CHAP. IT.] 



LIGHTHOUSES. 



223 



pieces, Fresnel adds : " He had not paid attention moreover 

 apparently to the great advantage presented by the separate working 

 of the surface of each ring which almost entirely corrects spherical 

 aberration, when the rings are sufficiently multiplied, by deter- 

 mining by calculation the centre and radius of curvature of 

 each of the generating arcs. For, after having first conceived the 

 lens determined by a spherical surface, he supposes it to be cut 

 down in echelons, but in such a manner that the new portions of the 



Elevation. Plan. 



FIG. 155. Fresnel's first lenticular apparatus : in elevation and plan. 



spherical surfaces are concentric with the first, which is not the true 

 way to correct the spherical aberration. Calculation teaches that the 

 generating arcs of the rings not only ought not to have the same 

 centre, but again that these different centres are not situated in the 

 axis of the lens, and that they get more distant from it as the arcs to 

 which they belong are themselves more distant from the centre of the 

 lens; in. such a manner that these arcs by revolving round the axis, 

 do not produce portions of concentric spherical surfaces, but to 



