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is assured if the conditions under B are fulfilled. These conditions should, however, always be applied to a Berthon equatorial, as if the mechanical setting of the vernier has not been sufficiently exact, the conditions under B will not be fulfilled.

With either form of instrument if B is realized, and therefore the setting of the vernier is correct, the meridian position can be obtained as follows :—Select a six hour star, and having noted its declination error by comparing its vernier reading with the catalogue amount, firmly clamp the vernier to the catalogue declination. As the telescope must be moved to do this, the star will have shifted from the centre of the field, it must be brought back to that position without shifting the declination setting. If there is an azimuth motion it must be employed in addition to that in right ascension, but if there is none, the foot must be moved. The direction of this movement will depend on the nature of the ascertained error. If the star is six, hours W. and the vernier reading is + (or if E. —) the upper end of the polar axis or the north foot must be moved towards the E. If the star is W. and the reading is — (or E. and +) the upper end of the polar axis or the north foot must be moved towards the W. The foregoing adjustments will most likely ensure the correct conditions of A.

With the Berthon equatorial the E. and W. declinations may not fulfil the conditions of B, but do so with C. In that case the vernier may be corrected as follows :—If the vernier readings are +, the vernier must be moved towards the south of the circle, the amount of the error; if —, the reverse. The vernier can be best altered by meridian observations, and afterwards the latitude must be re-adjusted as before described (III).

But as it is not likely that the preliminary setting of the meridian position was sufficiently exact to allow of C being fulfilled, D is most likely to be the condition of a Berthon equatorial when it is first placed in rough adjustment; and therefore the following plan may be employed to accurately adjust one of those instruments, even when it is placed on a stone whose upper surface is not level.

Having approximately placed the instrument facing the south, and adjusted the polar axis as before described (III), read the declinations of a six hour E. star and a six hour W. star, and compare each result with the position as given in a catalogue. Subtract the smaller from the larger amount in each case, and add the remainders together. Half this will be the vernier error, which may be corrected, and the telescope placed in the meridian as just described. If the ordinary rule for indices be followed, the nature of an error will easily be identified. Examples i and 2.

Another plan may be employed, though perhaps it is inferior to that just described. It is as follows :—Observe an E. or W. six hour star, and having set the vernier to the catalogue declination, centre the star by shifting the foot and the right ascension movement. When the star is exactly central in the field of view, turn the telescope to

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