Bluestone and slate are both used as building stone, but the properties and uses of the two types of rock are very different. Both bluestone and slate, however, are built of sedimentary deposits which have been altered over millennia of geologic processes. Today, both bluestone and slate are used architecturally, though to very different purposes within a construction due to the differences in each rock's properties and composition.
Bluestone is a feldspathic sandstone, composed of largely uniform rock particles deposited over a long period of time. Bluestone is a product of ocean or tidal sediments settling out of water which has since disappeared. These sediments were then compacted over a long period of time, resulting in a very strong stone. It has a distinct grain that enables it to be split smoothly along the layers laid down by sediment.
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Slate is a sedimentary rock that is composed of hardened clay, or mica, particles. In the early stages of slate's composition, mica sediments were compacted and water was forced out of the clay, forming shale. Shale was then further compacted and exposed to very high temperatures, hardening the mica particles and forming the cleavage direction which makes it possible to form slate into large, thin sheets of rock.
While the geologic processes forming bluestone and slate are related, the composition of the rock and the exact processes are different enough to yield stones with very different properties and distinct uses. Slate is often used as a roofing material because it can be cut thinly enough that it will not be too heavy for the supporting building structure, and because it is smooth enough that it will shed water without trapping any and causing leaks.
Bluestone, however, is used as a structural stone because its uniformity makes it both easy to shape and good for carrying the weight of stones above it. Both slate and bluestone are used as paving stones because of their ability to cleave smoothly, making an even surface to walk on.