Jefferies tubes, in the Star Trek fictional universe, are narrow tunnels or corridors inside a starship. They can be vertically or horizontally oriented, and form a network that allows travel throughout large volumes of a starship even when the turbolifts are not functioning. Plumbing, power, and other infrastructure utilities are frequently routed through them.
The term "Jefferies tube" was originally an inside joke among the original Star Trek production staff, a reference to original series art director Matt Jefferies, the man who designed the original starship Enterprise. The term was used frequently throughout Star Trek: The Next Generation, Star Trek: Deep Space Nine. and Star Trek: Voyager. The term first became officially used in the script of the original series episode "Journey to Babel", but did not become canon until stated in the Next Generation season 3 episode "The Hunted." Matt Jefferies is quoted as saying, "Somebody hung the name Jefferies Tube on it (the prop). It wasn't me, but the name stuck and I used it in some of my sketches!" 
Another in-joke reportedly appearing in the Jefferies tube sets on the original Star Trek series are labels on the pipes marked "G.N.D.N." This stands for "Goes Nowhere, Does Nothing."  The labels are usually written so small as to be invisible to the audience, but can be seen in certain scenes from the Star Trek films.
Types of tubes
These tubes were characterized as being circular shaped, small, and poorly lit. Crewmembers traveling along one to repair an engineering or electrical pipe would have to walk bent over in the cramped space. The vertical tubes were lit behind the ladders so the crewmembers could see their path.
Although still circular shaped, the Jefferies tubes in the original series were better lit and less cramped. In this century, they have the added feature of having diagonal tubes -originally referred to in creator Matt Jefferies sketches as "power shafts." The diagonal tubes had the added function of system controls, conduits, engineering circuits, and could act as passageways through the nacelle pylons to the ship's warp nacelles. The vertical tubes, also known as gangways, were also equipped with three-way ladders, which could allow multiple crewmembers to climb during a time of emergency which can be seen in the episode "Amok Time".
The name of "Jefferies tube" is officially established in the Next Generation episode "The Hunted". In the previous centuries, they were referred to as "access tunnels", "service chutes", or "access tubes". By the late 23rd century, the tubes had less of a cramped shape, which carried over into the 24th century. The other main features of the tubes were that they became more simplified and had less exposed tubing within. Instead, the vital electrical systems were hidden behind removable panels. Like the 22nd century, the vertical tubes were fitted with dim lighting behind the ladders so the crewmembers could see where to step.
Life on Ship
The Jefferies tubes have been described as "relatively cramped and provided only enough room for a single technician."  Besides their original engineering purpose, the tubes can also be used for recreation, maintenance, training, transportation, and security. In the Next Generation episode "Lessons", the character Neela Daren uses the fourth intersection of Jefferies tube 25 on the Enterprise-D to have an acoustic "sweet spot" where she could practice her musical instruments. Also in Star Trek: Voyager it is shown in episode "Learning Curve" that the Jefferies tubes were used for physical fitness training.
Within the Star Trek: Alternate Original Series graphic novel Spock and Kirk climb through a Jefferies tube to reach his trapped crewmembers without using the main hallways or turbolifts. This illustrates the concept that the Jefferies tubes can be navigated as passageways to connect to different sections of the ship during Alert status and reduced power scenarios since the turbolifts may not be functional or prohibited. In one panel, Spock turns back to Kirk and makes a reference to how small and cramped the tubes are, saying that, "his (the alien Keenser) small size would be an advantage in the Jefferies tubes." 
In the Next Generation novel Losing the Peace, the character Trys Chen recounts how in her childhood she explored the Jefferies tubes, stating that "even on the smallest vessels, there were literally kilometers of the service tunnels". Later on in the book, when Chen joins Starfleet she displays how some of her duties were to repair the inside of the Jefferies tubes that she used to explore when she was younger. This shows that the Jefferies tubes could be used for educational purposes as well as for their practical purpose of exposing core electrical wiring and tubing for easy access, as well as transportation from one point of the ship to the other.
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