According to the following Google Ngram, in the U.K. the modals should, shall, and must were virtually missing from English writing during the 18th Century (I’ve added will for a comparison modal which was unaffected).
I have never seen this mentioned anywhere, and I couldn’t find it in a brief web search. What happened? Was this a real phenomenon, or could this somehow be an artifact of Google Ngrams? Were these modals absent from speech, or just formal writing? More interestingly, how did they get reintroduced? A brief search shows that Shakespeare definitely used these words quite frequently.
This was a problem with Google’s optical character recognition (OCR) mistaking the long s (ſ) as an f.
However, Google has since improved their OCR:
When we generated the original Ngram Viewer corpora in 2009, our OCR wasn’t as good as it is today. This was especially obvious in pre-19th century English, where the elongated medial-s (ſ) was often interpreted as an f, so best was often read as beft. Here’s evidence of the improvements we’ve made since then, using the corpus operator to compare the 2009 and 2012 versions:
Here’s the original chart from the question, with the 2009 corpus:
Here’s a chart with the same words but with the new 2012 corpus. This is much smoother and no longer has the large dip:
Here’s the chart from the other answer, with the 2009 corpus:
And here it is with the new 2012 corpus. This shows hardly any muft or fhall type words: