In The Lord of the Rings: The Fellowship of the Ring, Saruman summons Gandalf to his abode of Isengard in the Gap of Rohan. After revealing that he has been a double agent for Sauron for decades, he asks Gandalf to join him.
The White Wizard's plot is not to simply "join the Dark Side" as Peter Jackson's adaptation seems to show. He wishes to serve Sauron only as a means to an End. That End... is the possession of the One Ring.
Gandalf refuses, of course. Saruman sends him up to the roof of Orthanc, a prison where the bars are replaced by five hundred foot drops on all sides. Gandalf escapes on the back of Gwaihir, a Lord of the great Eagles of the Misty Mountains.
This is where things get interesting. In Unfinished Tales of Númenor and Middle-Earth, Christopher Tolkien mentions three separate narratives written later, to delve into what the Nazgûl were doing at the time.
In narrative A and B, the Black Riders capture Gríma Wormtongue en route to Isengard, and arrive there themselves two days after Gandalf escapes the tower. Saruman tells them that Gandalf is gone, and claims that he knows nothing of the Shire (the land the Riders seek, betrayed by Gollum during his torture in Barad-dûr), but in this the Nazgûl know he lies, as the terrified Wormtongue has told them.
In C, though, we have a thoroughly different look at the leader of the White Council. The Nazgûl arrive at the doors of Isengard while Gandalf is still a prisoner. Saruman meets them at the gate and acknowledges that he has Gandalf imprisoned within. "Perceiving the full horror of service to Mordor", however, Saruman resolves to ask Gandalf for forgiveness, and go back on his treasonous actions. He tells the Ringwraiths he will interrogate Gandalf, and if unsuccessful deliver him up to them. He hurries up to the summit of Orthanc—and finds Gandalf gone. In the far distance, heading for Edoras, he sees Gwaihir soaring. His momentary repentance is now swamped by a wave of rage, and he returns to the gate, lying to the Nazgûl that he had gotten the relevant information from Gandalf. He tells the Witch-King the location of the Shire, and gives some general directions. The Nazgûl hasten away toward the land of the Halflings.
This additional narrative brings additional depth to Saruman's character arc, and helps to further flesh out the relationship between Isengard and Mordor.
P.S. Jeff LaSala wrote a wonderful article for Tor on Saruman's story and motivations. His explanations are excellent (funny too) and helped spur me on to read ever more of the Legendarium, so I definitely recommend giving the piece a read.
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