Indeed, why do they?
Well, it’s because the north-east side of the Gallery was used to calibrate land chains. A series of brass plates were embedded in the base of the building to facilitate calibration of land chains manufactured to measure distance in links or feet.
For more information on this see here.
Addendum
Evidently the original imperial calibration chain was installed on the parapet in front of the University Old College when the College was substantially completed in 1826.
Apparently the Royal Institution (now Royal Scottish Academy) refused a similar calibration chain when completed in 1827.
The Old College calibration chain was lost in mid-19th century when the front Area was infilled for road-widening.
The National Gallery of Scotland was built 1850-59, so the present calibration plates were probably a replacement at that time for the Old College chain.
For those interested in reading more about land surveying in Scotland, see pages 2-5 in an article about the background and purpose of the “little known” Society of Scottish Land Surveyors:
https://ice-museum-scotland.hw.ac.uk/wp-content/uploads/CAIRT_newsletter_no.38_2021.pdf.
This information was provided by John Riddell (January 2026).