some very notable parts of the Heaven, with a three foot Tube, me thought I now and then, in several parts of the constellation, could perceive little twinklings of Starrs, making a very short kind of apparition, and presently vanishing, but noting diligently the places where they thus seem’d to play at boe-peep, I made use of a very good twelve foot Tube, and with that it was not uneasie to see those, and several other degrees of smaller Starrs, and some smaller yet, that seem’d again to appear and disappear, and these also by giving the same Object-glass a much bigger aperture, I could plainly and constantly see appear in their former places; so that I have observ’d some twelve several magnitudes of Starrs less then those of the six magnitudes commonly recounted in the Globes. It has been observ’d and confirm’d by the accuratest Observations of the best of our modern Astronomers, that all the Luminous bodies appear above the Horizon, when they really are below it. So that the Sun and Moon have both been seen above the Horizon, whil’st the Moon has been in an Eclipse. I shall not here instance in the great refractions, that the tops of high mountains, seen at a distance, have been found to have; all which seem to argue the Horizontal refraction, much greater then it is hitherto generally believ’d. I have further taken notice, that not onely the Sun, Moon and Starrs, and high tops of mountains have suffer’d these kinds of refraction, but Trees, and several bright Objects on the ground: I have often taken notice of the twinkling of the reflections of the Sun from a Glass-window at a good distance, and of a Candle in the night, but that is not so conspicuous, and in observing the setting Sun, I have often taken notice of the tremulation of the Trees and Bushes, as well as of the edges of the Sun. Divers of these _Phænomena_ have been taken notice of by several, who have given several reasons of them, but I have not yet met with any altogether satisfactory, though some of their conjectures have been partly true, but partly also false. Setting my self therfore upon the inquiry of these _Phænomena_, I first endeavour’d to be very diligent in taking notice of the several particulars and circumstances observable in them; and next, in making divers particular Experiments, that might cleer some doubts, and serve to determine, confirm, and illustrate the true and adæquate cause of each; and upon the whole, I find much reason to think, that the true cause of all these _Phænomena_ is from the _inflection_, or _multiplicate refraction_ of those Rays of light within the body of the _Atmosphere_, and that it does not proceed from a _refraction_ caus’d by any terminating _superficies_ of the Air above, nor from any such exactly defin’d _superficies_ within the body of the _Atmosphere_. This Conclusion is grounded upon these two Propositions: