Check the date of manufacture on your gun. That may help? We have yet to gather up Parker screws to research what Parker my have used and when the used it but the following information will give you an idea of what was going on back "in the day".
The issue of screw threads has been discussed between a few of us but not here on the forum, just to many questions unanswered. But, one must realize that the thread has not always been what it is today, they evolved about the same time as Parker.
1800 - The standardization of screw threads began with Henry Maudslay.
1841 - Joseph Whitworth created a design that, through its adoption by many British railroad companies, became a national standard for the United Kingdom called British Standard Whitworth.
1864 - William Sellers presented a paper to the Franklin Institute in Philadelphia, proposing a new standard to replace the U.S.'s poorly standardized screw thread practice
1860 – 1880 - The Sellers thread, easier for ordinary machinists to produce, became an important standard in the U.S. during the late 1860s and early 1870s, when it was chosen as a standard for work done under U.S. government contracts.Over the next 30 years the standard was further defined and extended and evolved into a set of standards including National Coarse (NC), National Fine (NF), and National Pipe Taper (NPT).
1869 – 1874 – Parker back action lifter
1869 – 1875 – Parker front action lifter
1878 – 1881 – Parker front action lifter with latching forend1881 – 1917 – Parker top action with & without dolls head extension
1898 - They were mostly unified in 1898 by the International Congress for the standardization of screw threads at Zurich, which defined the new international metric thread standards as having the same profile as the Sellers thread, but with metric sizes.
1908 - British Standard Fine (BSF) thread was introduced in 1908 because the Whitworth thread was too coarse for some applications
1914 – 1918 - A tremendous amount of engineering work was done throughout World War I and the following interwar period in pursuit of reliable interchangeability.
1888 – 1934 – Parker hammerless
1900 – 1999 - Efforts were made in the early 20th century to convince the governments of the U.S., UK, and Canada to adopt these international thread standards and the metric system in general, but they were defeated with arguments that the capital cost of the necessary retooling