Although able to diagnose hydatid disease he thought the condition arose because ‘some people have hydatic constitutions.’

Cases in Surgery
In 1772 Hill published  Cases in Surgery a summary of his lifes work as a surgeon. Cases deals with the infectious disease sibbens, with cancers and with ‘disorders of the head from external violence’. Sibbens
Sibbens is now known to be endemic syphilis, a Treponemal infection spread by non-sexual social contact and seen in association with deprivation, especially overcrowded living conditions, poor sanitation and malnutrition. Hills account is written ‘to rectify the mistakes’ in the MD thesis on the topic submitted to the University of Edinburgh on the topic by Adam Freer in 1767. Hill concluded that syphilis and sibbens were the same disease and that sibbens, having been introduced into a family by sexual means, could then be transmitted around the family by close non-sexual contacts, giving his own family as an example of this mode of transmission. His apprentice Benjamin Bell, who was the first to show that syphilis and gonorrhoea were different diseases, also subscribed to this mode of transmission. Hill, like Freer before him and Bell after him, believed that the most successful treatment was mercury, supplemented on occasion by Peruvian bark. Hill was clear that sibbens and what he termed West Indian yaws were distinct diseases. Subsequent writers credited Hill and his physician colleague and friend Dr Ebenezer Gilchrist (bap1708-1774) with providing the most precise description of the clinical features and natural history of the disease in Scotland.
Polymelia is a birth defect in which an affected individual has more than the usual number of limbs. It is a type of dysmelia. In humans and most land-dwelling vertebrates, this means having five or more limbs. The extra limb is most commonly shrunken and/or deformed. The term is from Greek πολυ- "many", μέλεα "limbs". Sometimes an embryo started as conjoined twins, but one twin degenerated completely except for one or more limbs, which end up attached to the other twin. Sometimes small extra legs between the normal legs are caused by the body axis forking in the dipygus condition. Notomelia (from Greek for "back-limb-condition") is polymelia where the extra limb is rooted along or near the midline of the back. Notomelia has been reported in Angus cattle often enough to be of concern to farmers.Cephalomelia (from Greek for "head-limb-condition") is polymelia where the extra limb is rooted on the head. Origin
Tetrapod legs evolved in the Devonian or Carboniferous geological period from the pectoral fins and pelvic fins of their crossopterygian fish ancestors. Fish fins develop along a "fin line", which runs from the back of the head along the midline of the back, round the end of the tail, and forwards along the underside of the tail, and at the cloaca splits into left and right fin lines which run forwards to the gills.