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Quantities of Materials.

I. Volumes from Cross Sections.

2. Volumes of Single Prismoids.

Accuracy of Results.

If the Planimeter used, instead of having an adjustable arm, should be the simpler form of instrument and only capable of giving areas in one unit, say sq. inches, it is evident that a considerable modification would be necessary from the operation just described. In fact, the operation would have to be exactly the same as it would have to be were no Planimeter at all used except for the saving in time and effort effected by the Planimeter in measuring the number of sq. inches contained in the three sections. As to the degree of accuracy with which these results are obtained in the manner just described, it is evident that much depends upon the accuracy of the plotting of the Sections, as well as upon the care with which the tracing of the plotted sections is accomplished. Repeated trails made to test the accuracy of results obtained in the manner described have shown that, with ordinary care in the plotting of the Sections, and with that attention to the requisites for correct tracings which should be taken in all instrumental work, the error in measurement of a prismoid need never be greater than two cu. yds. in one thousand or 0.2 of 1 per cent.

In fact, even in cases where time is a very necessary factor, and where the rapidity with which the measurements are made precludes the attaining of any but a very ordinary care in operating, the results obtained have always proved to be far within the accuracy of any but the most accurate and precise field work and quite equal even to that.

As to the relative saving of time and labor of the Planimeter measurements and the same measurements made by any other known method, either table or diagram, that the proportion in favor of the Planimeter is easily within the ratio of 1 to 3 is easily demonstrated.

As this subject of accuracy must come up for more detailed discussion later, it will not be enlarged upon here further than to say that when once the Engineer has used the Planimeter as an aid in this form of computation he will never again return to any— even the most accurate— which he may have used before, a remark which applies with equal truth to every form of calculation coming within range of the Polar Planimeter's capacities.

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