438 PHILOSOPHICAL TRANSACTIONS. [ANNO 179Q. 



image as before. The ship a moving on the horizon, b continued to move with it, 

 without any variation in its appearance. 



The next ship I directed my telescope to, was so far on the other side of the 

 horizon xy, as just to prevent its hull from being seen, as is represented by a, fig. 3. 

 And here I observed only an inverted image of part of the ship; the image y of 

 the topsail, with the mast joining that of the ship, the image x of the top a of the 

 other mast, and the image z of the end c of the bowsprit, only appearing at that 

 time. These images would suddenly appear and disappear very quickly after each 

 other; first appearing below, and running up very rapidly, showing more and less 

 of the masts at different times, as they broke out; resembling, in the swiftness of 

 their breaking out, the shooting out of a beam of the aurora borealis. As the ship 

 was descending on the other side of the horizon, I continued my observations on it, 

 in order to discover what changes might take place; when I found, that as it con- 

 tinued to descend, more of the image gradually appeared, till at last the image of 

 the whole ship was completed, with their main-masts touching each other; and, 

 on the ship descending lower, the image and the ship separated; but I observed no 

 2d image, as in the first case; a 2d image however might probably have appeared, 

 if the ship had continued to descend. 



On moving my telescope along the horizon, in order to examine any other ships 

 which might be in sight, I observed, just at the horizon xy, in fig. 4, the top a of 

 the mast of a ship; and here an effect was observed which had not been before dis- 

 covered; for there was an inverted image b, vertical to a, an erect image c, both 

 of them very perfect and well defined, and an image vw of the sea between them, 

 the water appearing very distinctly. As the ship was coming up towards the horizon, 

 I continued to observe it, in order to discover the variations which might follow, 

 and found, that as the ship approached the horizon, the image c gradually disap- 

 peared, and at last it vanished; after that, the image vw of the sea disappeared; 

 and during this time the image b descended; but the ship did not rise so near to the 

 horizon as to bring the main-masts together. Had I directed my telescope to the 

 same point of the horizon a little sooner, I should have seen the 2 images before 

 the ship itself was visible. In fact, the images were visible when the whole ship 

 was actually below the horizon; for, from the very small part of the mast which 

 was at first visible, that part must then have been below the horizon, and appeared 

 above it by the usual refraction; the altitude of a, above the horizon, having then 

 been much less than the increase of altitude which arises from the common hori- 

 zontal refraction. The discovery of ships in this manner might, in some cases, be 

 of great importance; and on such occasions it might be worth while to appoint 

 proper persons to make observations for that purpose. 



The cliffs at Calais being very visible, I directed my telescope towards them, in 

 order to examine whether there was any thing unusual in their appearance; when 

 I observed an image of the cliffs, above the cliffs themselves, together with an 

 image of the sea separating them, as is represented in fig. 5 ; in which, xy repre- 



