You know, dear Sir, that I have traversed a great part of this globe, not without giving some attention to the peculiarities of each climate; and I can fairly pronounce, that I never felt such heats any-where as in Georgia. I know experiments on this subject are extremely liable to error; but I presume I cannot now be mistaken, either in the goodness of the instrument, or in the fairness of the trials, which I have repeatedly made with it. This same thermometer I have had thrice in the equatorial parts of Africa; as often at Jamaica, and the West India islands; and, upon examination of my journals, I do not find, that the quicksilver ever rose in those parts above the 87th degree, and to that but seldom: its general station was between the 79th and 86th degree; and yet I think I have felt those degrees, with a moist air, more disagreeable than what I now feel. In my relation of the late expedition to the north-west, if I recollect right, I have observed, that all the changes and variety of weather, that happen in the temperate zone throughout the year, may be experienced at the Hudson’s Bay settlements in 24 hours. But I may now extend this observation; for in my cellar the thermometer stands at 81, in the next story at 102, and in the upper one at 105; and yet these heats, violent as they are, would be tolerable, but for the sudden changes that succeed them. On the 10th of December last the mercury was at 86; on the 11th it was so low as 38 of the same instrument. What havock must this make with an European constitution? Nevertheless, but few people die here out of the ordinary course; tho’ indeed one can scarce call it living, merely to breathe, and trail about a vigorless body; yet such is generally our condition from the middle of June to the middle of September. Dear Sir, Yours most affectionately, Henry Ellis. CIII. _The Invention of a General Method for determining the Sum of every 2d, 3d, 4th, or 5th_, &c. _Term of a Series, taken in order; the Sum of the whole Series being known. By_ Thomas Simpson, _F.R.S._ [Read Nov. 16, 1758.] AS the doctrine of Series’ is of very great use in the higher branches of the mathematics, and their application to nature, every attempt tending to extend that doctrine may justly merit some degree of regard. The subject of the paper, which I have now the honour to lay before the Society, will be found an improvement of some consequence in that part of science. And how far the business of finding fluents may, in some cases, be facilitated thereby, will appear from the examples subjoined, in illustration of the general method here delivered.