At least two plates of each field were taken. In any case the two best plates were put on the “blink” comparator, and only those objects clearly nebulous on both plates were marked. The better plate was then placed on a Gaertner measuring machine. The nebulae and all the A.G. stars fainter than the seventh magnitude were measured in _X_ and _Y_ with the same screw. After an interval of a day or two the plate was remeasured. Settings were read to 0.01 mm, corresponding to about 0.87" on the scale of the plate. The two measures of a nebula differed but seldom in this unit, and if faint reference stars could have been used, a higher degree of accuracy could have been maintained throughout the work. In order to orient the plate, two stars were selected with as large a difference in right ascension and as small a difference in declination as possible. The difference in _X_ was then computed in millimeters, assuming a scale-value of 87.4″ per mm. The plate was placed in the measuring machine with the meridian roughly perpendicular to the screw, and adjusted with the tangent slow-motion until the setting on the two stars gave the computed difference to the limit of accuracy of the settings. This method reduced the constant of orientation of the plate to an almost negligible quantity. Turner’s method (_The Observatory_, 16, 373, 1893) was used as the basis for reducing the measures. The six plate-constants for each field were determined from the five or six A.G. stars most symmetrically distributed about the optical center, and graphs were constructed from which the values of _Y_-_Y₀_ and _X_-_X₀_ were corrected. The Δα and Δδ were then added directly to the α₀ and δ₀ of the assumed center, and final corrections to the positions were read from graphs constructed from Turner’s formulae. Any A.G. stars not included in the determination of plate-constants furnished checks. Since the distribution of the stars was about the same as that of the nebulae, it was hoped that the reduced positions of the latter would be of the same order of accuracy as those of the stars. For the 62 A.G. stars on the seven plates measured, the average difference from the A.G. positions was 1.0″ in either co-ordinate. The settings on the nebulae could be made with greater precision than on the stars, hence these results justify placing the accuracy of the nebular positions at about 2.0″ in either co-ordinate, except for such as were near the edge of the plates.