Is he a son of Thomas FOSTER BARHAM d Penzance 1844 (or 43)? See561 Eustace is “3rd son of Thomas Foster (1812)” = Thomas matric 1812 Cambridge? This would fit the Thomas b 1794 (see below).
“M.D” if he’s father of Ellen (q.v.), but Eustace’s father was a solicitor, wasn’t he?
Are these publications his?:  
“Barham, Thomas Foster, 1794-1869
Philadelphia: or, The claims of humanity. A plea
for social and religious reform. By Thomas Foster
Barham . . . -- London : Chapman and Hall 1858 viii, 448 p”
GUIDE TO THE MICROFILM COLLECTION
Economic Literature, 1851-1900
Publications from The Seligman
Collection at Columbia University
From the holdings of the Rare Book and
Manuscript Library of Columbia
  
“British and Commonwealth Literary Studies
British Poetry of the Romantic Period Catalog
BARHAM (Thomas Foster) and MONTGOMERY (James) Abdallah; or the Arabian
Martyr; a Christian drama, in three ats: with a poem on the same subject, by
James Montgomery Esq. Second edition, revised and enlarged. By Thomas Foster
Barham, Formerly of St. John's College, Cambridge. Printed for the author and
sold by Hatchard, Piccadilly; Seeley, Fleet Street; Holdsworth, St. Paul's; Westley,
Stationers' Court; Deighton, Cambridge; Binns, Bath; Bulgin, Bristol; Upham,
Exeter; & Vigurs, Penzance. 1821 [Printer: Vigurs, Printer, Penzance]
Quarto. First edition. Bound in paper boards. Spine blocked in gilt. 45 pp. 1/2-
title.
NCBEL III,392: Montgomery's entry where it is listed as Abdallah and
Labat. 1821. Montgomery's poem is actually titled: Abdallah and Sabat.
Jackson, Annals, p. 467. Jackson cites it as: Abdallah and Labat. Johnson 49.
The Johnson copy.
BARHAM (Thomas Foster) Elijah; a sacred poem; in four cantos. By Thomas Foster
Barham, Formerly of St. John's College, Cambridge. Printed for the author, and
sold by Hatchard and Son, Piccadilly; Seeley, Fleet Street; Westley, Stationers'
Court; Holdsworth, St. Paul's; Deighton, Cambridge; Binns, Bath; Bulgin, Bristol;
Upham, Exeter; Congdon and Earle, Plymouth Dock; and Vigurs, Penzance. 1822
[Printer: Vigurs, Printer, Penzance]
Octavo in 4s. First edition. Rebound in light blue paper wrappers, uncut. 38 pp.
1/2-title.
Jackson, Annals, p. 480. Johnson 50. The Johnson copy.”562

Correspondence in Harvard College Library:
bMS Eng 265.1 Southey, Robert, 1774-1843. 30 letters to various correspondents, 1793-1835. 1 box.
Acquired from various sources at various times.
* (1) ALs to Thomas Foster Barham; Keswick, 1818 June 16. 1s.(2p.) in 1 folder.563
Death reg Newton Abbot Vol 5b p 106 Barham, Thomas Foster, [aged] 7576