As I fear the title of my paper to our Society to-night contains two
misstatements of fact in its three words, I must commence by
correcting it. In the first place, the instrument to which I propose
to draw your attention to-night is, in the narrow sense of the words,
neither an integrator nor new. The name "integrator" has been
especially applied to a class of instruments which measure off on a
scale attached to them the magnitude of an area, arc, or other
quantity. Such instruments do not, as a rule, represent their results
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 praeterea 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.
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