*Project Gutenberg*. Public domain.

*The Engineer.*

[Illustration: WATCHMAN’S DETECTER]

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## INTEGRATING APPARATUS.

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