drawing board, and
of having a fairly wide range on it, i.e., it must not be limited to
working where the primitive is at one part only of the board.

This condition takes out of every day practical drawing use the
integraph invented by Professors James and Sir William Thomson, in
which the sum curve is drawn on a revolving cylinder. It is essential
that the sum curve should be drawn on the board not far from the
primitive, and that this sum curve can be summed once or twice again
without difficulty. The time involved in drawing the four sum curves,
for example, required in passing from the load curve to the deflection
curve of a simple beam, if these curves were drawn on different pieces
of paper and had to be shifted on and off cylinders, would probably be
as long as the ordinary graphical processes. Coradi's integraph works
on an ordinary drawing board, but since there are nearly 10 inches
between the guide point and tracer, the sum curve is thrown 10 inches
behind the primitive in each integration. Thus a double summation
requires say 26 inches of board, and it is impossible to integrate
thrice without reproducing the primitive. The fact that the primitive
and sum curve are not plotted off on the same base is also troublesome
for comparison, and involves scaling of a new base for each summation.
I have endeavored to obviate this by always drawing the second sum
curve on a thin piece of paper pinned to the board, which can then be
moved back to the position of the first primitive. But this shifting,
of course, involves additional labor, and is also a source of error.

I should like to see the trace and guide chariots on the same line of
rails, one below the other, were this possible without producing the
bad effect of a skew, pull or push.

4. The practical integraph must not have a greater maximum error than
2 per cent. The mathematical calculations, which are correct to five
or six places of decimals, are only a source of danger to the
practical calculator of stresses and strains. They tend to disguise
the important fact that he cannot possibly know the properties of the
material within 2 per cent. error, and therefore there is not only a
waste of time, but a false feeling of accuracy engendered by human and
mechanical calculation which is over-refined for technical purposes.

For comparative purposes I have measured the areas of circles of 1
inch, 2 inches, and 3 inches radius, the guide being taken round the