Sarah Miles's half-brother Frederick William Miles (son of Elijah Miles by his second wife, Elizabeth Ann Harding) was the second husband of Elizabeth Delahoy and, hence, the step-father of Frederick Billing Miles who married Sally's granddaughter Ella Victoria Smith.
William Howe Smith was born in Oyster Bay during the Revolution while his father was a surgeon of a Loyalist troop. William Howe Smith was also a physician. 
1777 "June 8—William Howe, son of Nathan and Elisabeth Smith, baptised at Oyster Bay." The baptism is listed in the registry of baptisms of St. George's Episcopal Church in Hempstead, Long Island, NY. 
1822 William Howe Smith died on October 9 in Saint John, The City Gazette reported on October 10, "d. Yesterday morn., William Howe Smith, Esq., Surgeon, age 46, left wife, five children." 
An article in the Saint John Daily Telgraph, October 27, 1874, described the Old Burying ground ,
The Old Burying Ground No. 4 - ... Near this last is a well preserved slab - 'To the memory of William Howe Smith, Esquire, for many years a surgeon in this city, who departed this life Oct. 9th, 1822 in the 46th year of his age.' - The gentleman was the father of the late Wm O. Smith, Esq., formerly Mayor of Saint John and the grandfather of the present Mayor Smith. His residence was in Prince William street where the Bank of British North America now stands. His father was Nathan Smith, a physician of Rhode Island, who became surgeon of one of the Loyalist regiments and settled at St. John after the Peace of 1783. He died here in 1818, aged 81 years.
1822 "Smith, William Howe. City of St. John, St. John Co, Surgeon. Will dated 6 October 1822, proved 30 October 1822. Wife Sally all household furniture. Balance of estate to be equally divided among my children, Elijah Miles, William Odber, Fanny Cornwell, Edward Allison, and George Rufus. 'And as my wife is now pregnant, I wish the child she may be delivered of, should it survive, to share equally with my other Children.' Wife Sally Smith, friend Treadway T.O. Miles, and son Elijah Miles Smith executors. Witnesses: John Boyd, M.D., Henry Gilbert, and George Ball. Codicil dated 6 October 1822 empowers executors to sell real and personal property and divide the proceeds among the children at the end of ten years. Same Witnesses." 
A biographical sketch of Dr. William Howe Smith states, 
This physician was a son of Dr. Nathan Smith, by his first wife; the mother of Nathan Smith DeMill, the Apostle of Temperance in New Brunswick, was a daughter. William Howe Smith was brought up to the Apothecary business, preparing prescriptions for the patients of his father, and selling Friar’s Balsam, Court Plaster, Daffey’s Elixer, etc., to the residents of Lower Cove. In due time he graduated as a physician, and after the death of his father removed the Drug Store to the Market Square. His wife was a daughter of Col. Miles, of Sunbury, and did not long survive his father as he died in 1822, at the age of 45 years, leaving a widow, four sons and two daughters.
The residence of Dr. Smith at this time was in Prince William street, on the upper lot now occupied by W. H. Thorne & Co. It was a two story wooden building, and was destroyed in the first great fire in St. John, April 9, 1824, which burned 35 buildings, and extended to the water’s edge. The fire originated in a tobacco factory on Merritt’s wharf, the total loss was over $100,000.
At the time of Dr. Smith’s death, although his eldest son William O. Smith, was a lad of only eighteen, he successfully continued the business to his death in 1871, at the age of 67 years. Today the business of A. Chipman Smith & Co. is the oldest established business in New Brunswick, being in its second century. To the pestle and the mortar, this unique honor belongs.
1862 Sarah (Miles) Smith died on January 22 in Saint John. Saint John newspapers reported on January 24, "d. Wednesday, Sarah Smith widow of W.H. Smith, age 80. Funeral Saturday 2 o'clock from residence of her son, W.O. Smith, Esq., Germain St. (St. John)."  and "d. Wednesday, Sarah Smith widow of late W.H. Smith, age 80." 
 Family Document, Evelyn Miles Krase notes.
 John Sylvanus Haight, Adventures for God: A History of St. George's Episcopal Church, Hempstead, Long Island (Birmingham, NY: Vail-Ballou Press, 1932), 260, [HathiTrust].
 Daniel F. Johnson, New Brunswick Vital Statistics from Newspapers, Volume 2 Number 1441, October 10, 1822, City Gazette, Saint John, [New_Brunswick_Archives].
 Daniel F. Johnson, New Brunswick Vital Statistics from Newspapers, Volume 36, Number 268, October 27, 1874, The Daily Telegraph, Saint John, [New_Brunswick_Archives].
 R. Wallace Hale, Early New Brunswick Probate Records, 1785-1835 (Westminster, Maryland: Heritage Books, 2007), 421, [Google].
 W. 0. Raymond, "Old Townships on the River St. Joseph W. Lawrence, "The Medical Men of St. John, in its first half Century," Collections of the New Brunswick Historical Society Vol. 1, nos. 1-3 (1894-1897), 273-305 at 287-288, [HathiTrust].
 Daniel F. Johnson, New Brunswick Vital Statistics from Newspapers, Volume 19, Number 2008, January 24, 1862, Morning News, Saint John, [New_Brunswick_Archives].
 Daniel F. Johnson, New Brunswick Vital Statistics from Newspapers, Volume 19, Number 1314, January 24, 1862, Religious Intelligencer, Saint John, [New_Brunswick_Archives].