Ixxii Proceedings of Royal Society of Edinburgh. 
whose axis is vertical, and which therefore is capable of refracting 
light in horizontal directions only, it is evident that the rays now 
emitted by the lens will still emerge in horizontal directions, hut 
now no longer parallel to each other, but diverging each from some 
point of a vertical focal line whose length is equal to the diameter 
of the lens. The angle of divergence, it is evident, may be adjusted 
to any required amount by varying the curvature of the cylindrical 
face of the lense, and just as the central disc and sun surrounding 
lenticular rings of the Tresnel polyzonal arrangement replaces a 
simple plano-convex lens ; so, in place of a single cylindrical surface 
for the differential lens, may be substituted a central cylindrical hand 
bordered on either side by a series of straight lenticular prisms with 
vertical arcs. 
Mr Stevenson’s Differential Eefractor is the application of the 
same principle which has been described above for the lens to 
Fresnel’s Cylindrical Eefractor ; and, for like ends, Mr Stevenson 
also devised a Differential Eefractor, of which, in his own words, 
“ the vertical section must be parabolic, while in the horizontal it 
must he of such hyperbolic, elliptic, or other curve as will most 
advantageously give in each case the required horizontal diver- 
gence.” 
Professor Tait was kind enough to investigate the mathematical 
conditions of the differential mirror, and in the Proceedings of the 
Royal Society of Edinburgh of 1871, he gives by a quaternion inte- 
gration the formulae for its construction. For a description of the 
remainder of Mr Stevenson’s new optical condensing agents it must 
suffice to refer the reader to the descriptions to he found in his 
Treatise on Lighthouse Illumination. 
The preceding statement, I believe, will be found to include a 
tolerably complete enumeration of Mr Stevenson’s inventions in 
lighthouse optics ; but also nothing as yet has been said regarding 
the application of these to special cases of lighthouse illumination. 
Many such there are of very great interest ; but it is impossible to 
include any adequate description of them within the limits of the 
present notice. It must suffice, then, simply to point to one, 
namely, the Isle Oronsay Light, situated in the narrow and tor- 
tuous Sound of Skye. This light, according to the direction from 
which it is viewed, is visible at very different distances, varying 
