At a recent meeting of the London Physical Society, Mr. C. Vernon Boys
read a paper on "Integrating Apparatus." After referring to his
original "cart" machine for integrating, described at a former meeting
of the society, he showed how he had been led to construct the new
machine exhibited, in which a cylinder is caused to reciprocate
longitudinally in contact with a disk, and give the integral by its
rotation. Integrators were of three kinds: (1) radius machines; (2)
cosine machines; (3) tangent machines. Sliding friction and inertia
render the first two kinds unsuitable where there are delicate forces
or rapid variation in the function to be integrated. Tangent machines
depend on pure rolling, and the inertia and friction are
inappreciable. They are, therefore, more practical than the other
sort. It is to this class that Mr. Boys' machines belong. The author
then described a theoretical tangent integrator depending on the
mutual rolling of two smoke rings, and showed how the steering of a
bicycle or wheelbarrow could be applied to integrate directly with a
cylinder either the quotient or product of two functions. If the
tangent wheel is turned through a right angle at starting, the machine
will integrate reciprocals, or it can be made to integrate functions
by an inverse process. If instead of a cylinder some other surface of
evolution is employed as an integrating surface, then special
integrations can be effected. He showed a polar planimeter in which
the integrating surface is a sphere. A special use of these
integrators is for finding the total work done by a fluid pressure
reciprocating engine. The difference of pressure on the two sides of
the piston determines the tangent of the inclination of the tangent
wheel which runs on the integrating cylinder; while the motion of the
latter is made to keep time with that of the piston. In this case the
number of evolutions of the cylinder measures the total amount of work
done by the engine. The disk cylinder integrator may also be applied
to find the total amount of work transmitted by shafting or belting
from one part of a factory to another. An electric current meter may
be made by giving inclination to the disk, which is for this purpose
made exceedingly small and delicate, by means of a heavy magnetic
needle deflected by the current. This, like Edison's, is a direction
meter; but a meter in which no regard is paid to the direction of the
current can be made by help of an iron armature of such a shape that
the force with which it is attracted to fill the space between the
poles of an electro-magnet is inversely as its displacement. Then by
resisting this motion by a spring or pendulum the movement is
proportional to the current, and a tangent wheel actuated by this
movement causes the reciprocating cylinder on which it runs to
integrate the current strength. Mr. Boys exhibited two such electric
energy meters, that is, machines which integrate the product of the
current strength by the difference of potential between two points
with respect to time. In these the main current is made to pass
through a pair of concentric solenoids, and in the annular space
between these is hung a solenoid, the upper half of which is wound in
the opposite direction to the lower half. By the use of what Mr. Boys
calls "induction traps" of iron, the magnetic force is confined to a
small portion of the suspended solenoid, and by this means the force
is independent of the position. The solenoid is hung to one end of a
beam, and its motion is resisted by a pendulum weight, by which the
energy meters may be regulated like clocks to give standard measure.
The beam carries the tangent wheels, and the rotation of the cylinder
gives the energy expanded in foot-pounds or other measures. The use of
an equal number of turns in opposite directions on the movable
solenoid causes the instrument to be uninfluenced by external magnetic
forces. Mr. Boys showed on the screen an image of an electric arc, and
by its side was a spot of light, whose position indicated the energy,
and showed every flicker of the light and fluctuation of current in
the arc. He showed on the screen that if the poles are brought too
near the energy expended is less, though the current is stronger, and
that if the poles are too far apart, though the electromotive force is
greater the energy is less; so that the apparatus may be made to find
the distance at which the greatest energy, and so the greatest heat
and light, may be produced.
At the conclusion of the paper, Prof. W.G. Adams and Prof. G.C. Foster
could not refrain from expressing their high admiration of the
ingenious and able manner in which Mr. Boys had developed the subject.
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