Hector Frome's defense of William Falder appeals primarily to the jury's emotions. Frome does not try to convince anyone that Falder did not forge the check, which is the crime of which he was accused.
Instead, he provides numerous reasons for Falder's behavior. These include emotional distress and the unfairness of British divorce laws, as well as the physical abuse that Ruth Honeywell's husband had inflicted on her. However, Ruth's husband was not on trial. Frome also called Ruth as a defense witness; she testified that Falder had acted on her behalf. The prosecutors had decided not to charge Ruth as a conspirator, so the defense attorney had little choice but to use her to help her lover.
Frome hoped that the jury would be sympathetic to Ruth, but he took a chance that they would side with two adulterers. Because Frome's defense did not directly challenge the crime itself and was ultimately unsuccessful, it does not seem like a strong argument.
Frome does mount a very strong defense for Falder in the play. His speech is often cited for its eloquence, and for its historically important espousing of empathetic legal treatment for a man whose guilt is not in question. It's important to note that the play was written in Britain in 1910, a time and place where very harsh judicial punishment was common.
Galsworthy was an influential critic of the contemporary British justice system, specifically the conditions in prisons. He was one of the first intellectuals to posit that prison will turn someone who simply made a mistake into a hardened criminal. This view is vociferously expressed by Frome in his arguments for Falder. Unfortunately, the argument is unsuccessful and Falder is sent to prison.