No. 8 Queen Street - Register House - David Hume's Tomb - Charlotte Square
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Notes in italics from Pevsner Architectural Guides, Edinburgh by John 
Gifford, Colin McWilliam and David Walker (1991), Yale University 
Press. The quotations are extracts only, appropriate to the images.

No. 8 Queen Street is distinctively the work of Robert Adam, 1770-1 for Baron Orde. (Boswell wrote 'This respectable English judge will long be remembered in Scotland where he built an elegant house and lived in it magnificently.'). Working within the City's rules, he (Adam) used the long frontage for five generously spaced bays and exactly defined the proportions of the whole with the characteristic precision of Craigleith stone. Tripartite doorpiece with tiny guttae under the frieze, its smooth columns set against square-cut rustication which is separated by a Vitruvian scroll from the dead-flat upper wall. The mansard, but not the form of its windows, is original. ...

Register House, E end of Princes Street. Robert Adam's long frontage with corner turrets stands austerely elegant at the entry from the Old Town to the New. Begun in 1774 ... a domed rotunda within a quadrangle ... The basic formula is Palladian, a piano nobile over rusticated arches. The novelty is in the simplicity of its treatment, e.g. the expanse of plain wall between and above the upper windows, and the tall (but not giant) Corinthian columns of the centrepiece repeated at the ends. This cool authority is not Palladian but Neo-Classical in spirit, well attuned to the strong quadrangular form of the whole. The grace-notes that characterize Adam the decorator are few but telling, e.g. the fluted frieze with paterae that becomes a single panel over the central order, the chaste geometric turrets (miniatures of the main building), and the little roundel of the Royal Arms (originally of Liardet's cement) fixed in the pediment like a seal. ...

David Hume's Tomb. Old Calton Burying Ground ... The finest work is the David Hume Monument by Robert Adam, 1777, a grandly Roman cylinder of rough ashlar with a fluted frieze on the lower stage, a bold Doric entablature on the upper. Big urn in a niche above the doorpiece. Adam's preliminary sketches show that the tomb of Theodoric at Ravenna was the starting point for his design.

Charlotte Square is the grand finale of the First New Town (map) the last section to be built and the only one designed as a single unified scheme. The architect was Robert Adam (design 1791). ...
North Side. A row of eleven houses composed as a 100 m. palace-front of uncommon finesse and grandeur in which movement is always complemented by stillness, repetition by variety, plainness by intricacy. Vertically, the stonework graduates from rock-faced basement to regular ground-floor rustication, then flat polished ashlar on the first and second floors. Horizontally, this flat plane is dominant throughout the twenty-one bays, the rhythm maintained by not-quite-semicircular window heads through the ground floor of the pavilions and links. Pavilions slightly advanced, each with a doorway between overarched Venetian windows (Adam showed three windows), very broad pilasters above, and a crowning sphinx in front of the pyramidical roof. 

Centrepiece with four pairs of attached columns (Adam's own version of Corinthian), the ground floor breaking forward beneath each outer pair to unite the inner pairs whose frieze of inverted garlands is interrupted by a plain panel at the very centre. Statues were meant to stand on the pediment. Only the centre bay of the ground floor is arched. At the first floor, single windows alternating with overarched tripartite windows like those of the pavilions; the sidelights of the outer two were built up in the C19. ... 

East elevation. The E has overarched first-floor windows linked with a fluted frieze, and on the chimney-head, flanked by balustrades, a serpentine fluted panel like a Roman sarcophagus; not very well related to the main front, but entirely in the spirit of late Adam. The execution at least was by Alexander Stevens, who built the whole E pavilion. 

South Side of the Square. A repeat of the N side with larger windows and no sphinxes on the end pavilions, but the tripartite windows in the centrepiece are intact. ...

For the interiors and the east and west sides of the square, see the Pevsner publication above. Alternatively, essay here by Julian Small. 

Robert Adam at Wikipedia 

Full list of works by the Adam family.

More of Edinburgh at Astoft