The generic term "spar" includes all the pole-shaped wood (or, in later periods, metal) components of a ship's rigging (broadly defined to include everything from the weather decks up). A yard is a spar; a mast is a spar; a boom is a spar; a gaff is a spar. A full set of "spar dimensions" includes the dimensions of all of them, and a "spar plan" shows all of them. (The more common "sail plan" also shows the sails.)
Several sets of spar dimensions for the Constitution at various points in her career are extant, and are reproduced in various sources - including the new Anatomy of the Ship volume. All of them are different. In 1803, for instance, the main lower mast was 105' 6" long and the fore lower mast was 96' 0"; in 1815 the main lower mast measured 104' 0" and the fore lower mast 94'0". By 1826 the official USN dimensions for those two masts in a 44-gun frigate were 105' and 95', respectively. Not enough difference to matter much for any practical purposes - but enough to change the "ratline count" by one.
Sure, you can work out the spacing of ratlines by counting the ones on a good drawing. The ones in the Anatomy of the Ship series generally are quite reliable. But, with the exceptions of those that are reproductions of old documents, they're reconstructions by modern draftsmen on the basis of the same sources that people like James Lees consulted. (In most of the volumes in the series that deal with British sailing warships, the Lees book will be found in the bibliographies.) Since what's actually being discussed, in practical terms, is the spacing of a set of lines on a piece of paper, doesn't it make more sense to use the dimensions in a book like that (or a contemporary one, like Steel's Elements of Mastmaking, Rigging and Seamanship) than to take the trouble of counting the ratlines on a drawing?
The question of ratlines that don't go all the way across the full gang of shrouds is an interesting one. Lees tries his best to deal with it systematically: he says that "about every sixth ratline was taken to the swifter or aftermost shroud on some ships. [He uses the term "swifter" to describe the aftermost shroud in the gang when the total number of shrouds is odd. Note the wise use of the word "about" and the phrase "on some ships."] On some ships between 1733 and 1773 the first six ratlines started from the second shroud from forward, the rest of the ratlines being rigged as before. After 1773 the first six ratlines and the upper six ratlines started from the second shroud from forward and finished at the second shroud from aft: the remainder covered all the shrouds." At that point, unfortunately, Mr. Lees drops the subject.
R.C. Anderson's The Rigging of Ships in the Days of the Spritsail Topmast, 1600-1720 (first published in 1927; lots of other sources have become available since then) has this to say: "In English ships the ratlines on the fore and main usually stopped short of the aftermost shroud; on the mizzen and the topmasts they ran across the whole rigging. Foreign ships do not seem ot have followed the English example in this respect; their ratlines are always shown running right across."
The photos of contemporary models in Mr. Lees's and Dr. Anderson's books conform to those descriptions. I'm not convinced, though, that the matter was quite as straightforward as those fine scholars imply. And neither of them mentions merchant vessels. Contemporary paintings a photos suggest that in nineteenth- and early-twentieth-century merchantmen it was common for every sixth ratline (or maybe every fifth, or every seventh) to stop short of the foremost shroud. Many years ago I had a conversation with the chief rigger at Mystic Seaport in which I asked him why the ratlines of the Charles W. Morgan were rigged that way. His answer was that the foremost shroud in the gang wasn't really a shroud; it was a "stiffener," and was slacked off when the ship was working to windward, in order to give the lower yard a little more room to swing. The ratline configuration was designed to discourage people from putting their weight on the "stiffener," while preventing it from sagging awkwardly when it was slacked off. I can't recall having bumped into that explanation elsewhere (neither can anybody else with whom I've discussed it), but it makes as much sense as any.
Whatever the arrangement, it generally seems to have been applicable only to the fore and main lower masts. I imagine there were exceptions, but it appears that the ratlines on the mizzen lower mast normally went all the way across the gang of shrouds - as did those of the topmast shrouds.
What Mr. Lees and Dr. Anderson don't discuss is why the ratlines in British warships were rigged that way - and why the arrangement changed in 1773. When I bring up the question with seaman and other modelers, the usual answer is something to the effect that "the number of men climbing the ratlines was such that they just didn't need ratlines that stretched all the way across the whole gang of shrouds." I don't buy it. Any judgment about how many ratlines were necessary to accommodate a given crew would have to take into account the size of the crew, and we'd see the ratline configuration vary directly with the size of the crew. The photos and artwork make it pretty clear that it didn't.
In terms of the Constitution, this is one of the many instances where my strong inclination would be to rely on the old Isaac Hull model in Salem. The hull and fittings of that model are pretty crude, but the rigging appears to have been done by a sailor who was intimately familiar with the ship - and willing to take infinite pains to get it right. The photos I have in front of me aren't quite clear enough for me to be sure, but it looks to me like the ratlines on the fore and main lower masts stop short of the aftermost shroud. If I were building a Constitution in War of 1812 configuration, that's how I'd probably rig her.