To justify the imposition of an annual licence fee, BBC programming has always had to offer a combination of popularity and piety.
Television, which currently takes 55% of the ￡159 fee, has always tended to provide the popularity.
In the 1970s the comic double act of Eric Morecambe and Ernie Wise won audiences of over 20m.
Today, "Strictly Come Dancing", a game show, gets ratings of 7m.
Radio tends to do the piety.
The World Service broadcasts in 42 languages to 492m people.
Radio 3 offers programmes with such titles as "Discovering Music: Monteverdi Madrigals".
Radio 4 offers the implausibly wholesome "In Our Time".
Recent episodes have included "Hegel's Philosophy of History", "The Hittites" and "Tang Era Poetry".
The common man has not always been grateful for the BBC's efforts.
A 1950s sketch show described the BBC as a "part of the English heritage. Like suet pudding and catarrh".
But the BBC mattered.
Its news (despite grumbles about lefty bias) was trusted, its radio all but loved.
For Britons of a certain age not only the outspread century but humdrum daily life itself was, like a bourgeois Book of Hours, measured out by its tread: breakfast with "Today", supper after "The Archers" and insomnia with the shipping forecast, whose litany of names "North Utsire, South Utsire, Forties, Cromarty..."
- was as unintelligible as a religious chant and, to many, as comforting.
Now that bond is breaking.
Smartphones and streaming have switched off communal tvs and radios.
Programmes are consumed individually, and at will.
The particular blend of serendipity and boredom that led people to watch "Antiques Roadshow", or to listen to the wind forecast for the Faroe Islands, has gone.
Mr. Hendy observes that the BBC was born with an "umbilical link" to radio.
The technology, it turns out, wasn't there to serve the BBC; the BBC served the technology: the medium was the message.
In its triumphant first century, the BBC forgot this.
It is now being painfully reminded of it.
The message from the era of smartphones is brutal.
Viewing figures among the young have collapsed; in a typical week, a fifth of 16- to 34-year-olds consume no BBC content at all.
There is a sense that the BBC doesn't do enough to justify itself: it can cover a state funeral beautifully but it is increasingly irrelevant to many.
Too few shows are "Strictly" style hits; too many are tosh.
At a time when it needs to prove its worth, it has cut World Service jobs.
Catastrophe is unlikely, but decline of some sort probable.
The end of the BBC's first century has a less than celebratory feel.