The object of this paper is to communicate a series of observations made with a new instrument for the purpose of investigating the question of parallax. Though a much longer period of time will be necessary to elucidate this subject in a perfectly satisfactory manner, yet, from the observations already made, it seems highly probable that the parallax of α Cygni is too small a quantity to have had any share in producing either the discordances remarked by Dr. Brinkley, or those in the Greenwich observations already communicated to the Society. The method consists in continually observing the meridional difference in polar distance of α Cygni and β Aurigæ, (which pass through the field of the same telescope,) by means of a micrometer adapted to this purpose. A drawing of the instrument accompanies the observations.