Victoria Falls is a waterfall in southern Africa on the Zambezi River at the border between Zambia and Zimbabwe. David Livingstone, the Scottish missionary and explorer, is believed to have been the first European to view Victoria Falls on 16 November 1855, from what is now known as Livingstone Island, one of two land masses in the middle of the river upstream from the falls near the Zambian shore. Livingstone named his sighting in honour of Queen Victoria of Britain, but the indigenous Lozi language name, Mosi-oa-Tunya—"The Smoke That Thunders"—continues in common usage as well; the World Heritage List recognizes both names. Livingstone cites an older name, Seongo or Chongwe, which means "The Place of the Rainbow" as a result of the constant spray; the nearby national park in Zambia is named Mosi-oa-Tunya, whereas the national park and town on the Zimbabwean shore are both named Victoria Falls. While it is neither the highest nor the widest waterfall in the world, Victoria Falls is classified as the largest, based on its combined width of 1,708 metres and height of 108 metres, resulting in the world's largest sheet of falling water.

Victoria Falls is twice the height of North America's Niagara Falls and well over twice the width of its Horseshoe Falls. In height and width Victoria Falls is rivalled only by Brazil's Iguazu Falls. See table for comparisons. For a considerable distance upstream from the falls, the Zambezi flows over a level sheet of basalt, in a shallow valley, bounded by low and distant sandstone hills; the river's course is dotted with numerous tree-covered islands, which increase in number as the river approaches the falls. There are escarpments, or deep valleys; the falls are formed as the full width of the river plummets in a single vertical drop into a transverse chasm 1,708 metres wide, carved by its waters along a fracture zone in the basalt plateau. The depth of the chasm, called the First Gorge, varies from 80 metres at its western end to 108 metres in the centre; the only outlet to the First Gorge is a 110-metre wide gap about two-thirds of the way across the width of the falls from the western end.

The whole volume of the river pours into the Victoria Falls gorges from this narrow cleft. There are two islands on the crest of the falls that are large enough to divide the curtain of water at full flood: Boaruka Island near the western bank, Livingstone Island near the middle—the point from which Livingstone first viewed the falls. At less than full flood, additional islets divide the curtain of water into separate parallel streams; the main streams are named, in order from Zimbabwe to Zambia: Devil's Cataract, Main Falls, Rainbow Falls and the Eastern Cataract. The Zambezi river, upstream from the falls, experiences a rainy season from late November to early April, a dry season the rest of the year; the river's annual flood season is February to May with a peak in April, The spray from the falls rises to a height of over 400 metres, sometimes twice as high, is visible from up to 48 km away. At full moon, a "moonbow" can be seen in the spray instead of the usual daylight rainbow. During the flood season, however, it is impossible to see the foot of the falls and most of its face, the walks along the cliff opposite it are in a constant shower and shrouded in mist.

Close to the edge of the cliff, spray shoots upward like inverted rain at Zambia's Knife-Edge Bridge. As the dry season takes effect, the islets on the crest become wider and more numerous, in September to January up to half of the rocky face of the falls may become dry and the bottom of the First Gorge can be seen along most of its length. At this time it becomes possible to walk across some stretches of the river at the crest, it is possible to walk to the bottom of the First Gorge at the Zimbabwean side. The minimum flow, which occurs in November, is around a tenth of the April figure. In 2019 unusual low rain falls have lowered the water flowing down to a thin fall only. Global Climate change and changed climate patterns are suggested to have caused this. Victoria Falls are facing the worst drought in a century The entire volume of the Zambezi River pours through the First Gorge's 110 metres wide exit for a distance of about 150 metres enters a zigzagging series of gorges designated by the order in which the river reaches them.

Water entering the Second Gorge makes a sharp right turn and has carved out a deep pool there called the Boiling Pot. Reached via a steep footpath from the Zambian side, it is about 150 metres across, its surface is smooth at low water, but at high water is marked by enormous, slow swirls and heavy boiling turbulence. Objects and humans that are swept over the falls, including the occasional hippopotamus or crocodile, are found swirling about here or washed up at the north-east end of the Second Gorge; this is where the bodies of Mrs Moss and Mr Orchard, mutilated by crocodiles, were found in 1910 after two canoes were capsized by a hippo at Long Island above the falls. The principal gorges are First Gorge: the one the river falls into at Victoria Falls Second Gorge: 250 metres south of falls, 2.15 kilometres long, spanned by the Victoria Falls Bridge Third Gorge: 600 metres south, 1.95 kilome

A patented track crane is a crane with a bottom flange of hardened steel and a raised tread to improve rolling. In 1867, William Louden was issued a patent for a hay carrier. Rerolled from old car rails, this system handled loads of 250 pounds and was suspended by hairpin-shaped hanger rods nailed to the exposed barn rafters. There were a few industrial applications of this product during World War I, but Louden Machinery did not pursue the industrial applications after the war. Earl T. Bennington, an electric motor salesman, had installed some of the Louden systems during World War I. Realizing the sales potential of motor propelled systems, he convinced Cleveland Electric Tramrail to enter the industry. Two years a line of underhung cranes and monorails were developed and marketed by Cleveland Electric Tramrail; the company's rapid success in the industry caused Louden to re-enter the market they had created and abandoned. In 1925, two Louden executives, J. P. Lawrence and Frank Harris, resigned from the company to form American Monorail Company.

From 1923 to 1948, these three companies—Louden and American—held a virtual oligopoly in the market of underhung cranes and monorails. In 1947, Spencer and Morris, Cleveland Tramrail's Southern California representative, was acquired by the Whiting Corporation. S&M had been Cleveland Tramrail's representative for 23 years, but had begun to manufacture equipment identical to Cleveland Tramrail's during World War II. Soon after in 1950, Spanmaster was created as a product of Angelus Engineering Corporation in South Gate, California. In the late 1920s, Vern G. Ellen Company was formed as a dealer and installer of American Monorail Company Equipment. After the death of Ellen in 1957, the company was purchased by Frank Griswold, who ran the company in its purchased form until 1958, when he lost access to the American Monorail product line. On May 1, 1959, the Twin City Monorail Company was formed. In 1968, the assets of Twin City Monorail were sold to Dyson-Kissner Corporation, which operated Twin City Monorail until 1971, when they were acquired by Robbins & Myers.

They were purchased in March 1982 by Lague Enterprises, Inc.. In 1990, TC/American Monorail was formed by the merger of Twin City Monorail and American Monorail under the ownership of LEI. In October 1990, Spanmaster, a division of the Jervis B. Webb Company, was acquired and became part of TC/American Monorail. Patented track rails are engineered for overhead cranes and monorails. Unlike a symmetrical structural rail, the material in a patented track rail is placed where it is most effective allowing for a significant reduction in weight; the rails are engineered to be twice as strong as typical A-36 structural beams and have a hardened, raised tread track, providing a longer life and reduced wear on the wheels. Utilizing patented track rails significantly eases the installation process; the rails are inspected and straightened in factories, which reduces the need to manipulate the beams during installation and startup. In most cases, there is no welding involved in the installation process. All splices are joined with bolted splice joints.

Rails are cut with a slight taper on the ends, which allows for tight joints at the bottom of a splice allowing for a smooth transition between beams. Patented track rails were designed to be supported from the building. Not requiring a duplicate structure or columns allows for increased flexibility when maneuvering material. Due to the strength, versatility and prolonged life of the patented track rail, there are many applications where patented track rails are preferred over structural beams. ANSI MH27.2-2017 - Enclosed Track Underhung Cranes and Monorail Systems ASME B30.11 - Monorail and Underhung Cranes ASME B30.16 - Overhead Hoists ASME B30.20 - Below-the Hook Lifting Devices ASME HST-1 - Performance Standard for Electric Chain Hoist ASME HST-2 - Performance Standard for Hand Chain Manually Operated Chain Hoists ASME HST-4 - Performance Standard for Overhead Electric Wire Hoists ASME HST-5 - Performance Standard for Air Chain Hoists ASME HST-6 - Performance Standard for Air Wire Rope Hoists ANSI Z535.4 - Product Safety Signs and Labels NFPA 70 - National Electric Code AISC - AISC manual of Steel Construction: Load and Resistance Factor Design AISC - AISC manual of Steel Construction: Allowable Stress Design NEMA ICS 6 - Industrial Controls and Systems: Enclosures ANSI/AWS D1.1 - Structural Welding Code-Steel ANSI/AWS D14.1 - Specification for Welding of Industrial and Mill Cranes and other Material Handling Equipment ASTM E2349-05 - Safety Requirements in Metal Casting Operations: Sand Preparation and Core Making.

In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is similar to defining the Cartesian product of sets and the product topology of two topological spaces, except that there can be many natural choices for the product measure. Let and be two measurable spaces, that is, Σ 1 and Σ 2 are sigma algebras on X 1 and X 2 and let μ 1 and μ 2 be measures on these spaces. Denote by Σ 1 ⊗ Σ 2 the sigma algebra on the Cartesian product X 1 × X 2 generated by subsets of the form B 1 × B 2, where B 1 ∈ Σ 1 and B 2 ∈ Σ 2; this sigma algebra is called the tensor-product σ-algebra on the product space. A product measure μ 1 × μ 2 is defined to be a measure on the measurable space satisfying the property = μ 1 μ 2 for all B 1 ∈ Σ 1, B 2 ∈ Σ 2. In fact, when the spaces are σ -finite, the product measure is uniquely defined, for every measurable set E, = ∫ X 2 μ 1 d μ 2 = ∫ X 1 μ 2 d μ 1, where E x = and E y =, which are both measurable sets.

The existence of this measure is guaranteed by the Hahn–Kolmogorov theorem. The uniqueness of product measure are σ-finite; the Borel measure on the Euclidean space Rn can be obtained as the product of n copies of the Borel measure on the real line R. If the two factors of the product space are complete measure spaces, the product space may not be; the completion procedure is needed to extend the Borel measure into the Lebesgue measure, or to extend the product of two Lebesgue measures to give the Lebesgue measure on the product space. The opposite construction to the formation of the product of two measures is disintegration, which in some sense "splits" a given measure into a family of measures that can be integrated to give the original measure. Given two measure spaces, there is always a unique maximal product measure μmax on their product, with the property that if μmax is finite for some measurable set A μmax = μ for any product measure μ. In particular its value on any measurable set is at least that of any other product measure.

This is the measure produced by the Carathéodory extension theorem. Sometimes there is a unique minimal product measure μmin, given by μmin = supA⊂S, μmax finite μmax, where A and S are assumed to be measurable