Stephen Gray. The demonstration used damp hemp cords suspended by silk threads (the low resistance of metallic conductors not being appreciated at the time). However the first practical use of overhead lines was in the context of telegraphy. By 1837 experimental commercial telegraph systems ran as far as 20 km (13 miles). Electric power transmission was accomplished in 1882 with the first high-voltage transmission between Munich and Miesbach (60 km). 1891 saw the construction of the first three-phase alternating current overhead line on the occasion of the International Electricity Exhibition in Frankfurt, between Lauffen and Frankfurt. In 1912 the first 110 kV-overhead power line entered service followed by the first 220 kV-overhead power line in 1923. In the 1920s RWE AG built the first overhead line for this voltage and in 1926 built a Rhine crossing with the pylons of Voerde, two masts 138 meters high. In 1953, the first 345 kV line was built by The L.E. Myers Co. and put into service by the Ohio Valley Electric Corporation in the United States. In Germany in 1957 the first 380 kV overhead power line was commissioned (between the transformer station and Rommerskirchen). In the same year the overhead line traversing of the Strait of Messina went into service in Italy, whose pylons served the Elbe crossing 1. This was used as the model for the building of the Elbe crossing 2 in the second half of the 1970s which saw the construction of the highest overhead line pylons of the world. Earlier, in 1952, the first 380 kV line was put into service in Sweden, in 1000 km (625 miles) between the more populated areas in the south and the largest hydroelectric power stations in the north. Starting from 1967 in Russia, and also in the US and Canada, overhead lines for voltage of 765 kV were built. In 1982 overhead power lines were built in Soviet Union between Elektrostal and the power station at Ekibastuz, this was a three-phase alternating current line at 1150 kV (Powerline Ekibastuz-Kokshetau). In 1999, in Japan the first powerline designed for 1000 kV with 2 circuits were built, the Kita-Iwaki Powerline. In 2003 the building of the highest overhead line commenced in China, the Yangtze River Crossing. Mathematical analysis An overhead power line is one example of a transmission line. At power system frequencies, many useful simplifications can be made for lines of