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,