Photo credit: Lambeth Palace
The sitter, Charles Thomas Longley (1794–1868), was Bishop of Ripon, Bishop of Durham and Archbishop of York, before becoming Archbishop of Canterbury (1862–1868).
Other sculptures by Edward Davis on Art UK include ‘Sir Francis Rowlands (1788–1873)’, 1871, Kelmscott House and ‘Richard Quain (1816–1898)’, 1870, Senate House, University of London.
There are also several oil portraits of Longley in public collections.
Edward Davis was a student at the Royal Academy in 1833 and trained in the workshop of Edward Hodges Baily. Could Davis possibly have executed this work under Baily’s tutelage?
The National Portrait Gallery has a bust of him at Lambeth Palace by Davis which was exhibited at the Royal Academy in 1844. https://www.npg.org.uk/collections/search/personExtended/mp02792/charles-thomas-longley?tab=iconography
The entry is listed as The Lord Bishop of Ripon by E Davis catalogue number 1355.
Kieran's link shows that the bust was of Charles Thomas Longley in brackets after Lord Bishop of Ripon.
The Leeds Intelligencer, of Saturday 23rd November 1850, in a report on a "Conversazione at the Leeds Government School of Design" mentions that "Mr. Teale very kindly contributed Davis's bust of the Bishop of Ripon."
This Mr. Teale could be Thomas Pridgin Teale (1800 - 1867), MRCS 1823, FLS, the "capable surgeon of the Leeds General Infirmary who had diagnosed Anne Bronte's illness as pulmonary tuberculosis in January 1849". Both Longley and Teale feature in various connections to the Bronte family.
Edward Davis, from his address at 17, Russell Place, Fitzroy Square, contributed the work to the 1844 exhibition of the Royal Academy, under the title of "Marble Bust of the Lord Bishop of Ripon" and as catalogue number 1355.
Charles Thomas Longley (1794 – 1868) was headmaster of Harrow from 1829 to 1836; Bishop of Ripon from 1836 to 1856; Bishop of Durham from 1856 to 1860; Archbishop of York from 1860 to 1862, and Archbishop of Canterbury from 1862 to 1868 (the year of his death).
Finally, the bust was identified as being by Edward Davis and was dated to 1844 on page 136 of the "Dictionary of British Portraiture: ....Later Georgians and early Victorians, historical figures born between 1700 and 1800" by Richard Ormond, Malcolm Rogers and Adriana Davies (Oxford University Press, 1980).
Thus, assuming that it is the same work as identified above, this Discussion's bust can be dated to 1844, and the artist identified as Edward Davis (1813 - 1878).
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The given date of 1836 in the entry is presumably based on what is inscribed on the bust, although we cannot see it in the available images. The collection should confirm or clarify that date.