One of the more controversial things that Google has done (at least to authors such as myself) was to digitize and convert a wide variety of written material and present it to the public. (Writers were concerned about copyright issues, something that directly affects their profession.)
However, with that digitized material now available, it is possible to process it is many different and interesting ways. One of them is Google Ngrams, which is a search engine designed to track the appearance of certain words in the collection and relate them to specific eras when that word was used. In other words, this is a search tool to reveal the times in which a specific word became part of the literature and to track its popularity. The database only can provide information for the period 1800 to the present, however.
But since the word "hypnosis" and the related terms were created by James Braid in the 1820's, they definitely fall within the time range. So, just as an experiment, I entered the terms "hypnosis", "hypnotism" and "hypnotize" into the database and got this result. As I expected, the three terms started appearing in the 1820s, but what mildly surprised me was the jump in appearances in the early 1880's, probably coinciding with the increased interest in the subject in Victorian Britain and America.
In contrast, a comparison between "hypnotism" and "mesmerism" here shows a relatively similar rate of appearance since before the start of the data set, with a spike in the early 1840's and 1850's, then settles down to a relatively stable appearance rate up to the 1920's and slowly declining to present.
Another part of the search engine, one that has been around for a while, allows for searches inside the various books, magazines and articles in the database, This includes not only a number serious books on the subject but also a number of pieces of fiction as well. They're well worth investigating: one example here searched for anything in the 1800-1850 time frame that includes the word "mesmerism" and returns several items, including works by such early figures as James Esdaile and Thomas Buckland.
I plan on investigating this resource much more deeply in the future, but for now its an interesting tool in itself.