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