Toaru Kagaku no Railgun S Episode 13

is the thirteenth episode of the second season of the Toaru Kagaku no Railgun anime series and the 37th episode of the series overall. It was first broadcasted on July 5th, 2013. The screenplay was written by Tsuchiya Michihiro and is storyboarded and directed by Ishikawa Kensuke. The animation was co-directed Moroishi Kouta, Fujibe Ikuma, and Naoya Takashi.

Tree Diagram—the ultra-high speed super computer of Academy City that is boasted to even "predict the future". Mikoto invades a facility to try and hack the high-tech computer to end the abominable plan. However, a grim fact comes upon her.

The Tree Diagram has already been destroyed. Desperate, Mikoto lost sight of what to do, and raids a facility as a result, rationalizing that "since Tree Diagram has been destroyed, I only need to destroy everything related to the experiment."

However, something reflected in her eyes at the height of her rampage, the experiment, monitored by the facility. Meanwhile, while looking for the missing Misaka Imouto, Touma encounters an unbelievable sight in a back alley.

Major events

 * Accelerator explains to MISAKA 10031 that his ability is the ability to transform any vector. The MISAKA network is now cognizant of this fact for all of the future battles with Accelerator.
 * Misaka 10031 dies at the hands of the Accelerator, and is witnessed by Misaka Mikoto.
 * Touma yells in shock upon the discovery of Misaka 10031's corpse and later learns that Misaka Mikoto has clones after he briefly doubted his own sanity and thinking that he had hallucinated Misaka 10031's death.
 * Mikoto reveals that she has figured out the perfect, final way to end the experiment after thinking about the fact that the Level 6 shift project scientists had conjectured that Accelerator only had to kill  Railgun 128 times in order to induce a level 6 shift in the Accelerator.
 * Touma heads to Mikoto's room in the Tokiwadai dormitories located away from the main campus in an attempt to speak to her and approach her about the Level 6 Shift experiment.

Adapted From

 * Toaru Kagaku no Railgun Manga Chapter 034
 * Toaru Kagaku no Railgun Manga Chapter 037
 * Toaru Majutsu no Index Light Novel Volume 03

Characters

 * Misaka Mikoto
 * Kamijou Touma
 * Misaka 10032's cat
 * Accelerator
 * Misaka 10031
 * Misaka 10032

New Characters

 * Misaka 1

Locations

 * Academy City
 * School District 7
 * Book-On
 * School District 23
 * Tokiwadai Dormitory

New Locations
No new locations were introduced during this episode.

Abilities

 * Electromaster (Railgun variant) - Misaka Mikoto, Level 5
 * Electromaster - Misaka 10031
 * Accelerator (ability) - Accelerator, Level 5

New Abilities
No new ablities were introduced during this episode,

Trivia

 * Accelerator's flashback has him killing indirectly the first Misaka clone. The scene is taken from the tankobon version of the chapter instead of the magazine version, where it implies that Accelerator killed Misaka 1 instead of her own doing.
 * The direction set up in a way to make it seem that Touma was close in discovering Misaka 10031 and Accelerator's battle, unlike that of the previous adaptation of the scene which shows that it has been quite a while since Misaka 10031's death and then Touma discovering the corpse.
 * As a coup de grace to the Misaka 10031–10032 confusion, Misaka 10032 explains in detail her and Misaka 10031's role in the story.
 * The flashback with Misaka 1 implies that Accelerator's battle with Mikoto in episode 6  was the first time he fought another level 5.
 * The OST from episode 5 when Mikoto witnessed the death of Misaka 9982 was used here once again for when she witnessed the death of Misaka 10031.

Referbacks

 * Touma's meeting with Misaka 10031 and 10032 are referenced by Misaka 10032 to clear Touma's confusion.

Cultural References

 * Like the real world FN F2000 that the Toy Soldier is based on, it uses also uses a grenade launcher.
 * The gun that Misaka 1 uses is a variant of a M1911 pistol that is often seen in the series. It is most likely a Colt variant, which uses a skeleton hammer and picatinny rail, like the Colt XSE.

Animation Trivia

 * At least 20 seconds from the previous episode are reused for the cold opening of the episode.
 * Scenes from episode 11 and 12 are reused for various flashbacks.
 * In the beginning of this episode's ending (as the music was playing), the windmills near the bridge start to turn as Mikoto walks by hinting at the fact that Mikoto tends to give off electricity that makes windmills spin as a way of foreshadowing what will happen during the fight in episode 15.

Unanswered Questions

 * What happened to the thugs Accelerator fought in the alleyway?
 * How was even the Sisters even capable of cleaning the alleyways efficiently in such a short amount of time?
 * What happened to Touma's suit case and the book he bought?
 * What was Mikoto's conclusion at the end of the episode about how to stop the experiment for good?

Quotes

 * Accelerator: "C'mon, did you really just turn tail? Shaking your pretty little ass at me... Lemme guess, you're leadin' me on?"—to Misaka 10031 after she makes a retreat.
 * Accelerator: "I usually just leave it on reflect. But that isn't exactly what I'm doing now.,The correct answer was... vector transformation. Momentum, heat flux, and... electric current. I can control anything with a direction just by touching it."—to Misaka 10031 regarding the nature of his ability.
 * Mikoto: "I'll destroy them all. All their equipment, their funds, their desires, and their ambitions. I'll destroy everything until all that's left are ashes. And then, one day... One day? Will such a nice day ever come? How many of those Sisters have to suffer before it comes? Shut up! What d'ya want me to do?! How the fuck am I supposed to make them cancel the plans?!"—internal monologue.
 * Researcher: "However, the first experiment has yet to be concluded. It won't be until you dispose of the subject behind you. Completion of the project requires the disposal of 20,000 armed clones. The target has not yet ceased operation. Continue fighting."—researcher egging Accelerator on to kill Misaka 1.
 * Misaka 1: ""It's dark... It feels like I'm sinking into deep waters... Is this... death?" asks Misa... ka..."—death of Misaka 1.
 * Misaka 10032: ""Misaka has, in fact, died," announces Misaka."—said to Touma.