If you’ve been following this blog, you’ve probably guessed that I’m a great admirer of Edmond Halley and expect that I side with him in his difficulties with his lieutenant – yet when I first read about Edward Harrison and his book, I did have some sympathy and respect for the lieutenant.
Harrison was evidently a man of some, though limited, education. He described himself as “sea-bred”, indicating he’d been at sea from an early age, and these facts suggested someone of modest background and resources and so it seemed to me rather impressive that such a man had written a book, got it printed, distributed it to the Royal Society and the Admiralty – and I could feel some sympathy for his dismay when Halley then dismissed his enterprising efforts.
But then I read the book and that sympathy was gone in an instant. The book, Idea Longitudinis, was published by Harrison in 1696; he’d submitted a paper of his ideas to the Royal Society about 2 years earlier but received no encouragement and so determined to “appear on the Publick Stage”. 
The book includes a dedication to the Lords of the Admiralty, a preface, and 8 chapters including a conclusion, the whole about 97 pages long. The first 3 chapters cover: where to set a first meridian, a definition of longitude, a definition of time (solar, sidereal year), and chapters 4-7 consider the different methods of finding longitude: horological, magnetic variation, lunar, and Jovian.
I don’t have the expertise to comment on his ideas – though to be honest, I couldn’t really see that he proposed any. The book seems to me little more than a restatement of the problem of finding longitude at sea and a consideration of the pros and cons of the already-proposed methods, settling on the lunar method as the most useful at sea.
The book appears not without merit as a handbook for his “Brother Tar”; the chapters seem well-chosen and some of his remarks about the problems one would encounter (refraction, parallax, impossibility of using a long telescope (for the Jovian method) on a rolling ship) seem useful – but this was all commonplace to the fellows of the Royal Society and I would guess that that was the opinion Halley gave to their Lordships.
What Halley actually said about the book doesn’t seem to be extant, but a slightly later review of another paper of Harrison’s possibly gives us some indication. While Halley was away on his second voyage, Harrison submitted another paper to the Royal Society on tides and winds, and this was reviewed by Richard Waller, who ends his 2-page review with “between you and me [he’s writing to Hans Sloane] I see nothing in the Paper but what is better explained in the places I have above quoted”. 
Perhaps Halley gave a similar assessment, that it contained nothing new – an opinion reinforced, I should think, when he read the opening lines of Harrison’s chapter on magnetic variation (see image), copied almost verbatim from Halley’s 1683 paper on the same subject (there’s at least one other section copied directly from Halley’s paper).
Alan Cook describes Harrison’s book as “[s]cientifically and technically … poor, second-hand, and ill-digested. It is shot through with aspersions on mathematicians, the manner is aggressive, and it shows a deep inferiority complex”, and possibly the most interesting aspect of the book is what it reveals about Harrison’s personality, giving us some idea of what Halley had to deal with on board his ship. 
To me, Harrison comes across as chippy and having an inflated view of himself. He twice compares himself to Columbus, as being someone who “shewed the way”, and warns us that some “ordinary Mathematicians may hate to be out-done by a Tarpolin, if they have ought to say against him, its because his Practice and Experience may prove him to be a more Competent Artist in Navigation then [sic] themselves”. 
Hindsight makes the opening lines of the dedication wonderfully ironic: “It is a saying in the Navy, He that knows not how to obey Command, is not worthy to bear Command”. While this sentence seems rather revealing, given he’d lifted some passages straight from Halley and then gone on to despise him for dismissing his book: “If any Envious Person pretend I have borrowed most of my Book, may he be obliged to Quote the Authors, where I have not”. 
The passages I found most revealing of his personality were also the most unexpected:
“…if I know more than others, it is by Divine Authority, by Industry and Experience, by an Inborn Idea, and Instinct in Nature; it was ordained for me by God Almighty, from my Mother’s Womb.” 
And, when considering the location of a first meridian:
“I could Bafle and Impose on the World as our Predecessors have, false Arguments for other places, from whence they might account their first Meridian. God forbid I should be so wicked, Honour and Glory, and beginning of Good, belongs to God; a first Meridian may be represented, and if the Heads of our Church and State, think it good, let there be made a Figure, representing a first Meridian, and Erected over St. Pauls Church in London, with this Inscription, Glory be to God, good Will towards Men…” 
Blimey. These passages took me completely by surprise – it never occurred to me that Harrison would be religious – they changed my view of Harrison’s character and of how he would have interacted with Halley. Halley had a reputation for being irreligious, and while he evidently believed in God, he doesn’t seem to have been too interested in religion (except when trying to clear himself of the accusation, after failing to get a professorship on grounds of alleged irreligion). I think Halley must have had a very difficult time dealing with Lieutenant Harrison, and yet, as he tells us, he “endeavoured all I could to oblige him”. 
So, in summary, my feeling is that Halley gave an honest and justifiable account of Harrison’s book, but that Harrison was the type of personality unable to accept any criticism and so nursed a hatred towards Halley (whom possibly he may previously have admired, given his imitation of his works) and seized the opportunity to make his life a misery when chance put them together on board the same ship.
I think Harrison was very fortunate in the court’s verdict.
 Edward Harrison, Idea Longitudinis (London, 1696), preface
 Richard Waller to Hans Sloane, dated 4 Dec 1699, Royal Society, EL/W3/68
 Alan Cook, Edmond Halley: Charting the Heavens and the Seas (Oxford, 1998) p 264
 Harrison, preface
 Harrison, preface
 Harrison, preface
 Harrison, pp 3-4
 Captains’ Letter Book, National Archives, ADM 1/1871