Nineteenth and twentieth century astrologers assigned Uranus the significations of sudden change, disruption, invention, electricity, rebellion and the breaking of established form, and this was reinforced by the coincidence of its discovery with the American and French revolutions and the early industrial revolution, an argument that is rhetorically effective and evidentially weak. Most modern astrology gives Uranus the rulership of Aquarius, displacing or sharing with Saturn. Traditional practitioners, and the revived Hellenistic and medieval schools of the last thirty years, generally decline the reassignment on the grounds that the system of domiciles is built on a coherent geometry of the two luminaries and the five visible planets which the addition of further bodies breaks. Both positions are held by serious practitioners, and the honest description is that this is an open and unresolved disagreement within astrology rather than a settled doctrine.
Two facts about the planet itself bear on the argument. Its orbit takes about 84 years, so it spends roughly seven years in each sign and everyone born within a few years of each other shares its placement; whatever it signifies, it cannot signify anything individual without the house and the aspects to localise it. And it was not invisible before 1781. At magnitude 5.7 at its brightest Uranus is at the edge of naked eye visibility, and John Flamsteed recorded it as a star in 1690, cataloguing it as 34 Tauri, one of several such sightings by observers who had no reason to look twice. It was discoverable for as long as anyone had been looking; what changed in 1781 was recognition, not visibility.