He then turned his attention to the production of ever more precise chronometers. One of these travelled with the explorer James Cook during his second voyage to the southern Pacific Ocean in 1772–1775. His undoubted claim to fame in the field of marine chronometers is the first application of a helical balance spring. This allowed the balance to swing through larger or smaller arcs in a constant time, one of the fundamental requirements for accurate timekeeping.
Arnold set up a small factory in Chigwell, Essex for the production of chronometers and in 1788 produced the first pocket chronometer. This watch, "No. 1/36", greatly impressed the Astronomer Royal Nevil Maskelyne and was the first watch Arnold deemed worthy of the description "chronometer".