In the example just used to illustrate this use of the Planimeter the conditions were made of the simplest nature— the final surface being taken as a simple included plane— in order that the principles involved in both the preparation of the diagram and its measurement might be clearly understood. This knowledge having been acquired the extension of the principle to the case of any problem of similar nature and requiring similar form of treatment is easily accomplished regardless of the seeming complexity of any special set of conditions which might be involved in any given problem.

The theory and practical application is the same for every problem of the class under discussion regardless of the form or shape of the required final surface whose contours may be straight, curved, or irregular. In each case the diagram is constructed by plotting both sets of contours or their horizontal projections, original and final, one set being superimposed on the other and the elevations of both sets being referred to the same reference or datum plane. The total volume of the constituent prismoids into which this treatment divides the volume of material to be excavated is then measured by means of the method of Continuous Prismoids with the Planimeter in exactly the same manner as described in the example just described.

The factors given in Table 9 are to be used in all operations of the nature, proper correction being made to the final result when the contour interval in any given case varies from that employed in the calculation of the table which for convenience is taken as one foot.

The facility and ease with which calculations of this class are made with the aid of the Polar Planimeter has in many cases a very direct result of the very greatest importance, and especially in the case of problems similar to that about to be described since, by allowing the making of a number of different measurements by this method in the time required to make one by any other method, we are able to make the calculations and obtain the results of a number of possible Reservoir locations and thus intelligently select the best location by a comparison of the results obtained, and that with no greater expenditure of time or mental effort than is ordinarily given to one such computation.

The diagram shown of Plate VIII, shows the liens of a small storage Reservoir constructed some years ago by the writer for the Suburban Water Co., of Pittsburgh, Pa.

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