the tracer describes the whole
length of the curve. The registering wheels R, R' rest against the glass
sphere and give the values nA_n and nB_n. The value of n can be altered by
changing the disk H into one of different diameter. It is also possible to
mount on the same frame a number of spindles with registering wheels and
glass spheres, each of the latter resting on a separate disk C. As many as
five have been introduced. One guiding of the tracer over the curve gives
then at once the ten coefficients A_n and B_n for n = 1 to 5.

All the calculating machines and integrators considered so far have been
kinematic. We have now to describe a most remarkable instrument based on
the equilibrium of a rigid body under the action of springs. The body
itself for rigidity's sake is made a hollow [v.04 p.0981] [Sidenote:
Michelson and Stratton analyzer] cylinder H, shown in fig. 24 in end view.
It can turn about its axis, being supported on knife-edges O. To it springs
are attached at the prolongation of a horizontal diameter; to the left a
series of n small springs s, all alike, side by side at equal intervals at
a distance a from the axis of the knife-edges; to the right a single spring
S at distance b. These springs are supposed to follow Hooke's law. If the
elongation beyond the natural length of a spring is [lambda], the force
asserted by it is p = k[lambda]. Let for the position of equilibrium l, L
be respectively the elongation of a small and the large spring, k, K their
constants, then

[Illustration: FIG. 24.]

nkla = KLb.

The position now obtained will be called the _normal_ one. Now let the top
ends C of the small springs be raised through distances y_1, y_2, ... y_n.
Then the body H will turn; B will move down through a distance z and A up
through a distance (a/b)z. The new forces thus introduced will be in
equilibrium if

ak([Sigma]y - n (a/b) z) = bKz.

Or

z = [Sigma]y / (n a/b + b/a K/k) = [Sigma]y / (n (a/b + l/L)).

This shows that the displacement z of B is proportional to the sum of the
displacements y of the tops of the small springs. The arrangement can
therefore be used for the addition of a number of displacements. The
instrument made has eighty small springs, and the authors state that from
the experience gained there is no impossibility of increasing their number
even to a thousand. The displacement z, which necessarily must be small,
can be enlarged by aid of a lever OT'. To regulate th