Pursuit

"I think I just figured out how to find the name of the guy who was following me today." "How are you gonna do that?" "I'm gonna use the rules of the Death Note to my advantage."

- Light Yagami and Ryuk

Pursuit (追跡, Tsuiseki) is the fourth episode of the Death Note anime.

Synopsis
Light Yagami explains to Ryuk that he is trying to create an ideal world where no criminals are left unpunished, and "as the god of such a world," he cannot sacrifice half his life for the Shinigami Eyes, as that would limit his reign. He decides to experiment with the Death Note using incarcerated criminals. Chief Yagami and L are soon puzzled by reports they receive of prisoners dying in odd circumstances. Hacking into the notes for the ongoing investigation, Light discovers that L suspects they were tests and doesn't want this information reported to the media.

Later, Light creates a plan to discover the identity of the man following him without arousing his suspicion. He plans a date to Spaceworld with a classmate, Yuri. His tracker, though becoming less suspicious of him, follows Light onto the bus to Spaceworld, sitting directly behind the "couple." During the ride, a drug dealer and murderer named Kiichiro Osoreda who was recently in the news boards the bus and points a gun at the driver. Light hands a note to Yuri, saying that he will use a move his father taught him to knock out Osoreda. The man behind him notices and tries to talk Light out of it, but when Light accuses him of being in league with the hijacker, he eventually resorts to using his FBI ID to prove his innocence. Light drops the paper in the aisle and reaches for it, and Osoreda notices and picks up a note that contains plans for the date. However, the plans were written from a page in the Death Note, and after touching the page, Osoreda can see Ryuk. Intrigued, Ryuk walks toward him, and Osoreda panics and wastes his bullets trying to shoot him. Osoreda orders the bus to a stop and attempts to flee but is immediately struck and killed by a white sedan. As the police question witnesses and Raye Penber leaves, Light resumes the date, planning the FBI investigator's death.

Death Note Rules Revealed

 * How to Use It: III - If the time of death is written within 40 seconds after writing the cause of death as a heart attack, the time of death can be manipulated, and the time can go into effect within 40 seconds after writing the name.

Trivia

 * When Light is running his tests, he writes that all six criminals will die in one hour at 6 P.M. This would mean that it is 5 P.M. when Light writes their names down. This is impossible, because Light's cram school, which he has just returned from, doesn't start until 6:30 P.M. as shown in episode 1. It is also dark outside at the start of this episode, while it was still light out when Light left for cram school in the first episode.
 * When Osoreda fires his gun at Ryuk, his rounds simply phase through him. This isn't the case in the manga as Ryuk actually allows the rounds to hit him, albeit they garner no effect.

Episode Guide
Pościg Pousuite Takaa-ajo