All I have, I have obtained from Alexander Sproul's wife's Revolutionary war pension application (filed in Cumberland County, later Clinton County, KY). According to this, the only thing I know for sure is that Alexander's father was William Sproul of Augusta County, VA, and that Alexander married Jane Beard, daughter of William Beard who lived a mile or so away from William Sproul.
Other information I have come across...
AUGUSTA COUNTY, VIRGINIA - CHALKLEY'S CHRONICLES; Vol 3, PP 240 - 249
26th February, 1817. Charles Sproul's will—
To brother, John; sister, Jean Weir; sister, Mary Sproul; to brother, Joseph; brother, Oliver; sister, Martha Hutcheson; to sister, Fanny Thomson; sister Sidney Beard's children, viz: Polly, William, Susannah, Jeanatte, and John; to half-brother, James Sproul; to children of half-brother, Alexander Sproul; to half-sister, Margaret McCutchen; to Alexander Beard; to Wm. Beard; to Thomas Beard; to half-brother, William Sproul. Executors, brother John Sproul, Thos. Thomson. Teste: Joseph Beard, Hugh Dougherty, Ro. Hutchison. Proved, 28th April, 1817. Executors qualify.
26th June, 1813. William Beard's will—
To all children; to grandson, Thomas Beard; to grandson, Thomas Beard; to son Samuel Beard's son William. Executors, Joseph Beard, Wm. Sproul. Teste: James Hay, John McKee, Samuel H. McNutt. Proved, 26th May, 1817. Executors qualify.
AUGUSTA COUNTY, VIRGINIA - CHALKLEY'S CHRONICLES OF THE SCOTCH IRISH IN VIRGINIA
DISTRICT COURT RECORDS. JUDGMENTS.
APRIL, 1793 (A to Q). We, the undernamed jurors for the Commonwealth of Virginia, present that Alex. Sproul did, on the 18th day of January last, in the County aforesaid, unlawfully make a forcible entry into the house and possession of George Almarode, with arms, of which he was then possessed, and does continue to keep out the said Almarode, to his hurt and damage. In witness whereof the undernamed jurors have hereunto set their hands and seals this 13th day of February, 1792. (Signed) Francis Hull, John Summers, Robt. Morris, Robert Cooper, Samuel McCutchan, Andrew Donaldson, Thomas Boyd, John McCoskry, David Humphreys, James Cunningham, George Everts, Jacob Wehrly, John Cunningham, Robert Hanna, John McCutchan, Henry Venus, Ro. Tate, Hugh Dougherty, Henry Minger, William McCutchan, John Foulwidder, John Logan, Mexard Berryhill, James Henry.
(I'm sure there is more to the story...)
1810 Federal Census, Cumberland County, Kentucky
Page 170, Line # 21
(1) male 0-9, (2) male 10to15, (3) male 16-25, (1) male 26-44, (1)male 45+, (0) female 0-9, (1) female 10 to15, (0) female 16-25, (1) female 26-44, (0) female 45+, (1) Slaves
MAY, 1789.--JANUARY CAUSES James Sproul vs. William and Mary Hunter.--22d November, 1787. Dr. John Jackson lives in Pennsylvania.
FEBRUARY, 1763 (A?).
Mr. Sproule: Be pleased to let William Elet have as much linen cloth as will make him a shurte, and in so doing you will oblige your friend and humble servant. (Signed) James Dunlap. April 5, 1757. To Mr. William Sproule.
AUGUST, 1762 (B) Sproul vs. Bratton.--Sundry accounts which Dunlop assumed to Sproul to be used in the suit of Sproul against Ro. Bratton's Administrator, viz: Capt. James Dunlap, debtor, for the undernamed persons, viz: Thomas Vance, Halbert McClure, James McElhaney, John Low, Edward Howard, James Milliken, Thomas Smith, William Elliott, Alex. Sutherland, James Hamilton, John Gay and Capt. Dunlap.
Rockbridge County, VA Deed Book B, p. 340. 11 October 1791 270 Acres Robert Harvey and Marthew his wife, heirs-at-law to Benjamn Borden Dec'd of Botetourt County, VA to Charles Campbell. 270 Acres between said Campbell's plantation and John McCray's land, Robert Wardlaw's line. Signed: Robt. Harvey Martha Harvey Teste: William Buchanan William Wardlaw Wm. Wardlaw Alexr. Sproul
1820 Federal Census, Cumberland County, Kentucky
Page 153, Line 22
(0)Males 0-10, (1)Males 10-16, (0) Males 16-18, (0) Males 16-26, (1) Males 26-45, (0) Males 45+, (0) Females 0-10, (0) Females 10-16, (0) Females 16-26, (0) Females 26-45, (1) Females 45+
Also, in Cumberland Co, Ky, there is Alexander Sproul sold to George Swope and William Sproul. 1806, Deeds.
Also Alexander sold to William and Alexander Sproul.
All this info is disjointed, but perhaps helpful.