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 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.