All the MA students in this year’s MA course on Late Modern English Letters have to write blog posts on their findings. Here is the first one, and it is by Sabine Krouwels:
A couple of weeks ago, we discussed the subject of opening and closing formulas in the MA Linguistics course The Sociolinguistics of Late Modern English Letters. We learned that there are set rules for such formulas and that writers barely deviated from those rules.

Wikipedia
However, while conducting a pilot study for my research essay on the language in the correspondence of poet and dramatist John Gay (1685-1732), I came across a very free adaptation of opening and closing formulas in the following letter, written in Canterbury on Saturday 17 July 1717:
My Dear Belladine
O’re a Glass of Wine
We send you this line
On Purpose to tell
You & Miss Lepell
We are all very well
If news we should send you from Canterbury
That news to be sure you would think is a lye
And therefore we’ll say what before you did know
That we are Your Servants wherever we go.
Ann Pulteney
Wm. Pulteney.
J Gay.
This letter is written by John Gay and Ann and politician William Pulteney to Mary Bellenden, Maid of Honour to Caroline, Princess of Wales, or Belladine. It was written in Pulteney’s hand, though probably dictated by Gay. (The letter can be found in C.F. Burgess’s edition of Gay’s letters published in 1966.)
One instantly notices that this letter is written as a short, colloquial sounding poem. The second line “O’re a Glass of Wine” sets the scene: John, Ann and William are enjoying a glass of wine on a warm summer evening and decide to send word to their mutual friend Mary Bellenden and Mary Lepell, another Maid of Honour. This gives the letter/poem its light and amicable tone.
Let’s have a look at the opening and closing formulas. The opening formula is actually formulated as was expected in these days: “My Dear Belladine” shows no uniqueness as far as the formula goes. It is worth noting, though, that Mary is addressed by her nickname Belladine. There are two reasons I can think of why they would have used her nickname: they either knew her very well and therefore named her Belladine all the time; or, it was for the sake of the rhyme with the next sentence. However, a quick Google-search confirms that Mary Bellenden was called Belladine by friends (Crocker 1824), so a combination of these reasons seems very likely.
Looking at the closing formula, we can see that the style is very different from what we are used to from those days. To me, it seems a poetic version of the standard formula ‘I am/ Your Humble Servant’, since the last sentence says “we are Your Servants”. The last part of that sentence, “wherever we go”, might be a reference to the fact that the trio was traveling to the Continent at the moment this letter was written.
All in all, the closing formula sounds very amicable to me. These four or five people must have known each other quite well for them to deviate from the norms so strongly when writing each other. Either that, or they were just horribly drunk …
I have not been able to find more instances of such free interpretation of opening and, especially, closing formulas yet, however, perhaps someone has found similar instances in other letters?
References:
Crocker, John Wilson, ed. Letters to and from Henrietta, Countess of Suffolk, and Her Second Husband, the Hon. George Berkeley: From 1712 to 1767. Vol. 1. London: John Murray, 1824.
Gay, John. The Letters of John Gay. Ed. C.F. Burgess. Oxford: The Clarendon Press, 1966.