It will take but little consideration to discover how easily this “averaging” property of the Planimeter can be applied to any and every problem involving the principle in question and to realize how many problems there are of constant occurrence in the engineer's practice to whose solution this property of the Planimeter makes the instrument particularly adapted. Some of these we have already mentioned, and the list could be extended almost indefinitely. Enough, however, has been already said to show that even were the application of the Planimeter limited to the particular form of operation just described, its almost incredible accuracy of operation and the enormous saving in time and mental effort effected by its use would alone make it an indispensable aid in the engineer's labors.

In the highest form of the Planimeter, of which the Integraph and Integrator are examples, the principles just described have been developed even beyond the capacity of the Polar type we are dealing with, so that in addition to an ability to perform the operations possible to the simpler form they are capable of solving problems involving the finding of moments of inertia and stability, determination of stresses in framed structures, centers of gravity and gyration, and many others too numerous to mention.

This class of Planimeter will be more fully described later when the higher forms of the instrument are taken up for discussion.

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