This appears to be the family in 1871
https://familysearch.org/ark:/61903/1:1:KD8S-J9Z
& 1861 https://familysearch.org/ark:/61903/1:1:Q2MP-H5PM
William Moore married Elizabeth May nee Shipman on 22 May 1856 at Strood, Kent https://familysearch.org/ark:/61903/1:1:NLHT-WMS
You can view the marriage register entry via cityark.medway.gov.uk, the direct link to the image is here.
Elizabeth Shipman was previously married to James May in 1843. Entry on FreeBMD.
On the marriage certificate of William & Elizabeth, William was aged 65, a widower & his father was listed as Robert Moore.
This appears to be William in 1851 https://familysearch.org/ark:/61903/1:1:SGLW-BS9
& his baptism entry https://familysearch.org/ark:/61903/1:1:JWF5-VJM
According to the GRO Birth Index Arthur Moore was born in the Jun Qtr 1862 in Medway District Vol. 2a Page 335; mother's maiden surname: Shipman