100 PHILOSOPHICAL TRANSACTIONS. [iNNO I696. 



might be a very easy and natural reason given of its performance, which I shall 

 now endeavour to demonstrate, on supposition that the inferior surface of the 

 sphere is reflective. Let the circle in fig. 2, pi. 3, represent a sphere of water; 

 A an object placed in its focus, sending forth a cone of rays, two of which are 

 AB, AB, which coming into the water at b and b, will be refracted from their 

 direct course, and become bd. At d they will, at their passing into the air, be 

 again refracted into de, de, and so run parallel to each other, and to the axis 

 of the sphere aecg. Now it is a known and fundamental principle in optics, 

 that the angle of reflection is equal to the angle of incidence; therefore let the 

 rays bd, bd be imagined to come from some point of an object placed within a 

 sphere of water, by being reflected from the interior surface of the sphere at 

 B, b; cbd is the angle of reflection, to which making cbf equal ; so will f be 

 the place where an object sending forth a cone of rays, two of which are fb, 

 FB, which are reflected into the rays bd, bd, and then coming to the other side 

 of the sphere at d and d, they are refracted into de, de, as before, and con- 

 sequently be as fit for distinct vision, whether the object be placed in f within, 

 or in a without the sphere, if its interior surface be considered as a concave re- 

 flecting speculum. 



That the interior surface of glass, and consequently of water, is reflecting, 

 common experience shows; but whether any one has before observed, that the 

 air is specular, is to me unknown : but I have a very few days since, as I was 

 endeavouring to improve this natural catadioptric microscope, stumbled on an 

 aerial concave speculum, which ! shall now describe. 



A darkened room being somewhat troublesome to make, I thought it proper 

 to try, if this inconvenience might not be remedied ; so I took a stiflT piece 

 of brown paper, pricking a small hole in it, then applied the drop of water to 

 my eye, and holding the paper with the hole at a little distance before me, I could 

 see the globules therein little less distinctly than in a darkened room. But be- 

 fore I had removed the water, there appeared to me a very strange and sur- 

 prising appearance : I saw the needle's point, together with the water, inverted : 

 I could scarcely at first believe my eyes ; to be further satisfied, I removed the 

 water, and found that whether I held the needle perpendicular, horizontal, or 

 inclined, to all these positions it was inverted. I then made many holes, and in 

 every one I saw the inverted picture of the needle ; the nearer the needle was 

 to the holes, it was so much the more magnified, but less distinct : if the 

 needle's point was so held, as that its image was near the edge of the hole, its 

 point seemed crooked. So that it seems these small holes, or somewhat in 

 them, performs the effects of a concave speculum ; whence I take leave to call 

 them aerial speculums. But how the rays of light can be reflected, before 



