By collecting, comparing, and adjusting, all these materials, we have been enabled to construct variation-curves upon Dr. Halley’s mercator-chart, adapted to the year 1756; which will soon be in readiness to present to this Royal Society. As a work of this kind requires much time, and a multitude of observations, both by sea and land, to render it more perfect and general; we hope the ingenious in all nations will lend their assistance: By this means every periodic review will be productive of improvement. From the first instant that we made this affair the object of our more particular consideration, we have attended to the mode of increase and decrease in the variation: and as a considerable number of observations, made at periodic times, and duly registered, seem to be the most essential toward determining the laws of its mutation, or proving its irregularity, we have therefore formed a sett of tables, from actual observations collected for the years 1710, 1720, 1730, and 1744, the date of our last chart; which, together with Dr. Halley’s for the year 1700, and the present chart now publishing, compleat six reviews: These are tabulated, and shew the quantity of the variation, at those several periods, to every 5 degrees of latitude and longitude in the more frequented oceans; which we hope will prove acceptable, as nothing of the like kind has yet appeared, or can easily be obtained. Our materials have been so deficient, that even in the limits to which our tables are confined, we have been obliged to leave blanks in some of the above periods, for want of that concurrent testimony, on which the numbers inserted are founded: but, considering the difficulties unavoidably attending a work of this sort, and the little assistance which we have met with from private hands, we hope that this Royal Society will not only excuse those vacancies, but also those in the great tracts of sea, as well as land, concerning which we are very unwillingly obliged to be intirely silent. Agreeable to our former address, we lay only what appear to be facts before you, without attempting to introduce any hypothesis for the solution of these phænomena; some of which (being very extraordinary) we recommend peculiarly to the notice of those gentlemen, who may endeavour the investigation of their causes. Under the equator, in longitude 40° E. from London, the highest variation during the whole 56 years appears to be 17°¼ W. and the least 16°½ W.: and in latitude 15° N. longitude 60° W. from London, the variation has been constantly 5° E. but in other places the case has been widely different; for in the latitude 10° S. longitude 60° E. from London, the variation has decreased from 17° W. to 7°¼ W., and in latitude 10° S. longitude 5° W. from London, it has increased from 2°¼ W. to 12°¾ W.; and in latitude 15° N. longitude 20° W. it has increased from 1° W. to 9° W.