NavList:

I own a copy of Arnold's Lunarian which I bought for something like $75 about ten years ago. The current offer price from the two sellers who have copies available right now are wishful thinking. But I think I'll add mine to the mix at a number somewhere between $75 and $499, and we'll see if they are any nibbles on the hook.

Henry Halboth, you wrote:
"a check of Amazon.com demonstrates a reprint to be available at a hefty price. I have found this to be true of several old works of interest to me and feel it is probably now possible to download, reprint and re-copyright some of these older works - with the modern technology available today, a new cottage industry has apparently sprung up."

There is a cottage industry in on-demand printing and binding of whatever old book you may desire. But no need to get conspiratorial about it. They are not "re-copyrighting" these books. There's no such thing, for works like these at least, under US law (the governing law in this case). It's just print on demand pricing.

You wondered about downloading a copy. There's a link to a downloadable (or viewable online) copy, which is probably the exact same digital file formerly found on archive.org, listed in the index I maintain for NavList. Rather than posting yet another link to the index, which inevitably 'falls on deaf ears', I think this time I will paste in the full text of the index. You can scroll down to find the link to "Arnold's Lunarian":

Historical Navigation Books Online

An extraordinary number of books in the history of navigation have become available online. The majority of these are on Google books. These are listed mostly in alphabetical order except the list of Bowditch's Navigator immediately below.

“The American Practical Navigator” or simply “Bowditch”
Modern editions for quick reference. The most recent, published in 2002, is available online from several sources. The version here is compiled as a single pdf file (takes a while to download). The 1995 edition is divided by chapters.

• Bowditch 2002
• Bowditch 1995

Historical editions of “The New American Practical Navigator” by Nathaniel Bowditch:
Nathaniel Bowditch began working on a revised edition of Hamilton Moore's "Practical Navigator," a popular British navigation manual in the late 1790s (for editions of Moore, see below). Two editions of this Moore-Bowditch, Americanized and edited, were released in 1799 and 1800. The first true edition of Bowditch's "New American Practical Navigator" was published in 1802. There were editions released for the British market under the title "The Improved Practical Navigator" edited and somewhat re-written by Thomas Kirby.

• Moore-Bowditch 1799 (not available online)
• Moore-Bowditch 1800 (not available online)
• Bowditch 1st ed. 1802 (not available online)
• Bowditch-Kirby 1st ed. 1802 (British variant)
• Bowditch 2nd ed. 1807
• Bowditch-Kirby 3rd ed. 1809 (British variant)
• Bowditch 3rd ed. 1811 (not available online)
• Bowditch 4th ed. 1817
• Bowditch 5th ed. 1821
• Bowditch 6th ed. 1826
• Bowditch 7th ed. 1832
• Bowditch 8th ed. 1836 (not available online)
• Bowditch 9th ed. 1837
• Bowditch 10th ed. 1837

The revision of 1837 included many improvements and was the last in Bowditch's lifetime. It increased the number of lunars clearing methods to four. The first lunar method was Bowditch's refined method. The second was borrowed in its entirety from Thomson. The third was Bowditch's original method (known usually as the "method of Mendoza Rios" in British navigation manuals). The fourth was Witchell's method. Editions of Bowditch's Navigator from 1837 through 1880 are nearly identical (Nathaniel Bowditch died in 1838), but there are some minor, interesting differences. 

• Bowditch 11th ed. 1839
• Bowditch 12th ed. 1841
• Bowditch 13th ed. 1842 (not available online)
• Bowditch 14th ed. 1844
• Bowditch 15th ed. 1845 (not available online)
• Bowditch 16th ed. 1846
• Bowditch 17th ed. 1847
• Bowditch 18th ed. 1848
• Bowditch 19th ed. 1849
• Bowditch 20th ed. 1851
• Bowditch 21st ed. 1852
• Bowditch 22nd ed. 1852
• Bowditch 23rd ed. 1853
• Bowditch 24th ed. 1854
• Bowditch 25th ed. 1855 (first minor mention of Sumner's method, p.205)
• Bowditch 26th ed. 1856 (not available online)
• Bowditch 27th ed. 1857 (not available online)
• Bowditch 28th ed. 1859 (not available online)
• Bowditch 29th ed. 1860 (not available online)
• Bowditch 30th ed. 1861 (archive.org)
• Bowditch 31st ed. 1863
• Bowditch 32nd ed. 1864
• Bowditch 33rd ed. 1864 (not available online)
• Bowditch 34th ed. 1865 (not available online)
• Bowditch 35th ed. 1867 (not available online but see 1868)

In 1868 Bowditch's Navigator was published by the US government which purchased the copyright and the plates from the Bowditch family and other rights from Blunt. From 1868 through 1880, the plates from the 35th edition, slightly modified to reflect government printing, were used for new runs as needed: 

• Bowditch 1868
• Bowditch 1874
• Bowditch 1880

The above three editions are identical in content. There were no incremental changes. Other printings in 1876, 1879, probably other dates.

The first major revision, really a complete overhaul, was released in 1882, edited by P. H. Cooper. Note that 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. 

• Bowditch 1888 (archive.org)

Printings in 1882, 1883, 1885, 1886, 1887, 1888, 1892, 1893, 1894, 1896, 1897, 1898, 1899, 1900, without significant revision.

Another major revision, edited by G. W. Logan, was released in 1903. This relegated even Chauvenet's lunar method to an appendix:

• Bowditch 1903 (archive.org)
• Bowditch 1906
• Bowditch 1910 (archive.org)
• Bowditch 1912 (archive.org)

Lines of position and Sumner's method now receive relatively prominent treatment as these methods are starting to come into common usage around this time in the U.S.

Significant revision in 1914:

• Bowditch 1914
• Bowditch 1916
• Bowditch 1920

Updated for changes in the American Nautical Almanac in 1912 (lunars tables were dropped for example). The appendix on lunars is gone. A chapter on Atlantic ice was added (notably post-Titanic).

From 1914, new editions of Bowditch appear every year or two with incremental changes right through the middle of the Second World War. The first genuinely modern edition of Bowditch is the justly famous edition from 1958. The most recent, published in 2002, is available online from several sources. For reference, here is a version compiled as a single pdf file:

• Bowditch 2002

Several 19th century biographies of Nathaniel Bowditch, varying in quality are available online:

• "Nat the Navigator: A life of Nathaniel Bowditch", Henry Ingersoll Bowditch, 1870 
• "Memoir of Nathaniel Bowditch", Nathaniel Ingersoll Bowditch, 1841
• "Eulogy on Nathaniel Bowditch", John Pickering, 1838

The best modern biography of Nathaniel Bowditch is "Yankee Stargazer" by Berry, 1943. This work is still under copyright so it is not available online.

There are numerous pilot guides and coast guides available on Google books. These two are particularly famous and interesting to those familiar with US waters:
American Coast Pilot 1822 
American Coast Pilot 1847

The American Nautical Almanac in the early 20^th century is still only an extract from the hard-bound “American Ephemeris & Nautical Almanac”:
American NA 1911

Thomas Arnold's “Lunarian” does not seem to have found much commercial success but it has survived in libraries. It's similar in content and structure to editions of Bowditch from the same period. The method of clearing lunars in this work appears to have been extracted from an earlier edition of Moore's work on navigation. That method was itself a reverse-engineering of Bowditch's original lunar method:
Arnold 1822

A late 18^th century epitome of navigation:
Atkinson 1770

Blackburne was at the forefront of “selling” the new navigation of lines of position to navigators accustomed to separate latitude and longitude sights in the early 20^th century:
Blackburne 1914 and Blackburne Azimuth Tables 1908

Bowditch: see above.

The French “nautical almanac” provided the model for the British Nautical Almanac which was first published in 1767. It should be noted that the French model does not appear to have been used extensively at sea:
Connaissance des Temps 1769

Challice 1889

William Chauvenet's manual of spherical astronomy is still considered an important reference work in positional astronomy. Volume II is devoted to the instruments of astronomy including the navigator's sextant:
Chauvenet vol I 1864 , Chauvenet vol II 1863 

Students at the US Naval Academy in the late 19^th and early 20^th centuries learned navigation from J.H.C. Coffin's textbook in nautical astronomy:
Coffin 1898 

H. Wilberforce Clarke's textbook on lunar distances is dense with mathematics. It was written long after lunars ceased to be important at sea, but some land explorers still employed them, and accuracy was critical in the reduction of their observations:
H Wilberforce Clarke 1885 

“Hints to Travellers” was an explorers' guidebook. For a wealthy Englishman of the period intending to launch an expedition to a little corner of the unexplored world, this was the guide of choice to field science including positional astronomy:
Hints to Travellers 1878 , Hints to Travellers 1906 

More navigation manuals:
Inman 1849 , Jeans 1853 , Jeans pt I 1870 , Jeans pt II 1868 , Kerigan 1828 

Lecky's “Wrinkles in Practical Navigation” is a must-read. Lecky describes the state of navigation in his era and provides extensive practical advice still useful to navigators today. His writing style is humorous and clear:
Lecky's Wrinkles 1884 

Andrew Mackay's treatise on longitude includes detailed accounts of the mathematics of clearing longitudes by various methods and in addition a fascinating history of the quest for longitude as told by someone who was part of the process:
Mackay 1809 

F. Marguet has written some of the best histories of 18^th and 19^th century navigation. If you read French, these are highly valuable:
Marguet 1917 (French) , Marguet 1931 (French) [not Google Books]

Martin 1899 

Maury 1843 
The tables of Mendoza Rios (Jose de Mendoza y Rios) were highly prized and frequently counted among the best tools for nautical astronomy and especially clearing lunars:
Mendoza Rios Tables 1801 
[Note: the method of clearing lunars found in various navigation manuals and labeled the “method of Mendoza Rios” after his death was entirely different]

Merrifield 1886 

The most popular navigation manual in the late 18^th century in Britain and America was Moore's “New Practical Navigator”. Nathaniel Bowditch edited an Americanized version of this work in 1798-99. He and Edmund Blunt re-worked this into the “New American Practical Navigator”. Google Books has the 1791 edition: Moore 1791. There are also editions published after Moore's death which include a method of clearing lunars known as “Another Method” which is clearly Bowditch's method reverse-engineered:
Moore 1807 , Moore 1810

Numerous historical nautical almanacs are available on Google Books. This is a representative sampling:
NA 1767 , NA 1797 , NA 1811 , NA 1815 , NA 1828 , NA 1864 

After Moore, in Britain the popular navigation manual comparable to the American Bowditch was Norie's “Epitome of Navigation”. Norie included a large number of methods for clearing lunar distances. In later years, Norie published a method of clearing lunars using “Linear Tables” for the refraction. This term is archaic. Today we would simply call these “graphs” or a “graphical solution”.
Norie 1835 , Norie 1839 , Norie 1917 , Norie tables 1836

A popular 18^th century navigation manual:
Patoun 1734 , Patoun 1770

Benjamin F. Peirce was one of the principal mathematical astronomers of the United States in the middle of the 19^th century. His treatise on spherical astronomy was specifically designed to explain the math underlying the various calculational methods in Bowditch's Navigator: 
Peirce 1845

Another very popular British manual of navigation:
Raper 1840 , Raper 1882 , Raper 1908 

Riddle 1824 

Simms works on the adjustment and use of the sextant details many of the finer points required by high-accuracy sights. It's a bit dated but still good reading:
Simms 1858

Souchon's Treatise of Practical Astronomy includes many historical details in the history of navigation and positional astronomy not found elsewhere:
Souchon 1883 (French)

Sumner's booklet on finding lines of position. Though the method did not catch on for decades, this early work explains it in terms that seem modern even today:
Sumner 1845 , Sumner 1851

The “Tables Requisite” included refraction data, dip tables, mathematical tables and formulae, and all of the non-ephemeral data required by navigators in addition to the changing, ephemeral data on the Sun, Moon, stars, and planets published annually in the Nautical Almanacs of the era: 
Tables Requisite 1781
Tables Requisite 1802 

Janet Taylor taught celestial navigation in London in the mid-19^th century and wrote several important works on nautical astronomy. She also designed a few novel variants of the sextant:
Taylor 1833 , Taylor 1837 , Taylor 1851 , Taylor's Handbook 1865

Thomson's Tables for clearing lunars were extremely popular. Though no more accurate than any of a dozen other methods for clearing lunars (despite legends to the contrary), his method was very short and easy to work. Bowditch adopted Thomson's principal table into the “New American Practical Navigator” starting in 1837 where it remained through 1880. Though Bowditch's introduction claims the table was re-calculated, that is very unlikely. It was simply copied. Thomson's original tables also include many additional tables, advice on shooting lunars, and methods for identifying the stars: 
Thomson 1831 , Thomson 1845

Turner's Tables for clearing lunars were popular on some American vessels. They are short, easy-to-use, but somewhat less accurate than other widely available tables:
Turner's Tables 1845 

Wales 1794

Frank Reed
Conanicut Island USA