472 PHILOSOPHICAL TRANSACTIONS. [aNNO XJOQ. 



down some problems, which he not only exhibits without any demonstration, 

 but without any construction: yet the bare comparison between optics and 

 acoustics, does not seem sufficient to explain the latter, especially as they differ 

 in so many respects ; for light is always propagated in right lines, sound every 

 way, and in curve lines ; and notwithstanding the interposition of any opaqi>e 

 body, becomes sensible. 



And even what the archbishop lays down about the diffusion of sound, plainly 

 shows the difference between that and the propagation of light ; for he says 

 that sound glides with ease and great swiftness along walls, or very smooth 

 arches, of an elliptic or cycloidal, rather than a circular form ; and is also more 

 strongly conveyed along the soft surface of water, which yields to those so- 

 norous tremours by which the air is undulated. As to the ellipsis, this only is 

 demonstrated from catoptrics, that rays of light proceeding from one of its 

 foci D, fig. 10, pi. xi, and falling on the elliptic curve ABC, shall after reflection 

 be collected in the other focus e; but if the rays proceed from any other point, 

 besides the foci, they will no longer meet in one point, but be reflected in such 

 a manner, as to form, by their contacts, the caustic curve f f ; so that should 

 the eye be posited above its convexity, it would receive one or two reflected 

 rays, and no more ; but situated in the curve itself, some of the nearest rays 

 would fall upon it, and within its concavity it would have none at all reflected 

 to it. 



As to the cycloid, J. Bernoulli shows, in Act. Lips. 1697, that if a ray of 

 light should pass through mediums, whose densities in every point should 

 vary in the subduplicate ratio of their heights, it would be continually re- 

 fi-acted in such a manner, as to form a cycloid ; but I do not see how the 

 figure of a cycloid would contribute to the more easy propagation of light, 

 either by reflection, or a direct propulsion through the same medium ; for this 

 curve has no foci at all, so that it cannot collect rays in any point, but the 

 rays reflected from it form irregular curves ; excepting, when the rays pm 

 and QN, fig. 11, parallel to the axis kl, fall on the cycloid emknh, then 

 the caustic formed by the contact of the reflected rays mr, ns, would consist of 

 two cycloids erl, hsl, generated by a circle of half the diameter, and exhibit 

 the greatest number of reflected rays about l, the termination of both, and 

 the middle of the base of the reflecting cycloid : but in these, as well as in 

 other caustics, resulting from any position of the luminous point and the rays, 

 the same observations hold, as were said above, to agree to caustics formed by 

 the ellipsis. 



As to the plane superficies of water, it is manifest that the rays of light pass 

 through it, either altogether refracted, or regularly reflected towards the 



