But, using your sign convention, Gardner should be -12.
What do you mean by "sign convention?" Colorado, Swan, and Pelican all used -11 for the longitude of Gardner. That's what we used.
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The Navy regulation in force since 1920 required that their ships maintain standard zone times but provided exceptions when it was operationally convenient to use a different, non-standard, offset from Zulu time. The standard correction factors for converting one time to another used by navigators and, by regulation, the Navy is to use the sign that will convert local time to Zulu time, this is called the "Zone Description" (Z.D.) and must be recorded in the log book and next to the clocks. Itasca kept their clock set to 11:30 slow on Zulu so to convert Itasca time to Zulu their Z.D. was +11.30. Other users however see the problem in the reverse sense and use a correction factor that will convert Zulu time to local time so they would call to correction factor for Itasca time as -11:30 which added to Zulu time will produce the local time kept on Itasca. That is what I meant by the different "sign conventions." Either method will work as long as you keep it straight and don't get confused.
The standard time zone that is 12 hours slow on Zulu time extends from longitude 172° 30' west longitude to the 180th meridian. Gardner is located at 174° 32' west longitude so falls squarely within this time zone as does Howland. The Z.D., therefore, for Gardner is +12 hours (and for those going the other way, -12 hours.) Apparently for operational convenience, such as maneuvering in an area where you might cross back and forth across the dividing line between two time zones or to coordinate between ships that may be close to each other but on different sides of the dividing line, the ships you mentioned decided to keep their clocks set to Z.D. + 11 hours. But this doesn't change the fact that the standard time on Gardner (if someone were there) would have been 12 hours slow on Zulu in 1937. Since you purpose was to allow your readers to have sense of the actual time on Gardner, using the non-standard time kept on those ships instead of the correct time at Gardner will cause a one hour error and noon will happen at 13:00 instead of 12:00, sunrise will be at 7:00 a.m. and sunset at 7:00 p.m. (instead of 6 a.m. and 6 p.m.) and will not be symmetrical around noon and this will also affect the local time for the tides which might be significant for the operation of the radios in the plane sitting on the reef.
We have seen that the Itasca, using the authority of the Navy regulation, set their clocks to a non-standard offset from Zulu, for their convenience, and did not maintain their clocks on the standard time zone in the vicinity of Howland which is 12 hours slow on Zulu, these other ships were doing the same thing.
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