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tlie vertical axis. The divisions of the limb are read off bymeans of three microscopes : one at the bottom, opposite to thelowest part of the circle: the other two respectively opposite‘he left and right extremities of the horizontal diameter. Thisshort description is sufficient for our purpose: a fuller descrip-tion has been given by Dr. Brinkley in the Irish Transactionsf or 1815.

It was the original intention of the maker of the instrument^hat meridional observations should be made with it. -And theinstrument can readily be placed in the plane of the meridian:b «t, in that case, only one observation of the same star can bemade with it on the same day. Such (see pp. 67, &c.) is to bemckoned only half an observation: we must wait twenty-fourhours at least before we reverse the instrument and complete the°hservatiou. If the weather should be unfavourable we may beobliged to wait several days. But, even in the interval of one day,)h° temperature may have altered and affected the instrument.J° prevent this evil, or to obviate the objection that may beounded on its supposed existence, Dr. Brinkley observes thestar with the face of the instrument to the east, once or twicee f°re it reaches the meridian, and then, as often, with the face°I the instrument to the west, after the star has passed theme ndian. Thus the two essential parts of an observation aremade within the space of ten or twelve minutes. But the ob-s p r vations thus made are, in a certain sense, imperfect ones,r‘ nce they are not observations of meridional zenith distances.he y may, however, by the aid of calculation, be made tofconre, or be reduced to, such observations. The main con-111011 necessary to be known is the time of the observation, or,^ther, the interval of time between the observation of the zenith’stance and the star’s transit over the meridian. This is easilyaf I hi an Observatory. What else remains is a matter altogether°I calculation, which, as on like occasions, will furnish us witha formula and rule of solution.

We will now direct our attention to the formula, which is0 express the difference of the meridional zenith distance of*' star » and of its zenith distance observed very near to the

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