_Fig. 3._ Is the Logarithmick Curve A C _c_, with its Ordinates A B, C D, _c d_, K δ representing Absolute Numbers, and its Abscissæ, C G or D B, I _c_ or B d and B δ, representing their Logarithms, whose famous Property it is, that one Ordinate as A B, is to another Ordinate as C D, or _c d_ or K δ, as that unlimited Space between the Curve and Asymptote above the one, is to that above the other; and whence is deduc'd the Proportion of the Air's Rarity at all Altitudes whatsoever; that at 7 Miles high it is 4 times as rare; at another 7, or 14 Miles, it is 16 times as rare, and so for ever, in a Geometrical Proportion of Rarity, compar'd with the Arithmetical Proportion of its Altitude; tho' all this is here upon the Hypothesis that the Distances are not so great, that the real Gravity of the Parts be sensibly diminished. For in that Case, _Fig. 4._ Gives the Scheme, which is made use of to discover the Air's Rareness, even at such Distances, as imply a considerable Alteration in that Gravity; whence it will appear, that the Density of the Air is diminished in that Case more than 4 times for every 7 Miles of Altitude. [[Plate IIII. ― I. Senex sculp.^t]] PNEUMATICKS. 18 An Explication of the Fourth PLATE. Figure 1. Is a compound Instrument, to shew, why in a Storm the Mercury in the Barometer vibrates so much, by a parallel Case in an Imitation of such a Storm. A A is a large hollow Brass Sphere, into which by the means of the Syringe in _Fig. 2_. Air is crouded till it is 8 or 10 times as dense as usual. H F and L K are Two Barometers, with their Basons in the Boxes F F, K K, which Boxes communicate by a long hollow Tube I I. E E is a Brass hollow Tube, to convey the crowded Air near the Surface of one of the Basons of Quicksilver, which Air passes out of that into a larger hollow Pipe G G, and so into the open Air. Upon the turning of the Stopcock C to give vent to the condensed Air, it rushes with great Force along the hollow Pipes E E, G G; and as it passes not far off the Surface of the Bason of Quicksilver F F, it causes the Mercury in both the Barometers H H, and L L, to descend and vibrate several Inches, as the great Storm made Barometers descend and vibrate in Chambers at a distance from it.