to some copies of The Naval Chronicle at Google Books(they have copies for 1800,1807.1808 and 1809)

And do note JA's friend, The Reverend Stainer Clarke's association with it ;-)

According to his biography by Chris Viveash:

A rapport sprang up immediately between John McArthur and James Stainer Clarke at that fateful meeting of the three men(with John Hunter-JW) which took place at McArthur's house at York Place off Portman Square. They all deplored the fact that so much of the history of the navy would be lost unless something was done to record the life and details of the men and the ships in service at that hisptic time(1798-JW).

Out of this fireside chat was born Clarke and McArthue's Naval Chronicle a twice yearly publication which first appeared in print the following year
page 31.