They are here focused (so far as the rays in the primary plane are concerned) upon the circle **OQ**' A, and the outstanding aberration is of the fourth order.

The grating at A and the eye-piece at 0 are rigidly attached to a bar AO, whose ends rest on carriages, moving on rails **OQ**, AQ at right angles to each other.

Dt \c3g.) 3qr **Oq**,~

8, we have O'Q'/**OQ** = a' tan w' la tan w = 1/N, where N is the " scale " or magnification of the image.

If Q lb be the weight of the poise Q, the position of Q when the steelyard is exactly in balance is given by the equation I T: X q.d Q X **OQ**, or **OQ** =p X q X T -.

After the image of the body is brought into coincidence with the cross threads, the instrument is turned through 180° on the axis, which results in the line of sight of the telescope pointing in a certain direction **OQ**, determined by the condition QOZ = ZOP. The telescope is then a second time pointed at the object by being moved through the angle QOP. Either of the angles QOZ and ZOP is then one half that through which the telescope has been turned, which may be measured by a graduated circle, and which is the zenith distance of the object measured from the direction of the axis OZ.