Ctesibius improved surveying instruments. His dioptra, an instrument corresponding to a theodolite, was a plane table set on a tripod, furnished with compass points and two sights. The plane was adjusted by screws and a water level. This instrument was used by engineers for leveling, laying out irrigation works and farm lands, sinking shafts for mining and prospecting purposes, and for tunneling. A cyclometer for measuring angles of dip and elevation of rock beds and mountains was also used with this instrument. The Greeks owed much of their knowledge of hydrostatics, mechanics, pneumatics, and physics generally to Ctesibius. He was not only a great inventor and lecturer, but also a writer of valuable textbooks dealing with physical and mechanical sciences. Hero edited a number of editions of the textbooks of Ctesibius, and is credited with inventing some of the theories and machines discussed. He, too, published numerous scientific books. Hero's work in trigonometry was important. He described a formula for estimating the area of a triangle which still bears his name. He defined spherical triangles and arranged methods for determining the volumes of irregular solids by measuring the water displaced by them. The steam turbine is the best known of Hero's machines. Scholars read much about his wonderful musical instruments operated automatically by pneumatic means resembling the mechanisms of player-pianos, and particularly about his mechanical toy mimicking a number of singing birds. A group of birds were made alternately to sing and to whistle. The mechanism consisted of air tubes operating various kinds of whistles. A running stream was made to operate an air compressor. The air from the compressor tank operated the various movements of the birds and supplied air for blowing the whistles. The numerous mechanisms of this character which Hero and his master made indicate that they were as much at home in making pneumatic and similar mechanical toys as is any expert to-day. They not only knew the scientific principles, but had the engineering and mechanical ability to design them and make them work. Hero's fire engine is not as well known as his steam engine. It was a remarkable invention, however. It was worked by levers and force pumps and resembled the engines still employed by fire companies in some remote rural districts. Not the least interesting machine described by Hero was his slot machine for dispensing wine and other liquids. This machine consisted of a cylindrical container with a slot hole on top through which coins were dropped. Beneath this there was a lever with a receptacle for the dropped coin. The weight of a falling coin depressed one arm of the lever and raised the other, which opened a valve and allowed the liquid to escape. When the lever arm had moved a certain distance, the coin slipped off and the valve was automatically closed.