On 25 May 1750, Jack received patent #656 for a "quadrant for taking the altitude of the sun or moon by refraction" and also "a refracting telescope with four spherical lenses" jointly with the successful London instrument maker George Adams. They claimed that their design offered 30 levels of magnification and eliminated color abberations. Although those claims were vigorously disputed by rival instrument makers, Jack and Adams seem to have been vindicated by some practical and authoritative test in early 1752 and made a sizeable profit on the design. None of the devices are known to still exist but, on the basis of surviving records, Millburn considers it likely that representatives of the Admiralty or Board of Ordnance praised the patent telescope's high level of magnificationthe most essential attribute for long-range firedespite the accuracy of other complaints about its faults. Jack advertised his lectures on math in London in 1751 and 1754. He also lectured on experimental philosophy, fortification, and gunnery.
