The Gate of Ptolemy is a rite invented by Ptolemy of Alexandria. It is essentially a "reverse summoning", by which a magician separates their spirit from their physical body and propels their spirit into the Other Place.
The actual process of invoking the Gate is surprisingly simple. A participant simply draws a regular pentacle, but then breaks it by creating a small slash or smudge to the border. This is done to allow the participant's spirit to depart and return from the physical world. Ptolemy also recommends keeping some traditional herbs (rosemary, rowan wood, etc.) and/or some iron or silver in the circle to protect the body from magical attack while the spirit is absent, although such measures are not meant to be taken to excess, as doing so can hinder the reunification of the body and spirit. From there, the participant speaks an incantation similar to that in a normal summoning, but the words for "come" are replaced with words meaning "go", the participant's name is substituted for a djinni's, and at the end, the name of a "benign" spirit is called three times. If all goes well, the participant's spirit is then propelled into the Other Place.
The physical Gate is more like a hallway, as Kitty describes the elemental walls as four walls that "towered above, plummeted below, and stretched to infinity on either side", one "was dark and solid, and threatened to crush her with remorseless weight" (Presumably Earth), "the next was a raging fluid, wich surged avidly to carry her away (Water). The third barrier tore at her with the unseen tumult of a hurricane (Air), the fourth was an implacable wall of unquenchable fire (Fire)." This implies that the Gate is a hallway instead of a cube, because where a cube has six faces, there are onlyfour elements refferred to here.The idea of a corridor is also supported by the quote that they only stretched to infinity on either side, not at the top or bottom.
Using the Gate allows a human to visit the Other Place, an act that is otherwise impossible. However, if the procedure goes wrong, it can cause physical deformities and/or insanity. Even in successful cases, using the Gate induces a permanent accelerated aging effect and a temporary loss of equilibrium and muscle meory (though the actual time depends on how long one was in the Other Place). It is intimated that staying in the Other Place too long will cause the body to die completely and/or rot away. While a human is in the Other Place, they are also subject to the authority of the resident spirits (even as spirits are slaves to magicians on Earth).
As of the conclusion of Ptolemy’s Gate, only Ptolemy and Kitty were successful in invoking the Gate, as (according to Bartimaeus) doing so requires one to willingly separate from their physical body and leave it behind, an act which few people (and fewer magicians) can accomplish. Kitty also makes the observation that, during the crossover, a participant must keep a detached, observational manner about them, or they will feel completely helpless, grow unbearably anxious, and subsequently go insane.