NavList:

George H wrote:

"we have only been considering those times in the month when the
declination is changing at its fastest, twice a month near when the
declination passes through zero. Twice in the month the declination stops
changing, and anywhere near those times Dunbar's method would be quite
useless."

 

Twice a month really does not render a method for finding longitude useless, even if it were intended for use at sea (the above was not). As I've pointed out on several occasions, the venerable "lunar distance method", which most certainly was practical at sea, was typically used ony for a few days around First Quarter and Last Quarter. Yes, a navigator had the option of using stars for lunar distance observations to extend the period for observation during the week around Full Moon, but it seems that practicing navigators at sea usually didn't bother (italicize that word "usually").

 

Lunar distance observations were one thing in theory... and another in practice. In theory, lunar distance observations might have been done on a daily basis using stars as frequently as the Sun with distances ranging from 20 to 125 degrees. In practice, lunar distance observations were mostly Sun-Moon observations, done for a few days every two weeks, and mostly with distances between 70 and 100 degrees. This rendered them less likely to be affected by errors in the measured altitudes, the Moon's altitude especially (that "Ninety Degree Miracle" business that I've mentioned), and also considerably shortened the calculation in series methods since the quadratic correction could be ignored (it's proportional to 1/tan(distance)). In addition, this consistency in practice implied a consistency in the clearing procedure. Sun-Moon lunars are always "Near Limb" sights. Sun-Moon lunars at wide distances like this are almost always "Upper Limb" sights for the Moon's altitude because of the positioning in the sky and Lower Limb sights for the Sun out of habit (and so for every lunar, a navigator could use -20 for the Moon and +12 for the Sun for the combined semidiameter/dip correction of the altitudes). All of these little things streamlined the practice of lunars and made them useful for the purpose to which they were best suited: a fortnightly check on the longitude by dead reckoning (in the period up until roughly 1835) or the longitude by chronometer (in the period from roughly 1835 to 1855).