Geoffrey Radcliffe did not become invisible because he wanted to. Along with his beloved brother Radcliffe, Michael and their cousin Richard Cobb, Geoffrey ran a mining company in England. He also had a fiancee, Helen Manson, and was good friends with Jack Griffin's brother, Frank Griffin.
He was very well-liked by all of his employees because he worked hard to make the mines as safe as possible, and treat the miners fairly. Then one day Michael turned up dead, murdered, and Willie Spears testified in court that he had seen Geoffrey kill him. Geoffrey was tried and convicted, and sentenced to die. Desperate to save himself and to find his brother's killer, Geoffrey persuaded Frank to inject him with his own late brother's formula when the scientist visited him in prison shortly before he was scheduled to be executed.
Once invisible, Geoffrey remained in his cell until the guards came for him, then slipped out and escaped when they opened the door. Once out in the wilderness he found a suitcase of clothes, bandages, and goggles left for him by Frank and Helen, who was also in on the plan, and went to stay with her at the house of a friend, Ben Jenkins. Above all else, Geoffrey feared he not be able to prove his innocence in time, for Jack Griffin's invisibility formula contained a drug called duocane that would drive him insane after a short period of time.
While Frank worked on a cure, Geoffrey did some detective work and learned from Willie Spears that Michael's killer was in fact their own cousin, Richard. Geoffrey's efforts to bring Richard to justice were hampered by the interferance of the well-meaning and shrewd Inspector Sampson, not to mention the effects of the duocane, which did indeed begin to slowly drive Geoffrey insane, and like Frank's brother he began to entertain thoughts of world domination.
Ultimately, Geoffrey was shot by Inspector Samspon while trying to kill Richard, who eventually fell to his death anyway, and was instantly hospitalized and put in Frank's care. While Frank was giving Geoffrey a blood transfusion to save him from the bloodloss that had resulted in being shot, this purged the duocane from Geoffrey's system, restoring both his visibility and his sanity. He was reunited with Helen, and presumably the two were married and the murder charges dropped against him (as Richard, on his deathbed, confessed to killing Michael).