the Air; and since I have found, by several Experiments made on places comparatively not very high, and have yet found the pressure sustain’d by those parts of the Air at the top and bottom, and also their differing Expansions very considerable:  Insomuch that I have found the pressure of the Atmosphere lighter at the top of St. Paul’s Steeple in London (which is about two hundred foot high) then at the bottom by a sixtieth or fiftieth part, and the expansion at the top greater then that at the bottom by neer about so much also; for the Mercurial Cylinder at the bottom was about 39. inches, and at the top half an inch lower; the Air also included in the Weather-glass, that at the bottom fill’d only 155. spaces, at the top fill’d 158. though the heat at the top and bottom was found exactly the same with a scal’d Thermometer:  I think it very rational to suppose, that the greatest Curvature of the Rays is made nearest the Earth, and that the inflection of the Rays, above 3. or 4. miles upwards, is very inconsiderable, and therefore that by this means such calculations of the height of Mountains, as are made from the distance they are visible in the Horizon, from the supposal that that Ray is a straight Line (that from the top of the Mountain is, as ’twere, a Tangent to the Horizon whence it is seen) which really is a Curve, is very erroneous.  Whence, I suppose, proceeds the reason of the exceedingly differing Opinions and Assertions of several Authors, about the height of several very high Hills.

8.  Whether this Inflection of the Air will not very much alter the supposed distances of the Planets, which seem to have a very great dependence upon the Hypothetical refraction or inflection of the Air, and that refraction upon the hypothetical height and density of the Air:  For since (as I hope) I have here shewn the Air to be quite otherwise then has been hitherto suppos’d, by manifesting it to be, both of a vast, at least an uncertain, height, and of an unconstant and irregular density; It must necessarily follow, that its inflection must be varied accordingly:  And therefore we may hence learn, upon what sure grounds all the Astronomers hitherto have built, who have calculated the distance of the Planets from their Horizontal Parallax; for since the Refraction and Parallax are so nearly ally’d, that the one cannot be known without the other, especially by any wayes that have been yet attempted, how uncertain must the Parallax be, when the Refraction is unknown?  And how easie is it for Astronomers to assign what distance they please to the Planets, and defend them, when they have such a curious subterfuge as that of Refraction, wherein a very little variation will allow them liberty enough to place the Celestial Bodies at what distance they please.