William was born on November 20th, 1849 in Ashton-under-Lyne and his baptism took place there on April 10th, 1853.12
Birth Notes
Aged 1 on 1851 census Aged 11 on 1861 census
BOOTHROYD, WILLIAM HENRY STOCKS GRO Reference: 1849 D Quarter in ASHTONUNDERLYNE Volume 20 Page 58
Name William Henry Boothroyd Gender Male Birth Date 20 Nov 1849 Baptism Date 10 Apr 1853 Baptism Place Ashton-under-Lyne, Lancashire, England Father William Boothroyd Mother Mary FHL Film Number 1538435 Reference ID item 5 p 136
Acording to a letter to uncle Joseph Stocks, William had a son, Walter Boothroyd and a baby Mary in 1875 and was living at Ashton-Under-Lyne. However, on another transcription of the letter it appears it was James and Alice who had the son Walter and baby Mary in Jun 1875. This is more consistant with census records.
There is no trace of William and Mary and their family William, George and Sarah E after 1861. Perhaps they emigrated to the USA with the other members of the family.