In response to the demand from the engineers of the country, systems of plane coordinates for each of the various States were computed by the U. S. Coast and Geodetic Survey. After these were completed there was need of a manual of computations that would show clearly how the resulting grids could be used in actual calculation. Although two different systems were used in adapting the grids to the different States, yet the method of using the results after the coordinates have been computed is essentially the same in both of the systems. It is hoped that the sample computations given in the text will illustrate the close similarity in the methods of application. We believe that enough material has been included to serve as a model for practically any case that may arise in actual engineering operations.