Help Interpreting 1819 Stampless Cover

This cover is one of my earliest pieces. It is an 1819 stampless cover with a Philadelphia postmark stamp. According to the Phillips "American Stampless Cover Catalog," such a cover traveling from Philadelphia to Boston (about 300 miles) should cost 18 1/2 cents.

Here is my question. In the upper right corner there is writing that is old and could be original. I see the number 18 and then a squiggle. Is this a mark denoting the 18 1/2 cent postage rate? Is that how this would be done? Is this wishful thinking on my part that it would be marked this way?

You did not need us.

Another 18 1/2:

Thanks for the quick response and the image of the similar cover. I did need you for understanding if I was interpreting this correctly. It is so nice to be able to ask questions in this forum.

You are correct that it is "18 1/2", done in one stroke of the pen. If you had a pile of hundreds of letters to mark up like this with pickup due in a short time, you'd probably settle for barely legible. Think of how many times you'd have have to dip your pen in the inkwell besides.

Its funny, what I had thought (or hoped) to be the case seems so obvious now that I've asked and see this other example. Although, I admit I am also always hesitant about handwriting on covers as so many have later writing. Thank you both!

Here is a cover from the mid 1830s sent at the later 18-3/4 rate and illustrating similarly that the fraction portion of the rate was often reduced to an incomplete scribble, essentially eliminating the numerator or denominator, knowing that the clerks and postmasters knew the basic rate structure and what the fraction had to be.

Fantastic. I presume these rates were prepaid and so it was the postmaster or clerk at the city where the piece was sent who wrote it? At the same time the postmark was added?

Partially correct.
The rates were marked at the point of origin. These three were all sent un-paid (as they are not specifically marked "paid"). The recipient had to pay to get these letters.

Thanks much for that added piece of information. Very helpful.

Of course, the person collecting the fee from the recipient would also know the fee structure.

A lot of money for one letter. Equivalent to $3.86 today.