Let's start with what C.S. means; it stands for Continuous Service. This had been introduced in the 1850s, and stood in opposition to how the Royal Navy worked in the Napoleonic Wars. Before Continuous Service was introduced, men were tied more to a ship than to the Navy as a whole; when a ship's service was complete, the crew would be paid off, and in essence, leave the Navy. After it, seamen would join the Navy at 15 or 16. Once they reached 18, they would sign 12-year contracts. However, they could leave their contracts early by buying out their remaining time. Your great-grandfather took advantage of this option, hence the 'cancelled by purchase' marking. Your grandfather joined as a sixteen-year-old, and served as a boy until the age of 18, when he became an ordinary seaman. This explains why there are no sub-ratings after the first few lines - these were typically only used for boys, rather than for seamen.

Your great-grandfather was mostly employed on the old hulks the RN used as shore bases. Boscawen was previously HMS Trafalgar, a 120 gun first rate built in 1841, but was now a training ship at Portland. Here, he received his basic training, as a Boy 2nd Class, being promoted to Boy 1st Class after about a year. Minotaur and Agincourt had been built as ironclad frigates in the 1860s, but by the time of your great-grandfather's employment had joined Boscawen at the Portland training establishment. Here, he would have received additional training, before joining the fleet. His first actual sea service would have come aboard HMS Cossack, a third-class cruiser which served on the East Indies station. On returning to the UK, he was discharged to HMS Duke of Wellington, a first-rate built in 1852, and serving as a barracks ship in Portsmouth harbour. From here, he went to Firequeen II, a local tender for the naval base at Portsmouth. After a brief service aboard her, he spent a few months aboard Apollo, a protected cruiser in the Reserve Fleet. From here, he went back to Firequeen, before heading to HMS Bellona, another cruiser in the Reserve Fleet. After Bellona, he went to Vernon. Vernon was the main school for the Navy's torpedo branch, teaching about the use and maintenance of torpedoes, as well as electrical systems and radio systems. He then went to Victory, now a museum ship, but then serving as a barracks ship in Portsmouth. From here, he was assigned to HMS Powerful; Powerful was a protected cruiser on the Australian station, so it's not clear if he actually served aboard her, given that he as only assigned to the ship for two weeks, not long enough to travel to and from Australia. After a period aboard Victory, he was assigned to Dryad, a torpedo gunboat (an early precursor to the destroyer), which was acting as a tender to the navigation school. After this, he went back to Vernon and then to Victory, before buying out his contract. This was not the most exciting naval career, but was typical for the RN in peacetime.