Sounds like you probably have an M 1839 (or M 1809) Prussian musket. According to John Spangler (Antique and Collectable Firearms and Militaria Headquarters), the city of Philadelphia used that marking on a number of different model guns procured for use by the city's militia during the Civil War. You may be able to find some info on numbers acquired by Philadelphia in either that city's records or the Pennsylvania Archives.
Grenville Dodge, first commander of the 4th Iowa (U.S.), wrote that his regiment was originally equipped with an old Prussian musket in 1861 (likely an M 1809 or M 1839) that shot round lead ball about the size of a quarter. They were considered third-rate weapons but proved deadly in the short range combat at the Battle of Pea Ridge in Clemons Field on March 7, 1862.
Doubtless some other regiments began the war with them as well. Would have to thumb through Todd's AME and look for references to Prussian muskets to determine this in more detail.
There is a Prussian M 1839 musket for sale at the following website that is apparently similar to yours. You may want to look at it for comparison purposes.
Chris Hubbard wrote quite a bit on the M 1839 arm and its older cousin, the M 1809, on a post on the Authentic Campaigner web site some time ago. Below is some of what Hubbard said:
FW is reportedly for Fredrick Wilhelm, King of Prussia, with the royal crown over it.
These arms were produced at several armories through the German states including Saarn, Niesse, Potsdam and others. And copied by the Belgians (suprise, suprise) Prussian arms generally have a light colored Beech wood stock.
Sometimes they are marked with importer or owner marks from United States entities, most notably the City of Philadelphia, and the state of OHIO.
All 1809's were originally manufactured as Fint lock arms. Almost all of the 1809's I have seen were converted to percussion ignition by the addition of a forged cone seat with a large and ugly cleanout screw in it. Sometimes the screw can be removed, but I would advise against it.
You encounter these with both iron and brass butt-plates. The Buttplates were brass for troops generally stationed in the countryside, or who were line infantry, and were iron for those who were generally intended to guard the cities. (cobblestone streets + sentry duty = beaten up brass plate)
They are usually maked near or on the buttplate or butt stock with a regimental number, and with either line infantry markings (LWR: Landwehr Regiment) or Jaeger Regiment (JR) markings, sometimes with militia markings (all Prussian of course).
Often these are encountered with the rear sight, a small and nearly useless block of iron on the barell tang, removed. If you can find a cone for them (replacement, I mean) you will likely pay a fortune for it (25 bucks would be a deal, for one nipple) The thread is unlike anything of domestic manufacture, and it unique in its shape.
Lock parts too are a pain to find, and sometimes it is more realistic to have a competent machinist make them for you.
Occasionally, and this is where the real fun starts, you find an 1809 Prussian that was manufactured as a flint lock arm, then converted to percussion, and dated, and then converted to a rifled-musket, with a long range rear sight added to the barrel (brazed mostly) and then dated with that conversion date. Sometimes those guns were later "reconverted" to their second original state by having their bores bored out (resulting in about a .75 calibre barell that is very thin), and the long rear sight removed. The outline of the rear sight will never be removed entirely though, so check it closely. Also, these arms generally have a longer front sight added to the barrell, (not the front band where the sight is normally) between the straps of the front band.
The 1809 type arms also had a shorter cousin, designed for Marine use, but this arm is fairly rare. You could have one of these, but like I said, they are rare.
The 1839 Prussian is very similar to its older cousin, but has a few distinctive differences. The bands are identical, but the stocks are different. The 1809 has a relieved (dish) cheek, while the 1839 has a raised cheek. The 1839 is also shorter than the 1809, noticably so, perhaps 6 inches. Sights and calibres are the same for both. All 1839's were originally manufactured as percussion arms. On a comparative scale, you will likely encounter 1809 and 1839 in a 20 to 1 ratio in favor of the 1809.
Hope this has helped.