by Sarah Bagby

Solvers are presented with eight extracts from a ship captain’s log and eight extracts from a naturalist’s correspondence. Each log entry gives a day and month (but not year); an observation of the sun’s altitude when it passes above the ship’s meridian, and the north or south bearing of the sun at that observation; an observation of the distance between the moon and the sun at local noon; a mention of a recent world event, news of which a different ship brought to the ship whose log it is; and a note of how many letters that other ship collected from the naturalist. Each of the naturalist extracts mentions a species by its Latin name and says that a specimen has recently been collected. In a couple of cases the naturalist also implies that his correspondent is Francophone, with references to the names of particular bones in French. Log entries are ordered by day and month; naturalist extracts are ordered alphabetically by species name.

Path to solution

Use the described historical events to work out the year for each log entry.

Log entry Event Year
07-14 Lewis and Clark depart 1804
07-26 Tea Act passed 1773
08-06 Transit of Venus observed by Cook 1769
08-16 French Revolution begins 1789
08-20 Jay Treaty ratified 1795
09-04 Penobscot Expedition sails 1779
10-06 Battle of the Nile 1798
12-28 Burning of Falmouth 1775

Look up the complete dates in that year’s Nautical Almanac (more precisely, The nautical almanac and astronomical ephemeris, for the year [year]). This reference is clued by the puzzle title: “Poor Richard” references a famous almanac, and “Goes to Sea” takes that reference and makes it nautical. For all of the years used, the Nautical Almanac is available online via the University of Cambridge Digital Library (e.g., https://cudl.lib.cam.ac.uk/view/PR-NAO-01789/1 for the 1789 edition); many years are also available at other sites.

Using the tables in the Nautical Almanac and the astronomical observations given, work out the ship’s latitude and longitude for each log entry. (See below for details. Note that the Nautical Almanac uses astronomical time, reckoned from noon to noon on a 24-hour clock; so “hour XXI” of a given day in an astronomer’s reckoning is 9 a.m. the following day in the civil reckoning. The sea day also runs from noon to noon, but the noon that starts a given astronomical day is the noon that ends the sea day of the same nominal date. All ship’s log dates specify that observations were taken at the noon that ends the sea day, that happy moment when civil, astronomical, and sea reckonings all agree on which day it is.)

Date Sun altitude Sun declination Latitude
07-14-1804 59°7′21″ N 21°42′27″ N 9°10′12″ S
07-26-1773 25°50′14″ N 19°21′20″ N 44°48′26″ S
08-06-1769 80°18′59″ N 16°35′56″ N 6°54′55″ N
08-16-1789 59°54′29″ S 13°33′29″ N 43°39′0″ N
08-20-1795 43°35′31″ N 12°24′20″ N 34°0′9″ S
09-04-1779 60°28′41″ S 7°10′30″ N 36°41′49″ N
10-06-1798 57°33′23″ N 5°18′53″ S 37°45′30″ S
12-28-1775 75°6′34″ S 23°17′51″ S 8°24′25″ S
Date Moon–sun distance Greenwich time at that distance Longitude
07-14-1804 86°33′49″ 21h previous day = 9 a.m. civil 45° E
07-26-1773 78°13′52″ Midnight previous day 180° E
08-06-1769 53°53′19″ 18h previous day = 6 a.m. civil 90° E
08-16-1789 59°19′51″ 3h = 3 p.m. civil 45° W
08-20-1795 66°41′30″ Noon 0° W
09-04-1779 74°14′7″ 9h = 9 p.m. civil 135° W
10-06-1798 49°49′13″ 15h previous day = 3 a.m. civil 135° E
12-28-1775 82°29′26″ 6h = 6 p.m. civil 90° W

Notice that every species the naturalist mentions is endemic to a particular island; so if the naturalist has recently collected a specimen of that species, he must be fairly near that island.

Species Common name Island Island latitude Island longitude
Amblyrhynchus cristatus Marine iguana Galapagos 0°42′ S 90°30′ W
Apteryx australis Southern brown kiwi New Zealand 45°9′ S 169°53′ E
Dryococelus australis Tree lobster Lord Howe 31°33′ S 159°5′ E
Lemur catta Ring-tailed lemur Madagascar 19° S 47°30′ E
Nesospiza acunhae Inaccessible Island finch Inaccessible 37°18′ S 12°42′ W
Oceanodroma monteiroi Monteiro's storm petrel Azores 39°3′ N 28°0′ W
Tupaia longipes Long-footed treeshrew Borneo 1° N 114° E
Urocyon littoralis Island fox Channel 34° N 119°48′ W

Use the ship’s calculated coordinates and the naturalist’s inferred islands to pair up the ship’s log entries with the naturalist’s correspondence. In the map below, purple dots show the islands’ locations; green dots show the corresponding locations of the ship.

Notice that the names of the ships encountered, in the order given, are the old Army/Navy radio alphabet code for SCAN W TO E; that the weather descriptions that begin each ship’s log entry form the acrostic USE LATIN; and that the sentence fragments that begin the naturalist entries form the acrostic FOX FIRST. So: sort the ships and islands from west to east, taking the Channel Islands (Island Fox) pair as the westernmost (resolving the ambiguity of whether to construe the New Zealand ship as 180°W or 180°E), and use the Latin names given as the source material for extraction. The extraction index is, of course, the number of letters from the naturalist that the captain reports having sent with the other ship.

Date Latitude Longitude Island Species Index Readout
09-04-1779 36°41′49″ N 135° W Channel Urocyon littoralis 3 O
12-28-1775 8°24′25″ S 90° W Galapagos Amblyrhynchus cristatus 2 M
08-16-1789 43°39′0″ N 45° W Azores Oceanodroma monteiroi 1 O
08-20-1795 34°0′9″ S 0° W Inaccessible Nesospiza acunhae 6 P
07-14-1804 9°10′12″ S 45° E Madagascar Lemur catta 1 L
08-06-1769 6°54′55″ N 90° E Borneo Tupaia longipes 4 A
10-06-1798 37°45′30″ S 135° E Lord Howe Dryococelus australis 15 T
07-26-1773 44°48′26″ S 180° E New Zealand Apteryx australis 4 E

Read off the answer OMOPLATE, the French word for shoulderblade.

Notes on celestial navigation

Every English or American ship sailing in these years would have carried copies of Robertson’s Elements of Navigation, Moore’s New Practical Navigator, or (after 1802) Bowditch’s New American Practical Navigator, in addition to a nautical almanac for the year(s) at sea. Most of the difficulty in celestial navigation arises from carefully applying a long series of corrections to the initial astronomical observations made. The puzzle does this part for the solver, and presents the true values for the sun’s meridian altitude (i.e., its altitude above the horizon when it passes the meridian of the ship, at the zenith of its arc from the ship’s perspective) and the distance between sun and moon.

With the sun’s altitude, the date, and the Nautical Almanac (in which to look up the sun’s declination on that date), finding the latitude is a simple matter of following Bowditch: “Having thus obtained the correct central altitude of the object, you must subtract it from 90°, and you will have the true zenith distance, with which, and the true declination at the time of observation, the latitude is found by the following rules… If the object bear south, when upon the meridian, call the zenith distance north; but if it bear north, you must call the zenith distance south. Place the zenith distance under the declination, and if they are of the same name, add them together; but if they are of different names, take their difference; this sum or difference will be the latitude, which will be of the same name as the greatest number” (Bowditch 1802, p. 151; complete text available via https://archive.org/details/newamericanpract00bowd/page/n7). Of course solvers may prefer to find modern references, e.g., https://astronavigationdemystified.com/latitude-from-the-midday-sun/. In either case, it boils down to the following.

  1. When altitude is measured, if the sun bears north, take the zenith distance to be south, and vice versa.
  2. Calculate zenith distance as 90° − true altitude.
  3. Compare the “names” (i.e., “south” or “north”) of the sun’s zenith distance and its true declination.
    1. If both are south or both north, calculate latitude as zenith distance + declination.
    2. If one is south and the other north, calculate latitude as the absolute value of zenith distance − declination.
  4. Compare the values of the sun’s zenith distance and its true declination.
    1. If the zenith distance is greater than the declination, assign the latitude the same name as the zenith distance.
    2. If the zenith distance is less than the declination, assign the latitude the same name as the declination.

This arithmetic is all slightly complicated by the observations’ being presented in degrees-minutes-seconds format, but obviously no one would have used degrees and decimal minutes at the time these ships were sailing.

Obtaining the longitude from the given information is actually easier than finding the latitude. Given the corrected distance between the moon and the second object observed (here, the sun), “In the Nautical Almanac . . . look for the computed distance between the moon and the other observed object for that given day; if it be found there, the time at Greenwich will be found at the top column . . . The difference between this Greenwich time and that at the ship, turned into degrees . . . will be the longitude of the place of observation, reckoned from the meridian of Greenwich, which will be east if the time at the ship be greater than that at Greenwich, but if it be less, the longitude will be west” (Bowditch 1802, 182).

The Nautical Almanac gives computed distances at three-hour intervals; navigators have to interpolate between these times for intermediate distances. The lunar distances in this puzzle were chosen to place the ship at a series of meridians for which the exact data is given in the Nautical Almanac. So with the date and lunar distance to the sun in hand, solvers can simply look up when at Greenwich the given distance would have been observed. They must then convert to degrees (at a rate of 15° per hour, the rate at which the Earth rotates through 360° per day) the interval between local noon (when the observations were made) and the time at Greenwich, and assign the ship to east or west longitude accordingly.