From The Notion Club Papers; page 170 of Sauron Defeated (1993) by JRR Tolkien.
Note 15 expands on this: In the original text... [Dolbear adds] "Then try reincarnation, or perhaps transcarnation without loss of memory."
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This is the exact point at which JRR Tolkien's Notion Club Papers (NCPs) takes a turn from mundane conversation among club members; towards the supernatural, or more accurately the occult.
Yet, I found this important passage to be very confusing at the time I first read it; and I am still unsure why Tolkien used the term "incarnation" in reference to the aim of space travel, of visiting another planet. I usually understand incarnation to refer to a spirit taking-on a body - and this is usually assumed to be irreversible except by death.
"Being born" seems to confirm this. Being born onto another planet can hardly be described as a viable way of 'landing' on a new planet - even if memory of one's previous life was retained. It means becoming somebody else. Incarnation seems not to be equivalent to visiting another planet - implicitly temporarily, so one could come back and tell other people! - by means of spaceship, miracle or magic (the previously discussed possibilities)
I turned to the earlier draft note, which mentions reincarnation - usually meaning the same soul being clothed by a series of at least two bodies. But again, this is a linear and irreversible process - and seems unsuitable for visiting other worlds.
Transcarnation may be a neologism: that is, a word here invented by Tolkien; which probably was intended to convey the idea of a soul transferring from one body to another without death.
By this, I presume he must have meant that someone's soul might go to another planet; either by temporarily inhabiting the body of someone being already there (something of this kind, a 'body swap' is mentioned in CS Lewis's unfinished Dark Tower, which Tolkien had heard); or perhaps by (temporarily) clothing itself in a body (or appearance of a body) while on that planet.
What actually emerges as the way in which members of the Notion Club visit other places, and times, has aspects of this (presumed) transcarnation, in the case of Ramer; and something like reincarnation in the case of Lowdham and Jeremy.
Ramer's soul or spirit seems to leave his body and visit other places during sleep. Ramer does not seem physically to incarnate; but he does report being present, aware and localized - rather as if he had condensed spatio-temporally, maybe clothed himself with a 'spirit body'.
This is sometimes called Astral Projection - for example Rudolf Steiner regarded this as what happened to us all, every night, during dreams. Our Astral body leaves the sleeping Physical and Etheric bodies; to go and do 'dream things' in another actual but spirit-realm of reality.
And (according to Steiner) the Astral body 'carries with it' our Ego, or sense of self, or 'I' - which is how we are self-aware during dreams.
Because the spatio-temporally limited Physical body (and its attached Etheric body) are left-behind (although still connected, as it were by an infinitely elastic thread) - the Astral body can be assumed to move freely through space; and perhaps also time.
These ideas are compatible with what Ramer reports; including his comment that "Dreaming is not Death. The mind is, as I say, anchored to the body."
(It is quite possible that Tolkien may have known of these ideas, either from general reading and converstaion, or specifically via Inkling-member Owen Barfield, who was Britain's leading Anthroposophist - i.e. Steiner follower. Indeed; the obviously referenced "Ranulph Stainer" is listed as a member of the Notion Club!)
By contrast; Lowdham and Jeremy were (probably) intended to be something-like (but perhaps not exactly, according to Tolkien's comments) reincarnations of paired souls; who had descended 'genetically' through history - including having inhabited Numenor, experienced its downfall, and been among those who escaped to Middle Earth.
This narrative plan was something Tolkien carried over from his earlier draft story The Lost Road - but there it involved father-son pairings.
In other words; Ramer's journeys were focused on space travel while Lowdham and Jeremny were primarily engaged in a kind of time travel. In her brilliant and inspiring monograph A Question of Time; Verlyn Flieger convincingly argues that Tolkien's idea of time travel was rooted in JW Dunne's ideas of the simultaneity of time. This enabled the mind to survey the past and indeed future.
The idea was probably that Lowdham and Jeremy's connection of heredity was activated - partly by purposive dreaming - such that the simultaneity of the downfall of Numenor, and the 'modern' activities of the Notion Club, became superimposed. The Numenorean catastrophe then overlapped with contemporary Oxford in this condition of simultaneity; leading to the massive storm experienced by the South and West of the British Isles that forms the climax of the second part of the NCPs.
Lowdham and Jeremy therefore do not engage in any kind of 'transcarnation' or Astral travelling; but instead become a kind-of simultaneous combination of their Numenorean and modern selves.
For clarity, it would perhaps have been easier for the reader if Tolkien had dropped the term 'in-carnation' and stuck with his original terms of re-incarnation and trans-carnation; and maybe given them at least a bit of definition. Something like this may have happened, had the Notion Club Papers been taken any further. But in the event, we are left to complete the jig-saw ourselves, using the clues JRRT left-behind and which his son Christopher assembled and published - nearly half a century after the NCPs had been abandoned.