The cathetometer is a precision instrument used in measuring the vertical distance between two points, that is, between the horizontal planes on which they lie, independently of whether or not they are situated on the same vertical plane.
It is essentially composed of a vertical staff capable of rotating around its axis on which a telescope with a reticle is fixed at a ninety-degree angle and can be moved up and down the staff and blocked in the desired position.
Wishing to measure the difference in level between two points, the telescope is aimed at one point and then at the other by moving it up or down the staff and, if necessary, by rotating it with the staff: the difference between the two readings on the scale corresponding to the two positions gives the difference in level.
The supporting staff of the cathetometer is a sturdy cast iron staff held vertical by a heavy tripod, it too cast iron, with three levelling screws standing on three brass disks with notches for the tips of the screws.
Along the entire length of the staff is a steel double guide in which a cursor and a small slide connected to each other with a long micrometric screw. The cursor holds the telescope which lies on the forks of a brass frame fixed by means of a horizontal pin. There is an air-bubble level on the telescope, which also has a reticle and a focusing screw.
The inclination of the telescope and its level can be varied by means of a screw that rotates the frame around the horizontal pin; another screw on the level allows adjustment of the latter with respect to the telescope.
The slide, which has a screw that clamps it to the staff, is only for the purpose of blocking the slide and, once blocked, allowing it to be moved slightly up or down by means of the micrometric screw connecting them.
The staff is free to rotate around its own vertical axis and has at the base a screw that holds it to the tripod. Once it has been blocked in a certain position it can be rotated slightly in either direction by means of the horizontal micrometric screw.
To move the telescope to the desired position, both slide and cursor are moved.
Movement of the entire system along the staff is facilitated by the fact that this, by means of a string on a pulley at the top of the staff, is balanced by a counterweight that is free to slide between two brass guides on the other side of the staff.
Since it is quite difficult the centre the telescope in this way, by leaving the staff free, it can be positioned so that the point to be sighted falls near the centre of the reticle and then, once the staff and the slide have been blocked, they are moved slightly up or down with the micrometric screw that connects the cursor to the slide until the point to be sighed is at the centre of the reticle.
The scale, graduated in millimetres (length 113 cm) is etched into a strip of silver inserted into the shaft between the two guides of the cursor; the index and a fifty thousandth vernier are etched on one side of a window in the cursor under the telescope, while on the other side there is an eyepiece with a guide that allows reading.


Bibliografia:
Battelli - Cardani (1922),Vol. I, p. 244
Daguin (1878), T. I, p. 22
Drigo - Alocco (1945), p. 219
Segnini - Vergara Caffarelli (1990), p. 111
Violle (1883), T. I, p. 318


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