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done. The upper disc having been replaced, a stride level was placed on the top of the body tube, and it was turned throughout the twenty-four hours, gently altering the declination by means of the tangent screw until the bubble remained central throughout the circuit. When this was so the index of the vernier was set to o° on the declination circle. As the above described operation is of too heavy a nature to be effected by an amateur, the following is a very good -plan to mechanically adjust all the verniers, and'may be used with with any form of equatorial :—Clamp the telescope to o° in declination, and by means of a level placed on the body of the telescope alter the right ascension movement alone until the telescope is perfectly level, pointing E. Now revolve the hour-circle until XXIV is read by the vernier. Shift the telescope through 12 hours, and without altering the declination or hour-circle, level the body as before described, but of course this time pointing W. If the vernier now reads XII whilst the declination is still o°, all the verniers are in correct position. But if the W reading is not at XII when the bubble is central, alter the right ascension until the reading is exact, and then correct the level by slightly shifting the declination. When the bubble is again central, alter the position of the declination vernier one half the ascertained error of reading. If the telescope be now moved through exactly twelve hours it will be exactly horizontal at each extreme when the declination is o°. All that will be requisite, if this is the case, will be to notice that the index of the second right ascension vernier reads exactly half way between the extremes. If it does not, correct its position.

But in a German equatorial (Figs. 4 and 21) in which a declination circle is on one side of the polar axis, instead of being over it as in the Berthon, the correct position of the vernier can be astronomically ascertained before proceeding further. Read the declination of any star within 30 minutes of its meridian passage with the circle facing E. Now revolve the instrument till the circle faces W. and re-direc the telescope to the same star and again note its declination. If the declination circle has been moved through exactly 1800, and therefore the two readings are precisely alike, the declination vernier is correctly placed. But if the two readings are not the same, alter the vernier half the difference between them. With a refracting telescope this operation may be repeated several times in order to secure the greatest exactness, but with some reflectors a persistent small error cannot be well avoided, it should not exceed 1 or 2 minutes of arc. This remark applies to all adjustments.

Example:—The declination reading of y1 Andromedse was 40° 34' with the circle E. and 40° 10' when W. ; half the difference 24' is 12', and therefore the vernier must be altered that amount. To do this, fix the telescope on the star, and alter the vernier till it reads

(4?° 34' — 12' E.

40° 2 2f = < or

(40° 10' 4- 12' W,

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