Human Nature

The Doctor and Martha narrowly escape an attack by the Family of Blood who are seeking the Doctor's Time Lord life force to prevent themselves from dying out. As the Doctor directs the TARDIS to Earth, he tells Martha that he must transform into a human for three months to escape the Family's detection while they die, and gives her a list of instructions to follow. He then uses the Chameleon Arch to transfer his Time Lord configuration to a fob watch which he entrusts Martha to guard.
After landing on earth in 1913, a year before the Great War, the Doctor adopts the persona of John Smith, a schoolteacher at Farringham School for boys, while Martha acts his maid. John's personality is nearly opposite of the Doctor's, being quiet and timid, but faint memories of the Doctor slip through, appearing as text and images he writes in his "Journal of Impossible Things". Though John carries the fob watch, the perception filter that it possesses prevents John from being curious about it. John has become infatuated with the new school nurse, Joan Redfern, and shares his journal with her; Martha remains concerned as the Doctor did not instruct her what to do should he fall in love. Timothy Latimer, a younger student at the school with extrasensory perception, discovers the fob watch and pockets it for himself, unbeknown to Martha.
Meanwhile, the Family of Blood have been able to track the Doctor to Earth, and cover their ship in an invisibility shield to keep it from being discovered. The various members of the Family seek out human victims to possess, including one of the school's prefects, one of Martha's fellow maids, a farmer, and a young girl with a balloon, allowing them to seek out the Doctor undetected. When Timothy briefly opens the watch and experiences portions of the Doctor's memories, the Family detects its presence at the school, and soon recognise Martha, trying to ply her for more information about the Doctor. Martha realises that the Family has found them and attempts to retrieve the watch in order to bring back the Doctor, but cannot find it. She attempts to talk to John to awaken the Time Lord persona, but instead causes John to become angry at her, forcing her out of his chambers as he prepares for a village dance with Joan that night. At the dance, Martha again tries to persuade John to become the Doctor by showing him elements of his past such as his sonic screwdriver, but is unaware the Family has overheard her conversation. Now aware that John is the Doctor, the Family capture both Martha and Joan. The cliffhanger ending leaves the Family asking John the question of "Maid or matron, your friend or your lover. Your choice."

42

After The Doctor adjusts Martha's phone for "Universal Roaming", they receive a distress signal from the S.S. Pentallian, a human spacecraft that is hurtling towards a nearby star, and the Doctor pilots the TARDIS towards it to help. After they materialise, the Doctor and Martha are separated from the TARDIS due to rising temperatures. They are forced to help the crew, lead by Captain McDonnell, to try to restart the engines to save the ship and themselves with only 42 minutes left before the ship will be destroyed by the nearby star. Martha teams with Riley to work their way through thirty deadlocked doors, secured via means of pop quiz questions, in order to reach the bridge controls while the Doctor helps the engineering team to repair the engines. Martha is able to call her mother, Francine, on present-day Earth in order to get the answers to some of the questions correctly, though she refuses to answer Francine's questions about the Doctor.
The Doctor learns that one of the crew, Korwin, McDonnell's husband, has been infected with something that is causing his body temperature to rise to incredible levels, and attempts to sedate him while they continue the repairs. However, Korwin manages to overcome the sedative and dons a welding helmet, proceeding to kill various crew members, and in one case, infecting another, named Ashton. As Martha and Riley continue to work through the doors, they encounter Ashton and take shelter in a nearby escape pod, which Ashton is able to launch despite Riley's attempts to stop him. As the pod falls towards the star, Martha calls her mother and apologises, but hangs up when Francine, guided by an official-looking woman listening on the conversation, probes Martha for more information on the Doctor. The Doctor learns of Martha's plight, and puts on a spacesuit to go outside the airlock and activate a magnetic pull control to recover the pod. As he returns into the ship, he looks directly into the star and becomes infected himself, while learning that the star is a living being. As the crew try to help the Doctor, McDonnell admits they drew matter from the star to use as fuel; the living being is fighting back to recover the parts it lost. Martha attempts to help the Doctor into a stasis chamber to prevent him from regenerating, while the crew continues to work towards the front of the ship. However, Korwin appears, and disables the chamber; the Doctor insists Martha to leave him and warn the crew to dump the fuel, which will allow them to escape, while the Doctor struggles to fight the star being from taking over his body.
Martha races through the ship just as the crew reach the bridge, and relays the Doctor's message. Meanwhile, McDonnell has encountered Korwin and, after apologising to him and the rest of her crew for her actions, ejects both of them out of an airlock. As the ship vents its fuel, the engines are able to be restarted and it pulls away from the star; the presence in the Doctor slowly dissipates as the ship moves away. The Doctor, Martha, and the remaining crew regroup and verify they will be safe and that the crew has send a request for more fuel so they can continue their mission. The Doctor and Martha depart in the TARDIS, the Doctor giving Martha one of the TARDIS keys. Martha places another call to her mother, and learning that it is Election Day, offers to meet her for tea. After Martha's call, the woman monitoring Francine's phone confiscates it and leaves, thanking her for her help and for her vote on behalf of Mr Saxon.

The Lazarus Experiment

The Doctor returns Martha to her flat, twelve hours relative to after she first stepped in the TARDIS. Clued in by a telephone call by Martha's mother Francine that her sister Tish is on the television, they watch a news report with a statement from the elder Professor Richard Lazarus, announcing that later that night, with one demonstration, he will "change what it means to be human". The Doctor leaves in the TARDIS, but quickly rematerialises when he recognises the impact of Lazarus' statement. They dress for the formal dinner party at Lazarus Labs, and meet up with Tish, who works for Lazarus; Francine, Martha's mother; and Leo, Martha's brother; Francine is immediately suspicious of the Doctor's interest in Martha. Their conversation is interrupted as Lazarus announced he will perform a miracle and steps into a capsule in the center of the reception room. Technicians start the machine, filling the capsule with strange energy, and the Doctor quickly steps in when he believes that the system is overloading. As the machine comes to a stop, Lazarus leaves the capsule, now a much younger man; his machine is able to manipulate the subject's DNA to make them younger. The Doctor, highly concerned of unknown side effects, is able to gain a sample of Lazarus' new DNA when Lazarus kisses Martha's hand, and, with Martha's help, discover that the DNA is unstable.
As they investigate, Lazarus returns to his office along with his partner, the elder Lady Thaw. She insists that she be the next to undergo the process so they can be young together, but he refuses as he didn't want to "waste another life with you [her]". As she threatens to have Mr. Saxon pull their funding, Lazarus begins to undergo a transformation into a scorpion-like being, and kills Lady Thaw by draining her life energy, leaving her a zombie-like corpse; after returning to his human form, Lazarus returns to the reception, while the Doctor and Martha shortly find Thaw's body, the Doctor surmising that Lazarus must drain the life energy to keep his DNA stable. The Doctor and Martha, along with Tish, quickly return to the reception area and warn everyone to escape as Lazarus transforms again. The Doctor lures Lazarus away as Martha and Tish use the sonic screwdriver to override the building's security lockdown and saving the remaining guests. Martha rejoins the Doctor and the two take shelter in Lazarus' device, the Doctor believing he will not harm his own invention. The Doctor also explains that Lazarus's transformation is the result of an evolutionary throwback locked away in dormant human genes that are now becoming dominant. Unfortunately, Lazarus manages to activate his device, but the Doctor reverses the polarity, causing the field to affect only Lazarus outside of the capsule. They emerge to find Lazarus in his human form naked and apparently dead.
As the police and medical workers arrive to take care of the wounded, Lazarus' body is taken by an ambulance. However, when the Doctor hears a nearby crash, he, Martha, and Tish race to discover the ambulance has crashed, its drivers drained of life. They find that Lazarus, alive but human, has taken shelter in Southwark Cathedral. The Doctor tries to reason with Lazarus but is unable to stop him transforming again. Martha and Tish, under the Doctor's orders, lure the creature to the top of the Cathedral's bell tower, while the Doctor manipulates the church's pipe organ to produce the maximum volume it can. The vibrations caused by the organ interfere with Lazarus' manipulated DNA, and he falls to his death to the floor below, transforming one last time to his human form.
Martha and the Doctor return to her flat, and the Doctor offers Martha on board, more than just as a passenger, which she accepts. As the TARDIS dematerialises from the flat, Martha's voice mail records Francine's warning to her daughter about the dangers of the Doctor as told to her by Mr. Saxon.