time. 
(b) In the final stages of a drawing intended improvements 
often overshoot the mark or cause unforeseen disturbances in 
the surrounding chequers. It seems well, therefore, to lay 
aside the indiarubber after a certain accuracy has been 
reached, and, placing a sheet of tracing-paper over the rough 
diagram, to draw the intended improvements upon this. 
And so with all later stages. The tracing-paper diagrams 
are then compared with one another and the best selected. 
(c) The graphic addition of two scalar functions of position 
is conveniently performed in the way described by Maxwell 
(' Elementary Treatise on Electricity ') by laying the contours 
drawn on a sheet of tracing-paper at equal intervals of the 
one over those of the other, covering the two with a clean 
