Just past the atrium and near the centre of the house was the master's office, or tablinium, which contained the family records (tabulae) and images of the family ancestors (imagines).
Here the master of the house, in his role of patronus would greet his clients (clientes) and present them with sportulae (food) or presents of money. Strategically located to enable the paterfamilias to keep a watchful eye on his household, while he conducted business, the tablinium was also the room where visitors were brought.
While the tablinium appears to be a passageway between the atrium and peristyle, slaves and servants were not permitted to use it or pass through. The tablinium was probably rendered private with either sliding doors or curtains, traces of which remain in some Pompeiian homes. Passage from the front to the back of the house was probably enabled by fauces, narrow corridors on either side of the tablinium to protect the paterfamilias's privacy as he ran the estate.
Marcus Vitruvius Pollio, in his book, De Architectura, gives the dimensions of the tablinium: "The height of the tablinum to the beam is one eighth part more than the breadth. The lacunaria are carried up one-third of the width higher. The passages (fauces) towards courts which are on a smaller scale, are to be one-third less than the width of the tablinum; but if larger, they are to be one half. The statues, with their ornaments, are to be placed at a height equal to the width of the alŠ. The proportions of the height and width of the doors, if Doric, are to be formed in that method: if Ionic, according to the Ionic mode, agreeably to the rules given for doors in the fourth book. The width of the uncovered part of the atrium (impluvii lumen) is not to be less than a fourth nor more than one-third of the width of the same; its length will be in proportion to that of the atrium."
References: Handbook to Life in Ancient Rome, Lesley Adkins and Roy A. Adkins (Oxford University Press, 1998); The Romans, their Life and Customs, E. Guhl and W. Korner, Senate Press, 1994