They took a cab to one Manhattan cinema where it was showing, but it was sold out. They tried a second, but it was the same story. In the end they settled for Luis Bunuel's That Obscure Object Of Desire, which neither of them could understand. Warhol spent $4 on popcorn. His diaries don't say if Jagger indulged.
The next night, they tried again, up to 86th Street this time. Success. "We finally hit Saturday Night Fever and were able to get in," Warhol writes. Jagger fell asleep but the artist loved the R-rated film, especially the shots of New York and the dance sequences featuring John Travolta's character, Tony Manero. "The movie was just great. That bridge thing was the best scene - and the lines were great. It's I guess the new kind of fantasy movie, you're supposed to stay where you are … It's about people who never even think about crossing the bridge."
The bridge is the Verazzano-Narrows Bridge that links Brooklyn and Staten Island. Here, Tony and his friends lark about on the cables, swinging out over the dark river below with tragic consequences. But it's Brooklyn Bridge, linking the borough with cosmopolitan Manhattan, that becomes the metaphor for that escape to a better life. Today, Brooklyn is seen as the epicentre of hipster cool, a name to be appropriated by celebrities for their offspring. Not so in the mid-1970s. "Right across there, right across the river, everything's different," says Karen Lynn Gorney's character, Stephanie Mangano, when Tony asks her out for coffee in a bid to make her his partner in an upcoming dance competition. By different, she means better, bigger, glossier, not Brooklyn.
Interestingly, Warhol's diary entry makes no mention of the Bee Gees or their music. But in the decades since, it's that which has come to define Saturday Night Fever. With the soundtrack still one of the biggest-selling albums ever, it's better known as a collection of songs than as a film, more celebrated for cementing disco's place in the white, heterosexual mainstream than for anything it did for cinema. Sure, everyone remembers the iconic opening scene - Travolta as Manero strutting down a Brooklyn street carrying a can of paint - and the fetishistic pre-club ritual in which he chooses his jewellery and his clothes as director John Badham's camera pans round a bedroom decorated with posters of Farrah Fawcett-Majors, Al Pacino as Serpico and Sly Stallone as Rocky. But the film's prompt re-editing into a PG version and its 1979 re-release as a double bill with Grease, which also starred Travolta, have rubbed out much of the authenticity and lurid potency Andy Warhol felt when he saw it.
This month, however, the film gets a one-day theatrical re-release in its original form courtesy of Glasgow-based distributor Park Circus. That means audiences can take a welcome second look at a movie that forms a continuum with works like Martin Scorsese's Mean Streets (another exploration of working-class Italian-Americans) while anticipating a new wave of gritty musical films - most obviously Fame and Flashdance - and even the work of Spike Lee, who was raised in Brooklyn and who took to the same streets as Badham to make films like She's Gotta Have It, Do The Right Thing and Jungle Fever.
As second looks go, this one will be eye-popping. Although based on a 1976 New York Magazine article by British journalist Nik Cohn that later turned out to be partly fabricated, screenwriter Norman Wexler brings a brutal authenticity to the script, as was expected at the time.
This, remember, was the tail end of the so-called Golden Age of American auteur filmmaking, when directors like Martin Scorsese, Francis Ford Coppola and Robert Altman were redefining what could and should be shown on screen. So Tony and his friends are real people with real flaws. They are sexist, racist, homophobic, vicious and nasty. They are loyal to their Bay Ridge neighbourhood and their caste and, as Wexler shows in extended sequences featuring the Manero family, they lead lives that are low in expectation and high in Catholic guilt. You could call it the best film Ken Loach never made.
The plot features an attempted rape, a gang rape, a death and the sort of activities that had even the moral guardians of the day tut-tutting about imitable behaviour. The F-word is used liberally, so is the C-word - usually to describe women - and according to John Badham there is the first use in mainstream cinema of the term "blow job".
"This horrified some of the professionals in Hollywood who came to see the film early on," he would later recall. "They were shocked that we would use such language and vulgarity." An executive on Badham's next film was so affronted by Saturday Night Fever when he saw it that he fired the director immediately.
What it doesn't have is those bit-part appearances by actors who will one day become household names, the sort of added bonus that makes a good film even better on subsequent viewings. Think of the young, scene-stealing Lee Marvin in Bad Day At Black Rock; think of Sean Penn in Fast Times At Ridgemont High or Dennis Hopper in Rebel Without A Cause.
Of Travolta's male co-stars, only Barry Miller (Bobby C) continued to make films, working with Martin Scorsese on The Last Temptation Of Christ and Michael Cimino on The Sicilian. Donna Pescow (Annette) went into TV and is best known for playing the first lesbian character in a daytime soap, though the makers of The Sopranos accessed a little of her Bay Ridge cachet when they cast the Brooklyn native as a mobster's wife in the final series of the groundbreaking show. Gorney, who had been a fixture in US soap All My Children from 1970, gave up acting after Saturday Night Fever and opened an art gallery in Manhattan. She returned to the profession in the 1990s and she too guested on The Sopranos.
The upshot is that first and last, then and now, Saturday Night Fever is John Travolta's film. He's in virtually every scene and he's captivating in all of them. Those who still hold to the belief that it was in a black suit that he gave his career-best performance - as Vincent Vega in Pulp Fiction - should remind themselves first how good he was in a white one.
Saturday Night Fever is back in cinemas on September 24