It is foreign to the present purpose to shew what the causes are which have most effect in raising or depressing the apparent horizon. It may be sufficient to mention, that changes in the relative temperature of the air and the sea must produce changes in the refraction near the surface. Dr. Wollaston has published two papers in the Philosophical Transactions on this subject, in the volumes for 1800 and 1803, and to these I beg to refer the reader for precise information upon this very curious subject. The object which this sector proposes to attain, is the actual admeasurement of the dip angle; that is, to ascertain how much the visible horizon is depressed below the horizontal plane passing through the eye of the observer. The instrument is so contrived as to measure double the dip angle twice over, so that we obtain four times the required dip, and one quarter of this angle is what must be applied to vertical angles, measured from that part of the horizon which has been observed. Figure I. is the instrument seen in perspective, and Fig. II. is a plan of it with the telescope removed. In order to explain its use, let A and B (Fig. II.) represent the two reflecting glasses at right angles to the plane of the instrument, and also nearly at right angles to each other. It is clear that when the plane of the instrument is held vertically, an eye situated at E, and looking through the unsilvered part of the glass A at a distant point C, will at the same time see by joint reflection from both glasses, another distant point D at 180º from C; and D will appear to correspond with C, if a suitable motion be given to the index glass B by the tangent screw F. The instrument may now be supposed to measure the arc CZD. If the points C and D be each three minutes farther from the zenith than 90º, the entire angle will then exceed 180º by double that quantity. The relative position of the glasses then corresponds to 180º 6', and the six minutes of excess would be shewn on the arc at F if there were no index error. But, by reason of the index error, the real quantity will not be known till a similar observation has been made with the instrument in an opposite direction. If the instrument be now inverted, so that the unsilvered glass is uppermost, the arc intended to be measured is CND, or the sum of the distances of the points C and D from the Nadir instead of the Zenith, which of course falls short of 180º by as much as the former arc exceeded that quantity. The difference of the two arcs is consequently twelve minutes, and if the index be now moved till the objects C and D appear to correspond, the amount of this double difference will be shewn by the _change of position_ of the vernier. Hence it is evidently unnecessary that the index error should be previously known, and even preferable that its amount should be such as to avoid the needless introduction of negative quantities by positions on different sides of zero.