This story is essentially a time travel story so there are several aspects of "historical geology" in play for the book. The first part involves the occurrence of a solar eclipse.
"I knew that the only total eclipse of the sun in the first half of the sixth century occurred on the 21st of June, A.D. 528, O.S., and began at 3 minutes after 12 noon. I also knew that no total eclipse of the sun was due in what me was the present year --i.e., 1879." Chapter 2As the story progresses it turns out that the narrator had the incorrect day and actually the eclipse occurred on the 20th. However that small change of a day does not really effect our interpretation in a scientific aspect.
The benefit of determining when solar eclipses have happened in the past is that eclipses have a pattern to them. They occur in cycles due to the repetitive motions of the sun, moon, and Earth. And it is possible to calculate out when exactly eclipses have occurred or will likely to occur. Luckily NASA has already done this for us. The link goes to a document which catalogs all of the eclipses that have occurred from 2000 BC estimated up through 3000 AD. Unfortunately, Twain did not have access to such a document, or even the knowledge of when eclipses occurred. Since there are no written records from the sixth century listing all of the solar eclipses we have to assume that what is in the list is mostly accurate. There is a possibility that the dates and the times may be off, but there is a strong certainty that they are not off by much. According to the list, there were 4 eclipses during the year 528 (Feb 6th, Mar 6th, Aug 1st, Aug 30th). And even then, only two of those were visible in the northern hemisphere (Feb 6th and Aug 30th). So even with problems linking up the calendars (prior to 1582 a different calendar was used, the Julian calendar), it is unlikely that there was any total eclipse during 528 AD and not even a partial one in May, June, or July (the months surrounding the incident in the book).
The second entry has to do with the formation of geology as a science in general.
"He said the most of Sir Dinadan's jokes were rotten and the rest were petrified. I said "petrified" was good; as I believed, myself, that the only right way to classify the majestic ages of some of those jokes was by geologic periods. But that neat idea hit the boy in a blank place, for geology hadn't been invented yet. He failed to catch on. However, I made a note of the remark, and calculated to educate the commonwealth up to it if I pulled through. It is no use to throw a good thing away merely because the market isn't ripe yet." Chapter 4Geology in and of itself is an ancient study. It is known from the period of Aristotle, where he made comments on the geological rates of features. One of his pupils, Theophrastus, who was born in 371 BC also wrote up a book called On Stones where:
"...he goes on to classify them based on their reaction to heat, on their hardnesses, and on their power of attraction. He describes a great variety of stones according to their use and origins. He writes on coal and it's use as a source of heat by metal-workers, he writes on the minerals used on the fabrication of glass, of different pigments, of plaster. He traces the origins of pumice-stones to volcanos, of pearls to shell-fish, and speaks about fossilized remains of organic life. Theophrastus was also the first known person to have made reference to pyroelectricity, the capacity, by certain materials, to produce voltage when heated or cooled. From his text as well as from a later text by Pliny the Elder (Naturalis Historia from 77AD) the science of mineralogy emerged, arguably the founding science for geology."Theophrastus could be considered as one of the founders of geology. However, modern geology does have a significantly different approach to it. The introduction of modern geology took a long road from these origins though. There are a couple of people who are credited with having founded modern geology. One of them being Nicholas Steno (1638-1686), who is credited with the main laws of stratigraphy: The law of superposition (the stuff on the bottom is older than the stuff on top), the principle of original horizontality (rocks are laid down horizontally), and principle of lateral continuity (rock units stretch over large areas of land). Later works by James Hutton (1726-1797) , such as his published ideas on uniformitarianism (everything happening now has happened in the past) are also credited with ushering us into the modern age of geological thought. Hutton is often considered to be the Father of Modern Geology although Steno surely also has a significant place at the top.
The narrator's comment also plays into the concept of the age of the Earth. The boy in the quote was not used to thinking of the Earth as an old place. To people before 1600, the bible was seen as a literal truth where everyone thought that the Earth was 6,000 years old. In the narrator's own time (1879 as mentioned before), Lord Kelvin had just estimated the Earth to be about 98 millions years old. Even though this is far younger than we now understand the Earth to be (4.55 billion years old), the narrator still understood his Earth to be much older than that of the boy in his presence. This lends weight to his "majestic ages" comment, where millions of years denotes the ages quite a bit better than thousands of years.
This paragraph involves two aspects of Historical Geology. The first part is that even though geological concepts were thought of prior to the "inventing of geology" in the 16 to 17 hundreds, it is possible to say that geology had not been "invented" yet. And it is without modern geology that the true age of the Earth was unknown with the only source for that information having been the Bible, which would have placed that age approximately 6,000 years before. The Earth being a very old place was the basis of the joke which the narrator tells to the boy, and without that long age, the joke would likely have fell on deaf ears.