Reincarnation and Transmigration

From Kardec’s Spirits book: Chapter 4 - Reincarnation (page 120) Questions 167-170, and 172-177

167. What is the aim of reincarnation? 

"Expiation; progressive improvement of mankind. Without this aim, where would be its justice?”

168. Is the number of corporeal existences limited, or does a spirit go on reincarnating himself for ever?

"In each new existence, a spirit takes a step forwards in the path of progress; when he has stripped himself of all his impurities, he has no further need of the trials of corporeal life."

169. Is the number of incarnations the same for all spirits?

"No; he who advances quickly spares himself many trials. Nevertheless, these successive incarnations are always very numerous, for progress is almost infinite."

170. What does the spirit become after its last incarnation? 

"It enters upon the state of perfect happiness, as a purified spirit."

Incarnation in Different Worlds

172. Do we accomplish all our different corporeal existences upon this earth? 

"Not all of them, for those existences take place in many different worlds. The world in which you now are is neither the first nor the last of these, but is one of those that are the most material, and the furthest removed from perfection."

173. Does the soul, at each new corporeal existence, pass from one world to another or can it accomplish several existences on the same globe?

"It may live many times on the same globe, if it be not sufficiently advanced to pass into a higher one."
- We may, then, re-appear several times upon the earth?
"Certainly."
- Can we come back to it after having lived in other worlds?
"Assuredly you can; you may already have lived elsewhere as upon the earth."

174. Is it necessary to live again upon this earth? 

"No; but if you do not advance, you may go into a world no better than this one, or even worse."

175. Is there any advantage in coming back to inhabit this earth? 

"No special advantage, unless it be the fulfillment of a mission; in that case the spirit advances, whether incarnated in this earth or elsewhere."
- Would it not be happier to remain as a spirit?
"No, no! for we should remain stationary; and we want to advance towards God."

176. Can spirits come to this world, for the first time, after having been incarnated in other worlds? 

"Yes; just as you may go into other ones. All the worlds of the universe are united by the bonds of solidarity; that which is not accomplished in one of them is accomplished in another."
- Some of those who are now upon this earth are here, then, for the first time?
"Many of them are so; and at various degrees of advancement."
- Is there any sign by which we can know the spirits who are here for the first time?
"Such knowledge would not be of the slightest use to you."

177. In order to arrive at the perfection and the supreme felicity which are the final aim of mankind, is it necessary for a spirit to pass through all the worlds that exist in the universe? 

"No; for there are a great number of worlds of the same degree, in which a spirit would learn nothing new."
- How, then, are we to explain the plurality of his existences upon the same globe?
"He may find himself, each time he comes back, in very different situations, which afford him
the opportunity of acquiring new experience."

In other words....

We reincarnate as many times as necessary, but we may not reincarnate back to earth.  We may find ourselves on another planet.  We are crazy if we think that the carbon-based life form we have on earth is the only form of life.  Just because we cannot always see it, there are other life forms.  Our soul is an energy that we can feel, but it is invisible to us in the material world.  On earth, our soul is sometimes in the spiritual world and sometimes in the material world.   

We might reincarnate to a lower planet or a higher planet (Kardec believed that Saturn was the best planet), or even back to earth.  When we reincarnate on another plane, Kardec called it transmigration.  A soul that has reincarnated several times on earth and shown no improvement might be sent to a lower planet - or that soul might reincarnate back to earth in a lower position. 

What is the reason for transmigration from one world to another?  Read more here:

http://mcmillinmedia.com/spirit/kardec-sb-b2-ch4/