In order to give our readers an idea of his process of investigation, we will state the signs which he found in the group surrounded by a ring on the Rosetta stone. These are the following: a square--half circle--a flower with the stem bent--a lion in repose--the three sides of a parallelogram--two feathers, and a crooked line. The square, Champollion considered the equivalent of the Greek letter Pi--the half circle, Tau--the flower with the stem bent, Omicron--the lion in repose, Lamda--the three sides of the parallelogram, Mu--the feathers, Eta,--and the crooked line, Sigma. This gave the name Ptolmês. At this stage of his investigations, Champollion supposed that he had obtained seven signs of an alphabet; but, could he have gone no further, he would have established nothing, and his researches would have passed off with the labours of the learned who had preceded him. To test his principle further, it was necessary, therefore, that he should be able to get at some other monument, on which there should be recognized some name also known by some Greek or other connected inscription. Such a monument was found in an obelisk discovered in the island of Philæ, and transported to London. On this was discovered a group of characters also enclosed in a ring, and containing more signs than the former, some of them similar. On a part of the base which originally supported the obelisk, there was an inscription in Greek, addressed to _Ptolemy_ and _Cleopatra_. Now, if the basis of Champollion was correct, there ought to be found in the name Cleopatra, such signs as were common to both, and they must perform the same functions which had been previously assigned them; and this was precisely the result. We have this strikingly set forth in a note of the translator, which is here presented. "To prove that the conjectures of Champollion were true, the first sign in the name of Cleopatra should not be found in the name of Ptolemy, because the letter _K_ does not occur in PTOLMÊS. This was found to be the fact. The letter _K_ represented by _a quadrant_. "The second sign (_a lion in repose_ which represents the _Lamda_), is exactly similar to the fourth sign in the name of Ptolemy, which, as we have already seen, represents a _Lamda_. "The third sign in the name of Cleopatra is _a feather_; which should represent the _single_ vowel _Epsilon_, because the _two feathers_ in the name of Ptolemy represent _double Epsilon_, which is equivalent to the Greek _Eta_. Such is its import. As Greppo remarks in a note, and as has been fully proved by subsequent investigations of Champollion, the sign which resembles two feathers, corresponds also with the vowels _Eta_, _Iota_, and with the diphthongs _Alpha Iota_, _Epsilon Iota_.