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I apologize if I'm repeating myself.  But it seems to me there is a
circular argument going on here.

The navigators in the story very clearly were determining the error in
their chronometers by land observations of sun or stars.  There would
be no need to do so if accurate time could be transmitted by cable.  So
one concludes that accurate time could not be transmitted by cable, or
was not transmitted very often.  (To do so, one would need to establish
accurate time at the transmitting station.  If that station were
located near the shore, and relayed signals from Paris or London by
land-borne telegraph, then I expect that accurate signals could not be
propagated to the station by land-borne telegraph, due to the time
delays introduced by relays along the way).

It would seem to me to be much easier to determine time at the
transmitting station by observing the moons of Jupiter or some such, in
place.  This also could be done at each cable station to determine
longitude accurately.  Once the longitude of a station were known, one
could determine the error of one's chronometers as described.  As
George Huxtable describes, simple triangulation from the level spot to
the benchmark spot could determine the location of the level spot, if
the location of the level spot differed from that of the benchmark
spot, which it might not.

   

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