Below is a letter signed by
Wm. P. Quarles Lieut:
formerly of the first Virginia Continental Reg
commanded by Col. Wm Davies
There is a date of Aug. 23, 1799 on the letter.
The letter is certifying the enlistment of James Farrell
when I was recruiting about March 1782.
If you go to the following page
(click on) WPQ Military Career
you will find a letter written in 1782 by Wm P Quarles, Lt,
to Col. William Davies requesting to be appointed as a recruiting officer.

DOCUMENT SOURCE: National Archives Publication Number M804;
Publication Title: Revolutionary War Pensions and Bounty-Land Warrant Application Files
National Archives Catalog ID: 300022; Case Files; Record Group 15; Virginia

The following image is the second page of a letter written by "Wm P. Quarles"
to Gen. James Wood concerning Cincinnati Society Funds.
The first page of the letter has the date October 21st 1803 written on it.
(The entire letter and source can be found on the website page
(click on) WPQ Military Career
under the Cincinnati Society topic)
[This is the letter Mr. Minor Weisiger, Secretary of the Virginia Society of the Cincinnati
in 2011, inferred was written by the Rev. War officer Wm. P. Quarles residing in
Fluvanna County, Virginia, at the time, and whose estate was administered in
1834 in Fluvanna County, VA.
The signatures (Wm P. Quarles) on these two letters appear to have been written
by the same person.]

The following image of a Bedford County, VA court record
shows the "Wm Quarles" signature.
It appears to match the previous two signatures.

The following image refers to "Captain William Pennington Quarles",
amd is the only document I (Roy Harrell Phillips) have yet seen with the
name "Pennington". The "William Quarles" handwriting looks like the other
"Wm Quarles" signatures shown in the other images, and if it is, this would be
confirmation of the middle name "Pennington".
(This document is from Virginia State Archives Court Records.
I failed to note the detailed source and when I find it again, I will
annotate this image with the source info.)