The difference in longitude between the observatories of Paris and Greenwich was long of fundamental importance to geodesy, navigation and timekeeping. Measured many times and by many different means since the seventeenth century, the preferred method of the later nineteenth and early twentieth centuries made use of the electric telegraph. I describe here for the first time the four Paris–Greenwich telegraphic longitude determinations made between 1854 and 1902. Despite contemporary faith in the new technique, the first was soon found to be inaccurate; the second was a failure, ending in Anglo-French dispute over whose result was to be trusted; the third failed in exactly the same way; and when eventually the fourth was presented as a success, the evidence for that success was far from clear-cut. I use this as a case study in precision measurement, showing how mutual grounding between different measurement techniques, in the search for agreement between them, was an important force for change and improvement. I also show that better precision had more to do with the gradually improving methods of astronomical time determination than with the singular innovation of the telegraph, thus emphasizing the importance of what have been described as ‘observatory techniques’ to nineteenth-century practices of precision measurement.