From A Genealogical Dictionary of The First Settlers of New England, Before 1692, by James Savage, vol. #1, pgs. 144-155:
"BEAMSLEY, WILLIAM, Boston 1632, freem. 25 May 1636, ar. co. 1656, by w. Ann had Ann, b. 13 Feb. 1633; Grace, 10, bapt. 20 Sept. 1635; Mercy, 9, bapt. 10 Dec. 1637; Samuel, and Habakuk, tw. 24 Jan. bapt. 7 Feb. 1641, both d. Apr. foll. Hannah, bapt. 17 Dec. 1643, "a. 4 days old;" beside Elizabeth and Mary, both, perhaps, b. bef. com. from Eng. and [vol. 1, p. 148] by w. Martha, wh. had been, I presume, wid. Bushnell, had Abigail, b. 8 Feb. 1646, wh. prob. d. young. In his will, made 14 Sept. pro. 28 Oct. 1658, provis. is made for wid. and for Ann, w. of Ezekiel Woodward; Grace, w. of Samuel Graves of Ipswich; Mercy, wh. m. 17 Oct. 1656, Michael Wilborne, and next Andrew Peters, of lpswich; Hannah, w. of Bushnell, wh. after m. 16 Oct. 1661, Abraham Perkins; Elizabeth w. of Edward Page; Mary w. of Robison, wh. after m. Thomas Dennis; and for Edward Bushnell, perhaps s. of his w. by her former h. The ch. made sale of the est. in Nov. 1668, when perhaps his wid. was dec."
William Beamsley's parents, place of birth and date of birth are unknown. He was probably born about 1607, based on the birth of his eldest child. It is possible that William's origins are in Lincoln, Lincolnshire, England, which is the only place the Beamsley name was found in England at that time.
Immigrated - 1632 - Boston
Robert Charles Anderson could not locate evidence for William Beamsley's place of origin in England or the ship on which he came to New England. William's first known record in America is the birth of his eldest child, Ann, born 11 Feb 1632/3 in Boston. Savage also puts his earliest date as 1632 in Boston. However, some presume that William and Anne Beamsley arrived together in America in 1630, aboard one of the eleven vessels of the Winthrop Fleet. The Winthrop fleet sailed from The Isle of Wight to Salem, Massachusetts, arriving in June and July of 1630 and carried 700 passengers. William Beamsley of Boston and his wife, Anne, are named on a compiled list of passengers of the fleet, but their names are not associated with a specific ship. Unfortunately, because William and Anne's names are not found on any specific ship's passenger manifest, their arrival in America in 1630 cannot be corroborated.
William Beamsley was described as a "laborer" when he was admitted to the Boston church in 1635. Labor was as scarce as land was plentiful in early New England, and they had to be paid a much higher rate than laborers in England. William Beamsley was also a yeoman and busy with improvements at his property, where he planted an orchard and gardens.
Married Ann by 1632
William married Ann ---- by 1632, whether they married in England or America is unknown. They had six children, all born in Boston. Ann died between Dec 1643 and early in 1645. They might have been married by 1630 in England, as they are listed as husband and wife on the list of passengers of the Winthrop fleet. William and Ann had the following children:
Anne, b.13 Feb 1632/3, m.Ezekiel Woodward by 1651;
Grace, b.10 Sep 1635, m.Samuel Graves by 1658;
Mercy, b.9 Dec 1637, m1.Michael Willborne 1656, m2.Andrew Peters 1659;
twin, Habakuk bap.7 Feb 1640/1, d.Apr 1641;
twin, Samuel, bap.7 Feb 1640/1, d.Apr 1641;
Hannah, b.Dec 1643, m.Abraham Perkins 1661.
First Church of Boston - 1635
William Beamsley, laborer, was admitted to First Church, Boston on 5 Apr 1635, or "1635 6th mo. 2d day" (2 Aug 1635).
Freeman - 25 May 1636
William Beamsley was admitted a Freeman on 25 May 1636, ninth in a group of twenty Boston men.
Land - 1636-1656
On 8 Jan 1636/37, he was granted sixteen acres at Muddy River, (based on order of 14 Dec 1635). In the Boston Book of Possessions, Beamsley held two lots: house and house lot, about half an acre; and sixteen acres at Muddy River.
On 6 July 1650, he purchased from William Phillips a lot in the Mill Field, and on 25 Jan 1655/56 he purchased an adjoining parcel from widow Mary Hawkins; on 25 Apr 1656 he sold the combined lot to Henry Shrimpton.
Married Martha (Hallor) Bushnell by 1645
William married second, by 1645, Martha (Hallor) Bushnell, widow of Edward Bushnell. Martha had three children surviving from her first marriage, who were all named in the will of William Beamsley. William and Martha had one child:
Abigail, b.8 Feb 1645/46, prob. d.bef.1658 as she was not named in her father's will.
Admitted to the Artillery Company 1656
William Beamsley held a number of Boston town offices and was also admitted as a member of the Artillery Company of Massachusetts in 1656/7, and attained the rank of Ensign. The Company was chartered by Gov. Winthrop 13 March 1638, and is the oldest chartered military organization in North America. By 1737, it became known as the "Ancient and Honorable Artillery Company".
Death - 1658
William died at Boston, Suffolk County, Massachusetts, on 29 September 1658, aged about 52-53.
Will and Probate - 1658
William Beamsley's will (#196) dated 14th September 1658 was recorded in the probate court at Pemberton Square, Boston, Massachusetts Bay Colony on 28 Oct 1658 and named the following:
"my 2nd wife full executrix and administratrix of all my houses, lands, orchards, goods and chattels whatsoever that she shall enjoy and possess the same unto her own proper use as long as she shall live provided she shall let Mercy have that chamber wherein she now lies for her own, and that there shall be with all conveniency made therein a chimney & she to enjoy it during her widowhood and I desire that my wife may take the charge and care of her and see that she wants neither meat, drink nor clothing during the time of her widowhood, and further my will is that after my wife's decease my whole estate shall be then prized and set to sale, the whole estate that is then left to be equally distributed amongst all my children, namely Anne Woodward, Grace Graves, Mercy Wilborne, Hannah Beamsley, Edward Bushnell, Elizabeth Page and Mary Robison..."
An inventory of William's estate was taken 15 Oct 1658 and totalled £251 14s. 1 d., of which £164 was real estate.
License to Distill & Retail 'Strong Waters' in 1663
Widow Martha Beamsley received approval from the court on 12 June 1663, in answer to her application for a license to distill and retail strong waters, and posted a bond "for the keeping of due order".  ['Ensign William Beamsley was an innkeeper and distiller' - no sources found.]
Property sold by Heirs in 1668
The heirs of William Beamsley sold his houselot in Boston on 16 Nov 1668, presumably after the death of his widow, Martha, who had been given that property for her lifetime in William's will.
↑ 2.02.12.22.32.4 Savage, James. "A Genealogical Dictionary of the First Settlers of New England, Showing Three Generations of Those who Came before May, 1962, on the Basis of Farmer's Register" Boston MA: Little Brown & Co., 1860. Accessed online at US GenNet. Vol. #1, pages 144-155.
↑ 3.03.13.23.33.43.5 Ferris, Mary Walton, “Dawes-Gates Ancestral Lines: A Memorial Volume Containing the American Ancestry of Rufus R. Dawes.” Accessed at HathiTrust, vol. 1, pg. 84-86.
↑ 4.04.14.2 Banks, Charles Edward. "The Winthrop Fleet of 1630." Genealogical Publishing Co., Inc. Accessed online at Ancestry.com. Page 59.
↑ 5.05.1 Peters, Eleanor Bradley. Peters of New England: A Genealogy and Family History. (Madison, WI, Knickerbocker Press, 1903) Access online at Archive.org. Pages 357-60: Quotes primary sources.
↑Abstracts from the Earliest Wills on Record in the County of Suffolk, Mass., The New England Historical & Genealogical Register. (New England Historic Genealogical Society, Boston, Mass., 1855). Accessed online at Google Books. Vol. 9, Page 37.
Ancestry Family Trees (Provo, Utah, USA: The Generations Network) Family Tree files submitted by Ancestry members. Ancestry Family Trees.
Public Member Trees, The Generations Network, Inc.; (Provo, Utah, USA; Date: 2006) Ancestral File Number: 2VJ5-GL Record for Hannah Beamsley. Ref. for Wm.'s Lincolnshire birthplace - not found.
Winthrop Society. Note: NS702593. Reference for Lincolnshire birthplace, DOD 29 Sep 1658. Source not found.
I cannot find a reference to William Beamsley at the Winthrop Society in the list of Freemen of Boston. It stops in March 1635/36 and he was sworn in May 1636.
Is there some other page (online or in print) where the society has referenced William Beamsley?
This source is given for evidence that William Beamsley was born in Lincoln, Lincolnshire, England, but Robert Charles Anderson in The Great Migration Begins says no parents or place of birth is known.
I would like to find a good source for the currently listed father, and place of birth, or else edit the text to remove the sentence and edit the profile to remove the father.