graphically, and we may take, as characteristic examples of them,
Amsler's planimeter and some of the sphere integrating machines.

An integrator which draws an absolute picture of the sum or integral
is better termed an "integraph." The distinction is an important and
valuable one, for while the integraph theoretically can do all the
work of the integrator, the latter gives us in niggardly fashion one
narrow answer, _et præterea nil_. The superiority of the integraph
over the integrator cannot be better pointed out than by a concrete
example. The integrator could determine by one process, the bending
moment, from the shear curve, at any one chosen point of a beam; the
integraph would, by an equally simple single process, gives us the
bending moment at all points of the beam.

In the language of the mathematician, the integrator gives only that
miserly result, a definite integral, but the integraph yields an
indefinite integral, a picture of the result at all times or all
points--a much greater boon in most mechanical and physical
investigations. Members of our Society as students of University
College have probably become acquainted with a process termed "drawing
the sum curve from the primitive curve." Many have probably found this
process somewhat wearisome; but this is not an unmixed evil, as the
irksomeness of any manual process has more than once led to the
invention of a valuable machine by the would-be idler. Thus our innate
desire to take things easy is a real incentive to progress. It was
some such desire as this on my part which led me, three years ago, to
inquire whether a practical instrument had not been, or could not be,
constructed to draw sum curves. Such an instrument is an integraph,
and the one I have to describe to you to-night is the outcome of that
inquiry. It is something better than my title, for it is an integraph,