To understand what was like in the 19th-century ranking, we need to understand the origin of the ranking and the background that lead to that. And some of them are still affecting us today.
First, the title 碁所 Godokoro (equivalent to the leader of the modern national Go association) is an official title for an office that governs all manners related to Go, and this job title has “salary” (in feudal Japan would make them small lords that own certain “land” to support this “salary”). Where Meijin is the description of the absolutely best Go player. And the job title Godokoro can only be held by a Meijin (名人, literally means a very famous and good person).
The definition of “absolutely best” in the era before any ranking system, before komi, means someone can always play any opponent as white (定先 josen) and win. And in an era before komi, the result of who is better is usually determined by a set of competitions (consist of many games of even number usually at ten 十番碁). And since a game might last a day to days, 10 games might last weeks even months, so direct competitions of top players happened not very frequent. This custom existed before Godokoro was made an official title,(in the 17th century) and its root can be traced back to ancient China.
The reason for even numbers of games per set is due to before komi, the way to ensure “fair competition” is to play several games and each one takes turns to play as black or white ( TagaiSen 互先), and if the result is when one side has more winning games above 4 in a set of 10 (that is 7 to 3, 6 to 2, 5 to 1, or 4 to 0, if one side wins more than 4 leads there is no need to play out the rest), he will be “superior” to the opponent and demotes your opponent. The next time the two players play against each other it will be 定先 josen, to compensate their strength difference. (if no clear winner after ten games 6/4 or 5/5, it means they are roughly equal in strength, this is the most basic form of win rate). The handicap stones can keep growing to 2 stones, 3 stones, etc (https://senseis.xmp.net/?MatchHandicapSystem). This is the basic form of dan system and also came from ancient China.
The interesting thing about this “raw form” of competing with each other is that there is no global consensus of how strong you are in a list of rankings. Every player has a list of players who he had played with, and what type of Teaiwari (手合割, TagaiSen, josen, or more handicaps) they should use to play each other. Player-A can beat Player-B, and Player-B can beat Player-C, but it doesn’t mean Player-A can use this to establish superiority over Player-C (and realistically Player-C can still beat the Player-A if their actual strength is close). Two players have to start with TagaiSen if they never met before in order to establish who is stronger. No one knew if there are some kinds of rock-paper-scissor type of strategies that can be used to counter each other.
Things always get complicated when money/salary is involved. In federal Japan in the 16th century, most Daimyo (federal lords) are Go lovers, especially Shogun (head of the federal lords, the de facto ruler of Japan), who held a national competition in 1588 and invited all the top Go players (上手 jouzu, literally means top players) in Japan to participate. And the winner Honinbo Sansa who was a monk and the Go teacher of the previous federal lord (who described him as Meijin) won it, and his temple was granted a hefty reward (this eventually led to the creation of the Godokoro job). During Sansa’s time, many of the Japanese Go rules and the system of competitions started to be established, and since Sansa was so strong, those who can withstand to play with him at josen became the first group of recognized jouzu, a group of dozens strong enough players who now became the measuring tools for everyone else.
In 1612, the Shogun established a series of “schools”, and picked top players (including Sansa) to established Go Houses granted with feudal hereditary titles and gave them annual funds to promote more players and trained them (iemoto system). Four later became the Four great Go Houses in the Edo period Japan (17th to 19th century). The house of Honinbo (Sansa’s house) had the most fund out of everyone and trained many good players over the years. The 4th leader of the Honinbo house Honinbo Dosaku had many students and he was a master and Miejin himself (one of the three 棋聖 Kisei of Edo period, the grandmaster of grandmaster). He started to issue diplomas of Go to the young lower dan players (1d to 4d) in the house, measured by his strong students. He also held the office of Godokoro, and he promoted the official diplomas to everyone in all the houses. And he devised a more refined way to determine strength, start with good players who can play josen with his top students - the high dan (5d in today’s rank), where six of the strongest students are the jouzu (7d). Dosaku himself as the Meijin is the measuring standard (9d in today’s rank) and can play josen with jouzu. At the same time, the rank between the 5d and 7d were established as who can play with 7d in sen-ai-sen. that is playing a sequence of two games in black and one game in white out of 3 (black white black, black white black, and so on). And this pattern goes on toward weaker and weaker players up to a difference of 4 ranks (1 rank difference is sen-ai-sen, 2 rank difference is josen, 3 rank difference is sen-ni - one game plays white followed by one 2-handicap game, 4 rank difference is jo-ni, which always play 2-handicap games, essentially each rank is 1/2 stone stronger than the next). Pro players start at 5d, those below them are mostly still students in the houses and not pros (1d to 4d didn’t get to have a salary so to speak). At the time, no one can play with Dosaku more than josen, so the hereditary title’s future successor (usually the top student or the head of each house) should be the second strongest to Meijin, became the first unofficial 8d (just referred to as those between jouzu and Meijin, later on was called half Meijin or Jun-Meijin, there were only 16 of them in the whole Edo period). And the title of gaining the title of Meijin was also established with an annual royal game played in the castle in front of the Shogun, and they knock each other down in Oshirogo. Only the leaders of the Four Houses and their Katoku (successors) had the right to attend this game.
This system continued all the way toward the end of the Edo period when the Shogun system collapses and the Meiji Restoration started (1868). All the old annual findings, titles no longer applied in the new government. And the dark period of the Go began. Jowa was the last Godokoro and last Meijin at Edo period, but not the last one to hold the old Meijin hereditary title. The Meijin as an independent honorary title without salary just as the original meaning of the best Go players existed all the way in the Oteai system to 1938 when the 10th and last old Meijin Honinbō Shusai retired and no longer wish to use the title. But the 9th and 10th Meijin although no longer officially recognized by the government, still held weight in the communities. The Oteai system established in 1927 is a modified competition system based on the old dan level system, only that the difference between 1 rank now reduced from 1/2 stone to 1/3 stone, where pro players of all ranks can compete with each other without komi. And under this system, players were no longer bounded by the jouzu cap of 7d. Oteai last all the way to the early 21st century in 2003 and was replaced by the new promotion system. The model of Oteai had been widely adapted for amateur dan ranking competitions (up till very recently) and some variations of this ranking system still existed today.
The conversion of named titles to numerical titles were a very long and slow process. And a lot of the countries only started to adapt them as late as in the 1970s or 1980s Simply put, in the 19th century there were no 9d or 8d or even 7d as numerical ranking, all the top players are jouzu numbered in the dozens only, and only 5d and 6d are pros and consist the majority of them. The 1d to 4d were usually not considered as pros (although they certainly can challenge top players). One thing made advancing to 5d ~ 7d so difficult in the old system is that you can actually got demoted by your opponent if you lose, but if you want to advance a level, not only did you have to beat better opponents and if someone in the Four Houses disagreed with your strength, they could challenge you in Jubango to see if you are actually that good (also all the Four Houses have to agree upon the decision to issue the official diploma). This process would take quite a long time when you applied for a diploma and waited for all the challengers to recognize your strength, (like a national wide review system, every high dan player should be in theory absolutely stronger than everyone below him), and all the leaders of four houses have to agree for advancing to Jouzu (since they are either potential recruits or competitors). And definitely, for Meijin title where every top player in all the houses (and after Meiji Restoration, include all the Go associations who start to issue diplomas competing with old Go Houses) would issue challenges if someone wanted to apply for it, and he had to beat and demote literally everyone to become Meijin. So naturally, there were gaps of years between each Meijin (thus without Godokoro title holder) since the settlement of all challenges for the next Meijin would take a really long time. Also, since Meijin is a title for life, usually, it’s toward the later stage of the previous Meijin’s life there were half-Meijin appeared.