In the "National Genealogical Society Quarterly" volume 30 pages 52-53 (March 1942) was published under the chapter title "Abstracts of Revolutionary War Pension Applications" the applications for Dr. James R. Alexander and later for his widow, Dorcas Alexander.
Their Bible record was recorded when Dorcas applied as a widow. The first child listed was Silas Alexander born 10 May 1791.
The other children listed were:
Amanda Alexander b. 6 Feb 1793 Charles Garrison (Grandison?) Alexander b. 27 Aug 1794 Mary Sample Alexander b. 10 Apr 1796 Mark Alexander b. 29 Dec 1797 Abigail Alexander b. 8 Nov 1799 Hannah Alexander b. 19 Aug 1801 James Rankin Alexander b. 5 Jul 1803 John G. Alexander b. 2 Mar 1806 Dorcas R. [Reese] Alexander b. 28 Dec 1807
If this is your Silas, you might want to find that article. There is a lot of good genealogical information in the piece - but too much for me to copy here. (NGSQ is in almost all genealogy libraries) and/or write for the full application from NARA. If I am reading this correctly, the application # is W2,901 and certificate #26,953. The widow's certificate was #4,654).