Elvet Gaol records could be in the archives at Durham County Hall or in durham University Archives in Old Elvet which is near the Gaol. A search on line may help, try the a2a (access to archives) which allows keyword search on documents held at various archives, you may find a summary of the document.
Hope this helps John Rowley
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DUNN - Cambuslang, LKS FORSYTH - Shotts, LKS FRAME - Hamilton, LKS HODGSON - Hamsterley, DUR HUMPHREY - Easingwold, NRY HUNT - Frimley, Surrey MCKECHNIE - Argyll - Shotts NETHERCLIFF(T)/ DRAYCOTT Sandhurst, BKS PEPPERCORN - Lolworth, Cambs PRATT - Thirsk, NYK REDSHAW - Hamsterley, DUR REYNOLDS - Fritton,Stratton,NFK ROWLEY - STS to DUR TALLACK - St Agnes Padstow,CON WALMSLEY - NRY,Brum WILSON - Hamsterley, Co Durham Census Information is Crown Copyright, from www.nationalarchives.gov.uk