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Cathetometer
Brief description
A cathetometer is an optical precision instrument designed to measure small vertical height differences between two points or liquid levels without physically contacting or disturbing the observed system. Pioneered in 1816 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit to measure thermal expansion and mercury column barometry, the cathetometer consists of a horizontal sighting telescope that slides along an accurately graduated vertical column. It provides non-invasive millimeter and sub-millimeter measurements essential for experimental physics, barometry, and fluid mechanics.
Use / Function
- Barometer and Manometer Reading: Measuring the height difference of mercury menisci in open or closed U-tubes and precision barometers without parallax or mechanical disruption.
- Thermal Dilatometry: Measuring the microscopic vertical thermal expansion or elongation of heated metal rods, ceramic bars, or columns.
- Capillary and Surface Tension Studies: Reading the exact height of liquid rise or depression in narrow glass capillary tubes.
- Elasticity and Creep Testing: Tracking the vertical deformation and deflection of loaded structural beams, wires, or springs under mechanical stress.
Operating principle
- True Vertical Axis: A heavy, rigid metal column is aligned precisely perpendicular to the local gravitational field using leveling screws and sensitive spirit levels.
- Horizontal Optical Alignment: A low-power sighting telescope with internal reticle crosshairs is mounted on a sliding carriage and leveled so that its optical axis is perfectly horizontal at all elevations.
- Non-Invasive Optical Sighting: The observer focuses the crosshairs on the bottom or top of a distant meniscus (or fiducial mark) through glass containers without touching the apparatus.
- Vertical Displacement Measurement: The carriage is translated vertically along the column until the crosshair aligns with the second reference mark.
- Vernier Reading: The precise vertical distance traversed is read directly from the column’s master scale using a vernier scale or micrometer drum, eliminating parallax error.
How to create it
- Machining the Base and Column: Turn and grind a rigid vertical brass or steel column (typically 1 meter long) mounted securely on a heavy tripod base with three leveling foot screws.
- Mounting Sensitive Levels: Affix a sensitive cross-level or spirit level vial to the base and the column carriage to ensure strict verticality.
- Cutting the Primary Scale: Precision-engrave a millimeter scale along the full vertical length of the column using an accurate dividing engine.
- Fitting the Sliding Carriage: Machine a bronze or brass carriage that glides smoothly up and down the column with negligible play, fitted with a clamp screw and fine slow-motion vertical feed screw.
- Mounting the Telescope: Mount a horizontal terrestrial telescope equipped with an internal spider-web or etched glass reticle on the carriage, incorporating a leveling vial on the telescope tube itself.
- Adding the Vernier Scale: Attach a vernier scale to the carriage adjacent to the column’s master scale to read measurements to 0.02 mm or 0.05 mm.
Materials needed
- Essential: Cast Metal (brass, bronze, or steel) for the heavy column, tripod base, and sliding carriage; optical Glass for achromatic telescope lenses and spirit level vials.
- Tools: Metal-turning lathe, dividing engine or precision ruler for scale engraving, fine files, taps and dies, collimator for optical alignment.
- Substitutes: A rigid wooden column with an inlaid steel scale can suffice for lower-precision workshop measurements; a simple peep-sight tube with wire crosshairs can serve in place of a full compound telescope.
Variants and improvements
- Dulong and Petit Cathetometer: The foundational laboratory model with a single sliding telescope and silver-inlaid scale.
- Dual-Telescope Cathetometer: Features two independent sighting telescopes on the same vertical axis, allowing simultaneous observation of upper and lower liquid levels during transient pressure pulses.
- Rotatable Column Cathetometer: Allows the column to rotate smoothly about its vertical axis through 360 degrees, enabling height comparisons between apparatuses placed side-by-side on the same bench.
- Micrometer Ocular Cathetometer: Adds a filar micrometer eyepiece to the telescope to measure minute displacements within the visual field directly without moving the main carriage.
Limits and risks
- Leveling Sensitivity: Any slight out-of-plumb tilt of the central column introduces geometric cosine errors and vertical parallax into the measurements.
- Thermal Distortion: Ambient temperature fluctuations expand or contract the metal column, requiring thermal calibration for extreme laboratory accuracy.
- Optical Distortions: Imperfect or curved glass walls in the experimental vessels containing the liquid can refract light rays and produce apparent vertical displacement of the target meniscus.