728 PHILOSOPHICAL TRANSACTIONS. [aNNO l^GS, 



{ace from which the rays pass into the air, must be 



78D-775 ^ ^^ ^^*"^' '" ^^'^ ^^^' 7 = 41. 7 — -H- 



Example 1 .—Let mj&cncm, fig. 8, be a double convex lens of water, confined 

 between the plano-concave mtln, and the meniscus mkncm, both of glass, and 

 having the radii of their surfaces contiguous to the water, equal to each other, 

 or to unity; and if a ray sp, parallel to the common axis of the lenses, after 

 being refracted by the aqueous lens, have its extreme rays, the red and violet, 

 divergent from the points d and d; the distance of f, the focus where all the 

 rays can meet, will be 8.898: and when this happens, the exterior surface of the 

 meniscus, that is, the surface represented by mpkn, will have its radius to that 

 of the inner surface mcn, as 139 to 154. 



Example 2. — When a double concave of glass, the radii of whose surfaces 

 are unity, is inclosed in water, as in fig. 9, the water being confined on one side 

 by a thin glass plate tl, and on the other by a concentric spherical shell mpkn ; 

 the semidiameter of this shell must be to unity as 47 1 to 547; and the focal dis- 

 tance CF, at which the colourless image is formed, will be 4.77-t' In these ex- 

 amples, the thickness of the lenses is neglected ; but it may easily be taken into 

 the account, if it be thought necessary. 



The same thing may be effected by means of any media of different refractive 

 powers; for the semidiameter of the last refracting surface being determined ac- 

 cording to the foregoing rule, the nearer distance of the points of divergence (d), 

 of the more refrangible rays, will be so compensated by their greater refrangibility, 

 that all the rays will converge to the same focus f. And this without introducing 

 any new principle into the science of optics, or any dispersion of light different 

 from the refractions discovered by Sir Isaac Newton near a hundred years ago. 



END OF VOLUME ELEVENTH. 



C. and R. Baldwin, Frinten, 

 New Bri«igc-«treet, London. 



