What does "a certain air of" mean? I met it in the Chapter 3 of "A Study in Scarlet" by sir A. C. Doyle:
He was a man with some amount of self-importance and a certain air of command.
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It means to exude an impression of command. You know, some people just give off a feeling that they are a certain way. It is not always a tangible thing that you can point to, it is often a mixture of obvious confidence and how they present themselves, and sometimes you pick up subconscious clues from how others around that person are deferring to them. But you just get a feeling that this person is a certain way - in this case of being a leader.
The flip side to that is the phrase "putting on airs" which is a derogatory term that a person is acting superior when they are not.
The word certain is being used in a frequently encountered sense, aptly described by the OED as its meaning 7d.
I looked at the link in @Fumble Fingers comment, but felt instinctively that the inclusion of specific as part of the definition was not entirely correct. I think the OED is right in not not including any implication of specific.
7d. Of positive yet restricted (or of positive even if restricted) quantity, amount, or degree; of some extent at least.
a1538 T. Starkey Dial. Pole & Lupset (1989) 9 Ther ys a certyn equyte & justyce among al natyonys & pepul.
1711 J. Addison Spectator No. 106. ¶6 His Virtues..are as it were tinged by a certain Extravagance.
1763 F. Brooke Hist. Lady Julia Mandeville I. 44 A prodigious passion for people of a certain rank, a phrase of which she is peculiarly fond.
1763 F. Brooke Hist. Lady Julia Mandeville I. 63, I knew her rage for title, tinsel, and ‘people of a certain rank’.
1810 G. Rose Diaries (1860) II. 476 Mr. Perceval..found a certain improvement in him.
1845 S. Austin tr. L. von Ranke Hist. Reformation in Germany III. 131 He kept up a certain degree of intercourse..with the Gonfaloniere Capponi.
1860 J. Tyndall Glaciers of Alps i. 123 The ice is disintegrated to a certain depth.
1875 W. S. Jevons Money (1878) 117 The bank makes a certain profit out of the business.
A synonymous expression to a certain air of, therefore might be to some extent an air of.