Final answer:
The anesthetic-soaked cotton ball under the grate in a bell jar is used to prevent escape and immobilize the subjects for study in a controlled environment.
Step-by-step explanation:
When using a bell jar, the purpose of placing the anesthetic-soaked cotton ball under the grate is to prevent escape of the experimental subjects, usually small organisms or insects. This method ensures that the subjects are safely contained within the bell jar during experimentation and observation. The anesthesia ensures that the organisms do not suffer and are immobilized, which facilitates a controlled environment for the experiment.