circumference by means of a "control lineal," first with an ordinary
Amsler's planimeter and then with the integraph. I have obtained the
following results:

---------+------------+-----------+-----------------------------------
| | | By integraph.
Radius | | By |--------+--------+--------+--------
of | Calculated |Planimeter.| | Upper | | Upper
circle. | areas. | |Middle. | end. |Middle. | end.
| | |p=2 in. |p=2 in. |p=4 in. |p=4 in.
---------+------------+-----------+--------+--------+--------+--------
in. | | | | | |
1 | 3.14159 | 3.140 | 3.140 | 3.138 | 3.120 | 3.120
| | | | | |
2 | 12.56636 | 12.55 | 12.36* | 12.546 | 12.568 | 12.552
| | | | | |
3 | 28.27431 | 28.24 | ...... | ...... | 28.280 | 28.288
---------+------------+-----------+--------+--------+--------+--------

* Cross bar had to be moved during tracing.

From this it follows that the error of the planimeter is less than 0.1
per cent. and that of the integraph about 0.5 per cent. Obviously we
could make this error much less if we excluded small areas measured
with large polar distances, or such polar distances that the cross bar
must be shifted. Excluding such cases, we see that the accuracy of the
integraph scarcely falls behind that of the planimeter and is quite
efficient for practical purposes. It must be borne in mind that the
above measurements were made with the "control lineal," an arrangement
which carries the guide round a circle of the exact test area. In most
cases the curve has to be followed by hand, and the error will be
greater--greater probably for the integraph than for the planimeter,
as the former is distinctly hard to guide well.

I think, then, we should be safe in saying that the error of the
integraph is not likely to be greater and is probably less than 2 per
cent., so that in this respect the instrument may be considered a
practical one.

5. A further condition for a good integraph is that it should have a
wide range of polar distances, and that it should be easily set at
those distances.

One of the conditions I gave to the maker of the instrument was that
it should be