A new photoelectric area scanner, designed primarily for observations of double stars, has been put into routine use at the Lowell Observatory. A description of the scanner and of the associated data acquisition system is given. The procedure of measuring the relative positions of double star components is described and the accuracy obtainable by this method is discussed. This contribution and a subsequent one (p. 170) will appear jointly under the title 'A Photoelectric Area Scanner for Astrometry and Photometry of Double Stars' in Lowell Observatory Bulletin No. 154. This work has been supported by National Science Foundation Grant GP-6983.