Bucrania images appear to cross all the architectural styles of the ancient world, and were a form of carved decoration often utilised in Classical Architecture. This may be why they were deemed appropriate to decorate a display of "the orders of architecture" as seen on the façade of Browsholme Hall.
The revival of these classical images from the ancients, seem to begin with Sebastiano Serlio's "L'Architettura" in 1537, but it is suspected that the carvings here at Browsholme are due to early knowledge of Palladio's work, who also used bucrania as a suitable image on friezes.
Neither of these revivalists really understood the origins of bucrania. The word is simply from the Latin for 'ox skull'. It comes from the image of ancient sacrifice, when different Gods required different animal sacrifices. Jupiter, it seems, liked garlanded heads of oxen - originally therefore, these images were seeking the God's protection of the building.
A sequence of these garlanded ox heads can be seen above the main doorway to Browsholme Hall, calling on the protection of Jupiter's protection on the building.