Final answer:
Robert Smirke employed a neoclassical architectural style in designing the British Museum, characterized by order and classical elements such as Doric columns, in line with the rationalist ideals of the Enlightenment.
Step-by-step explanation:
Robert Smirke designed the British Museum using the neoclassical architectural style, which hearkens back to the Classical elegance of ancient Greece and Rome. The British Museum’s design, with its grand facade and symmetrical layout, employs a classical vocabulary characterized by the use of strong lines, Doric columns, and pediments, which has come to represent the standard for many other grand museum buildings around the world.
Neoclassicism is known for its emphasis on order and rational design, a characteristic seen in the British Museum's balanced geometrical structure. This style is in direct contrast to the romantic opulence of the Rococo style and earlier Renaissance excesses but is in line with the rationality appreciated by Enlightenment thinkers.
Smirke's architectural choices create a sense of permanence and gravity appropriate for housing a venerable collection of historical artifacts. This rational elegance aligns with the late 18th and early 19th-century desire to revive the spirit of antiquity and is mirrored by the mention of works in the British Museum from different eras, reflecting the continued appreciation of classical forms throughout history.