Cecil makes some errors on the answer here. He seemed upset over the 33 stars on the flag over Ft. Sumter, even though there were 34 states in 1861. However, Kansas came into the Union in January of 1861; the flag act of 1818 said the star wouldn’t be added until July 4 following admission, so the Ft. Sumter flag properly only had 33 stars. As far as the design of the flag, it wasn’t until an executive order was issued in 1912 that the proportions of the flag and arrangement of the stars was formalized. Before that, there were some very interesting arrangements.
He missed that the flag over Ft. McHenry had 15 stars (and 15 stripes, but that’s another story), even though there were 18 states by that time. And he wants to quibble over just why a state admitted in January wasn’t on the flag by April? The next flag after the 15 star flag of 1795 was the 20 star flag of 1818.