The first major revision, really a complete overhaul, was released in 1882, edited by P. H. Cooper. Large sections have been completely excised and the book is now much shorter. Bowditch’s old chapter on lunars has been mostly dropped and the only method for clearing lunars is Chauvenet’s. Lunars were almost never used at sea in this period. Chauvenet as a paperback costs $ 15.99 dollar and as a hardcover $ 27.99, free shipment. Or see here for a simplified method with precomputed lunar distances.
Another method is to go this website with Bowditch editions. For instance click on Bowditch 11th Ed. 1839 and scroll down to the contents and you will find in the column on the right side several items about lunars. The only problem is that it is somewhat hard to read…
Going through a number of editions I found quite some changes on the subject.