This image is of HMS Galatea (fore) and HMS Challenger.
HMS Galatea was a 26 gun Jason-class wooden steam screw frigate launched in 1859. She served in the Channel Squadron, Baltic, Mediterranean, North America and West Indies. In 1866 she went on a world cruise, under the command of Prince Alfred, Duke of Edinburgh and in 1882 took the Duke of Edinburgh to the official opening of the new Eddystone Light. She was broken up in 1883.
HMS Challenger was a Pearl-class corvette launched in 1858. She served in North America and West Indies before becoming the flagship of the Australia Station between 1866 and 1870. She then undertook the first global marine research expedition (the Challenger expedition), a 68,890 nautical mile (127,580 km) voyage between 1873 and 1876, organised by the Royal Society, which led to the US Space Shuttle Challenger being named after her. She then became a HM Coastguard and Royal Naval Reserve training ship at Harwich in 1876, and from 1878 to 1883 was in reserve after which she was converted into a receiving hulk in the River Medway. She was sold and broken up in 1921.