to x', the height set on the vertical scale of the hypsometer, and h the height of the object above the observers eye-line in proportion to h', the reading from the horizontal scale of the hypsometer. Given that Tan (small yellow angle) = Opposite Side / Adjacent Side, therefore Tan (small yellow angle) = h / x = h' / x'. Therefore h = h'x / x'. Likewise the geometry involved in step 2 results in sketch d: two right angled triangles. Next in sketch e we see that the two triangles again have identical angles - each has a right angle, the same small angle shown in yellow, and the same larger angle shown in orange. Therefore in sketch f we see that using the principle of similar triangles, given that each triangle has identical angles, the sides will be in proportion: x the distance to the object in proportion to x', the height set on the vertical scale of the hypsometer, and d the depth of the object below the observers eye-line in proportion to d', the reading from the horizontal scale of the hypsometer. Given that Tan (small angle) = Opposite Side / Adjacent Side, therefore Tan (small angle) = d / x = d' / x'. Therefore d = d'x / x'. Thus the overall height of the object is x (d' + h') / x' Pressure hypsometer A pressure hypsometer as shown in the drawing (right) employs the principle that the boiling point of a liquid is lowered by diminishing the barometric pressure, and that the barometric pressure varies with the height of the point of observation. The instrument consists of a cylindrical vessel in which the liquid, usually water, is boiled, surmounted by a jacketed column, in the outer partitions of which the vapour circulates, while in the central one a thermometer is placed. To deduce the height of the station from the observed boiling point, it is necessary to know the relation existing between the boiling point and pressure, and also between the pressure and height of the atmosphere. See also List of length, distance, or range measuring devices References Measuring instruments Length, distance, or range measuring devices Vertical position