Summary...

Linnet was found the next day, shot in the head. Race takes charge of the situation and asks Poirot to handle the investigation. Various signs seem to incriminate Jacqueline - a "J" written in blood on the wall above the head of Linnet, for example - but Miss Bowers Poirot says Jacqueline was sedated and never left his cabin that night. He explains Dr. Bessner Linnet could not have written the "J" in his own blood, because the bullet would have killed him instantly. Poirot also ensures Simon's leg hurt him completely incapacitated, and therefore could not have moved from his bed, even if I wanted.
When Race announces booths pearls missing, Miss Bowers is seeking the return, hoping that Miss Van Schuyler took Linnet's cabin, because she secretly one kleptomaniac Poirot examines the collar and is found to be a fake , ie real pearls were stolen sometime before.
Poirot and Race enter Dr. Bessner cabin to tell the doctor what happened and Simon. Salome Otterbourne enters and says he knows who killed Linnet and Louise, because I saw that person in and out of the cabin Louise. Before he can finish his story, a shot is fired on the outdoor terrace, killing her. Before Poirot and race can go, the shooter is gone, having found the weapon that recognizes Poirot coming in the luggage of Andrew Pennington.