A short rehearsal of several Phaenomena_.  An attempt to explicate them:  the supposition founded on two Propositions, both which are indeavoured to be made out by several Experiments, What density and rarity is in respect of refraction:  the refraction of Spirit of Wine compared with that of common Water:  the refraction of Ice.  An Experiment of making an Undulation of the Rays by the mixing of Liquors of differing density.  The explication of inflection, mechanically and hypothetically:  what Bodies have such an inflection.  Several Experiments to shew that the Air has this propriety; that it proceeds from the differing density of the Air:  that the upper and under part of the Air are of differing density:  some Experiments to prove this.  A Table of the strength of the spring of the Air, answering to each degree of extension; when first made, and when repeated.  Another Experiment of compressing the Air.  A Table of the strength of the Air, answering to each compression and expansion; from which the height of the Air may be suppos’d indefinite; to what degree the Air is rarifi’d at any distance above the Surface of the Earth:  how, from this, Inflection is inferr’d; and several Phaenomena explain’d.  That the Air near the Earth is compos’d of parts of differing density; made probable by several Experiments and Observations; how this propriety produces the effects of the waving and dancing of Bodies; and of the twinkling of the Stars.  Several Phaenomena explicated.  Some Quaeries added._

1. Whether this Principle may not be made use of, for perfecting Optick Glasses?  What might be hoped from it if it were to be done?

2. Whether from this Principle the apparition of some new Stars may not be explicated?

3. Whether the height of the Air may be defin’d by it?

4. Whether there may not sometimes be so great a disparity of density between the upper and under parts of the Air, as to make a reflecting Surface?

5. Whether, if so, this will not explicate the Phaenomena_ of the Clouds.  An Experiment to this purpose?_

7. Whether the Rayes from the top of Mountains are not bended into Curve-lines by inflection?  An Argument for it, taken from an Experiment made on St. Paul_’s Steeple._

8. Whether the distance of the Planets will not be more difficult to be found?  What wayes are most likely to rectifie the distance of the Moon:  the way of fitting Telescopes_ for such Observations.  How to make the Observations, and how from them to find the true distance of the Moon at any time.  How the distance of the Sun may be found by two Observators.  The way by the Dicotomy of the Moon uncertain.  That the distance of the Moon may be less then it has been hitherto suppos’d. Kepler’s Supposition not so probable:  the explication of the Phaenomena by another Hypothesis._

Observ. 59.  Of the fixt Stars.